API¶
Top level user functions:
all (a[, axis, out, keepdims]) 
Test whether all array elements along a given axis evaluate to True. 
allclose (a, b[, rtol, atol, equal_nan]) 
Returns True if two arrays are elementwise equal within a tolerance. 
angle (x[, deg]) 
Return the angle of the complex argument. 
any (a[, axis, out, keepdims]) 
Test whether any array element along a given axis evaluates to True. 
apply_along_axis (func1d, axis, arr, *args, …) 
Apply a function to 1D slices along the given axis. 
apply_over_axes (func, a, axes) 
Apply a function repeatedly over multiple axes. 
arange (*args, **kwargs) 
Return evenly spaced values from start to stop with step size step. 
arccos (x[, out]) 
Trigonometric inverse cosine, elementwise. 
arccosh (x[, out]) 
Inverse hyperbolic cosine, elementwise. 
arcsin (x[, out]) 
Inverse sine, elementwise. 
arcsinh (x[, out]) 
Inverse hyperbolic sine elementwise. 
arctan (x[, out]) 
Trigonometric inverse tangent, elementwise. 
arctan2 (x1, x2[, out]) 
Elementwise arc tangent of x1/x2 choosing the quadrant correctly. 
arctanh (x[, out]) 
Inverse hyperbolic tangent elementwise. 
argmax (a[, axis, out]) 
Returns the indices of the maximum values along an axis. 
argmin (a[, axis, out]) 
Returns the indices of the minimum values along an axis. 
argtopk (a, k[, axis, split_every]) 
Extract the indices of the k largest elements from a on the given axis, and return them sorted from largest to smallest. 
argwhere (a) 
Find the indices of array elements that are nonzero, grouped by element. 
around (a[, decimals, out]) 
Evenly round to the given number of decimals. 
array (object[, dtype, copy, order, subok, ndmin]) 
Create an array. 
asanyarray (a) 
Convert the input to a dask array. 
asarray (a) 
Convert the input to a dask array. 
atleast_1d (*arys) 
Convert inputs to arrays with at least one dimension. 
atleast_2d (*arys) 
View inputs as arrays with at least two dimensions. 
atleast_3d (*arys) 
View inputs as arrays with at least three dimensions. 
average (a[, axis, weights, returned]) 
Compute the weighted average along the specified axis. 
bincount (x[, weights, minlength]) 
Count number of occurrences of each value in array of nonnegative ints. 
bitwise_and (x1, x2[, out]) 
Compute the bitwise AND of two arrays elementwise. 
bitwise_not (x[, out]) 
Compute bitwise inversion, or bitwise NOT, elementwise. 
bitwise_or (x1, x2[, out]) 
Compute the bitwise OR of two arrays elementwise. 
bitwise_xor (x1, x2[, out]) 
Compute the bitwise XOR of two arrays elementwise. 
block (arrays[, allow_unknown_chunksizes]) 
Assemble an ndarray from nested lists of blocks. 
broadcast_arrays (*args, **kwargs) 
Broadcast any number of arrays against each other. 
broadcast_to (x, shape[, chunks]) 
Broadcast an array to a new shape. 
coarsen (reduction, x, axes[, trim_excess]) 
Coarsen array by applying reduction to fixed size neighborhoods 
ceil (x[, out]) 
Return the ceiling of the input, elementwise. 
choose (a, choices[, out, mode]) 
Construct an array from an index array and a set of arrays to choose from. 
clip (*args, **kwargs) 
Clip (limit) the values in an array. 
compress (condition, a[, axis, out]) 
Return selected slices of an array along given axis. 
concatenate (seq[, axis, …]) 
Concatenate arrays along an existing axis 
conj (x[, out]) 
Return the complex conjugate, elementwise. 
copysign (x1, x2[, out]) 
Change the sign of x1 to that of x2, elementwise. 
corrcoef (x[, y, rowvar, bias, ddof]) 
Return Pearson productmoment correlation coefficients. 
cos (x[, out]) 
Cosine elementwise. 
cosh (x[, out]) 
Hyperbolic cosine, elementwise. 
count_nonzero (a) 
Counts the number of nonzero values in the array a . 
cov (m[, y, rowvar, bias, ddof, fweights, …]) 
Estimate a covariance matrix, given data and weights. 
cumprod (a[, axis, dtype, out]) 
Return the cumulative product of elements along a given axis. 
cumsum (a[, axis, dtype, out]) 
Return the cumulative sum of the elements along a given axis. 
deg2rad (x[, out]) 
Convert angles from degrees to radians. 
degrees (x[, out]) 
Convert angles from radians to degrees. 
diag (v[, k]) 
Extract a diagonal or construct a diagonal array. 
diff (a[, n, axis]) 
Calculate the nth discrete difference along given axis. 
digitize (x, bins[, right]) 
Return the indices of the bins to which each value in input array belongs. 
dot (a, b[, out]) 
Dot product of two arrays. 
dstack (tup) 
Stack arrays in sequence depth wise (along third axis). 
ediff1d (ary[, to_end, to_begin]) 
The differences between consecutive elements of an array. 
einsum (subscripts, *operands[, out, dtype, …]) 
Evaluates the Einstein summation convention on the operands. 
empty 
Blocked variant of empty 
empty_like (a[, dtype, chunks]) 
Return a new array with the same shape and type as a given array. 
exp (x[, out]) 
Calculate the exponential of all elements in the input array. 
expm1 (x[, out]) 
Calculate exp(x)  1 for all elements in the array. 
eye (N, chunks[, M, k, dtype]) 
Return a 2D Array with ones on the diagonal and zeros elsewhere. 
fabs (x[, out]) 
Compute the absolute values elementwise. 
fix (*args, **kwargs) 
Round to nearest integer towards zero. 
flatnonzero (a) 
Return indices that are nonzero in the flattened version of a. 
flip (m, axis) 
Reverse element order along axis. 
flipud (m) 
Flip array in the up/down direction. 
fliplr (m) 
Flip array in the left/right direction. 
floor (x[, out]) 
Return the floor of the input, elementwise. 
fmax (x1, x2[, out]) 
Elementwise maximum of array elements. 
fmin (x1, x2[, out]) 
Elementwise minimum of array elements. 
fmod (x1, x2[, out]) 
Return the elementwise remainder of division. 
frexp (x[, out1, out2]) 
Decompose the elements of x into mantissa and twos exponent. 
fromfunction (function, shape, **kwargs) 
Construct an array by executing a function over each coordinate. 
frompyfunc (func, nin, nout) 
Takes an arbitrary Python function and returns a Numpy ufunc. 
full 
Blocked variant of full 
full_like (a, fill_value[, dtype, chunks]) 
Return a full array with the same shape and type as a given array. 
gradient (f, *varargs, **kwargs) 
Return the gradient of an Ndimensional array. 
histogram (a[, bins, range, normed, weights, …]) 
Blocked variant of numpy.histogram() . 
hstack (tup) 
Stack arrays in sequence horizontally (column wise). 
hypot (x1, x2[, out]) 
Given the “legs” of a right triangle, return its hypotenuse. 
imag (*args, **kwargs) 
Return the imaginary part of the elements of the array. 
indices (dimensions[, dtype, chunks]) 
Implements NumPy’s indices for Dask Arrays. 
insert (arr, obj, values[, axis]) 
Insert values along the given axis before the given indices. 
isclose (a, b[, rtol, atol, equal_nan]) 
Returns a boolean array where two arrays are elementwise equal within a tolerance. 
iscomplex (*args, **kwargs) 
Returns a bool array, where True if input element is complex. 
isfinite (x[, out]) 
Test elementwise for finiteness (not infinity or not Not a Number). 
isin (element, test_elements[, …]) 

isinf (x[, out]) 
Test elementwise for positive or negative infinity. 
isneginf (*args, **kwargs) 
Test elementwise for negative infinity, return result as bool array. 
isnan (x[, out]) 
Test elementwise for NaN and return result as a boolean array. 
isnull (values) 
pandas.isnull for dask arrays 
isposinf (*args, **kwargs) 
Test elementwise for positive infinity, return result as bool array. 
isreal (*args, **kwargs) 
Returns a bool array, where True if input element is real. 
ldexp (x1, x2[, out]) 
Returns x1 * 2**x2, elementwise. 
linspace (start, stop[, num, chunks, dtype]) 
Return num evenly spaced values over the closed interval [start, stop]. 
log (x[, out]) 
Natural logarithm, elementwise. 
log10 (x[, out]) 
Return the base 10 logarithm of the input array, elementwise. 
log1p (x[, out]) 
Return the natural logarithm of one plus the input array, elementwise. 
log2 (x[, out]) 
Base2 logarithm of x. 
logaddexp (x1, x2[, out]) 
Logarithm of the sum of exponentiations of the inputs. 
logaddexp2 (x1, x2[, out]) 
Logarithm of the sum of exponentiations of the inputs in base2. 
logical_and (x1, x2[, out]) 
Compute the truth value of x1 AND x2 elementwise. 
logical_not (x[, out]) 
Compute the truth value of NOT x elementwise. 
logical_or (x1, x2[, out]) 
Compute the truth value of x1 OR x2 elementwise. 
logical_xor (x1, x2[, out]) 
Compute the truth value of x1 XOR x2, elementwise. 
map_blocks (func, *args, **kwargs) 
Map a function across all blocks of a dask array. 
map_overlap (x, func, depth[, boundary, trim]) 
Map a function over blocks of the array with some overlap 
matmul (a, b[, out]) 
Matrix product of two arrays. 
max (a[, axis, out, keepdims]) 
Return the maximum of an array or maximum along an axis. 
maximum (x1, x2[, out]) 
Elementwise maximum of array elements. 
mean (a[, axis, dtype, out, keepdims]) 
Compute the arithmetic mean along the specified axis. 
meshgrid (*xi, **kwargs) 
Return coordinate matrices from coordinate vectors. 
min (a[, axis, out, keepdims]) 
Return the minimum of an array or minimum along an axis. 
minimum (x1, x2[, out]) 
Elementwise minimum of array elements. 
modf (x[, out1, out2]) 
Return the fractional and integral parts of an array, elementwise. 
moment (a, order[, axis, dtype, keepdims, …]) 

nanargmax (x, axis, **kwargs) 

nanargmin (x, axis, **kwargs) 

nancumprod (a[, axis, dtype, out]) 
Return the cumulative product of array elements over a given axis treating Not a Numbers (NaNs) as one. 
nancumsum (a[, axis, dtype, out]) 
Return the cumulative sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. 
nanmax (a[, axis, out, keepdims]) 
Return the maximum of an array or maximum along an axis, ignoring any NaNs. 
nanmean (a[, axis, dtype, out, keepdims]) 
Compute the arithmetic mean along the specified axis, ignoring NaNs. 
nanmin (a[, axis, out, keepdims]) 
Return minimum of an array or minimum along an axis, ignoring any NaNs. 
nanprod (a[, axis, dtype, out, keepdims]) 
Return the product of array elements over a given axis treating Not a Numbers (NaNs) as zero. 
nanstd (a[, axis, dtype, out, ddof, keepdims]) 
Compute the standard deviation along the specified axis, while ignoring NaNs. 
nansum (a[, axis, dtype, out, keepdims]) 
Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. 
nanvar (a[, axis, dtype, out, ddof, keepdims]) 
Compute the variance along the specified axis, while ignoring NaNs. 
nan_to_num (*args, **kwargs) 
Replace nan with zero and inf with finite numbers. 
nextafter (x1, x2[, out]) 
Return the next floatingpoint value after x1 towards x2, elementwise. 
nonzero (a) 
Return the indices of the elements that are nonzero. 
notnull (values) 
pandas.notnull for dask arrays 
ones 
Blocked variant of ones 
ones_like (a[, dtype, chunks]) 
Return an array of ones with the same shape and type as a given array. 
outer (a, b[, out]) 
Compute the outer product of two vectors. 
pad (array, pad_width, mode, **kwargs) 
Pads an array. 
percentile (a, q[, interpolation]) 
Approximate percentile of 1D array 
PerformanceWarning 

piecewise (x, condlist, funclist, *args, **kw) 
Evaluate a piecewisedefined function. 
prod (a[, axis, dtype, out, keepdims]) 
Return the product of array elements over a given axis. 
ptp (a[, axis, out]) 
Range of values (maximum  minimum) along an axis. 
rad2deg (x[, out]) 
Convert angles from radians to degrees. 
radians (x[, out]) 
Convert angles from degrees to radians. 
ravel (a[, order]) 
Return a contiguous flattened array. 
real (*args, **kwargs) 
Return the real part of the elements of the array. 
rechunk (x, chunks[, threshold, block_size_limit]) 
Convert blocks in dask array x for new chunks. 
repeat (a, repeats[, axis]) 
Repeat elements of an array. 
reshape (x, shape) 
Reshape array to new shape 
result_type (*arrays_and_dtypes) 
Returns the type that results from applying the NumPy type promotion rules to the arguments. 
rint (x[, out]) 
Round elements of the array to the nearest integer. 
roll (a, shift[, axis]) 
Roll array elements along a given axis. 
round (a[, decimals, out]) 
Round an array to the given number of decimals. 
sign (x[, out]) 
Returns an elementwise indication of the sign of a number. 
signbit (x[, out]) 
Returns elementwise True where signbit is set (less than zero). 
sin (x[, out]) 
Trigonometric sine, elementwise. 
sinh (x[, out]) 
Hyperbolic sine, elementwise. 
sqrt (x[, out]) 
Return the positive squareroot of an array, elementwise. 
square (x[, out]) 
Return the elementwise square of the input. 
squeeze (a[, axis]) 
Remove singledimensional entries from the shape of an array. 
stack (seq[, axis]) 
Stack arrays along a new axis 
std (a[, axis, dtype, out, ddof, keepdims]) 
Compute the standard deviation along the specified axis. 
sum (a[, axis, dtype, out, keepdims]) 
Sum of array elements over a given axis. 
take (a, indices[, axis, out, mode]) 
Take elements from an array along an axis. 
tan (x[, out]) 
Compute tangent elementwise. 
tanh (x[, out]) 
Compute hyperbolic tangent elementwise. 
tensordot (a, b[, axes]) 
Compute tensor dot product along specified axes for arrays >= 1D. 
tile (A, reps) 
Construct an array by repeating A the number of times given by reps. 
topk (a, k[, axis, split_every]) 
Extract the k largest elements from a on the given axis, and return them sorted from largest to smallest. 
transpose (a[, axes]) 
Permute the dimensions of an array. 
tril (m[, k]) 
Lower triangle of an array with elements above the kth diagonal zeroed. 
triu (m[, k]) 
Upper triangle of an array with elements above the kth diagonal zeroed. 
trunc (x[, out]) 
Return the truncated value of the input, elementwise. 
unique (ar[, return_index, return_inverse, …]) 
Find the unique elements of an array. 
var (a[, axis, dtype, out, ddof, keepdims]) 
Compute the variance along the specified axis. 
vdot (a, b) 
Return the dot product of two vectors. 
vnorm (a[, ord, axis, dtype, keepdims, …]) 
Vector norm 
vstack (tup) 
Stack arrays in sequence vertically (row wise). 
where (condition, [x, y]) 
Return elements, either from x or y, depending on condition. 
zeros 
Blocked variant of zeros 
zeros_like (a[, dtype, chunks]) 
Return an array of zeros with the same shape and type as a given array. 
Fast Fourier Transforms¶
fft.fft_wrap (fft_func[, kind, dtype]) 
Wrap 1D, 2D, and ND real and complex FFT functions 
fft.fft (a[, n, axis]) 
Wrapping of numpy.fft.fftpack.fft 
fft.fft2 (a[, s, axes]) 
Wrapping of numpy.fft.fftpack.fft2 
fft.fftn (a[, s, axes]) 
Wrapping of numpy.fft.fftpack.fftn 
fft.ifft (a[, n, axis]) 
Wrapping of numpy.fft.fftpack.ifft 
fft.ifft2 (a[, s, axes]) 
Wrapping of numpy.fft.fftpack.ifft2 
fft.ifftn (a[, s, axes]) 
Wrapping of numpy.fft.fftpack.ifftn 
fft.rfft (a[, n, axis]) 
Wrapping of numpy.fft.fftpack.rfft 
fft.rfft2 (a[, s, axes]) 
Wrapping of numpy.fft.fftpack.rfft2 
fft.rfftn (a[, s, axes]) 
Wrapping of numpy.fft.fftpack.rfftn 
fft.irfft (a[, n, axis]) 
Wrapping of numpy.fft.fftpack.irfft 
fft.irfft2 (a[, s, axes]) 
Wrapping of numpy.fft.fftpack.irfft2 
fft.irfftn (a[, s, axes]) 
Wrapping of numpy.fft.fftpack.irfftn 
fft.hfft (a[, n, axis]) 
Wrapping of numpy.fft.fftpack.hfft 
fft.ihfft (a[, n, axis]) 
Wrapping of numpy.fft.fftpack.ihfft 
fft.fftfreq (n[, d]) 
Return the Discrete Fourier Transform sample frequencies. 
fft.rfftfreq (n[, d]) 
Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft). 
fft.fftshift (x[, axes]) 
Shift the zerofrequency component to the center of the spectrum. 
fft.ifftshift (x[, axes]) 
The inverse of fftshift. 
Linear Algebra¶
linalg.cholesky (a[, lower]) 
Returns the Cholesky decomposition, \(A = L L^*\) or \(A = U^* U\) of a Hermitian positivedefinite matrix A. 
linalg.inv (a) 
Compute the inverse of a matrix with LU decomposition and forward / backward substitutions. 
linalg.lstsq (a, b) 
Return the leastsquares solution to a linear matrix equation using QR decomposition. 
linalg.lu (a) 
Compute the lu decomposition of a matrix. 
linalg.norm (x[, ord, axis, keepdims]) 
Matrix or vector norm. 
linalg.qr (a) 
Compute the qr factorization of a matrix. 
linalg.solve (a, b[, sym_pos]) 
Solve the equation a x = b for x . 
linalg.solve_triangular (a, b[, lower]) 
Solve the equation a x = b for x, assuming a is a triangular matrix. 
linalg.svd (a) 
Compute the singular value decomposition of a matrix. 
linalg.svd_compressed (a, k[, n_power_iter, seed]) 
Randomly compressed rankk thin Singular Value Decomposition. 
linalg.sfqr (data[, name]) 
Direct ShortandFat QR 
linalg.tsqr (data[, compute_svd, …]) 
Direct TallandSkinny QR algorithm 
Masked Arrays¶
ma.filled 

ma.fix_invalid 

ma.getdata 

ma.getmaskarray 

ma.masked_array 

ma.masked_equal 

ma.masked_greater 

ma.masked_greater_equal 

ma.masked_inside 

ma.masked_invalid 

ma.masked_less 

ma.masked_less_equal 

ma.masked_not_equal 

ma.masked_outside 

ma.masked_values 

ma.masked_where 

ma.set_fill_value 
Random¶
random.beta (a, b[, size]) 
Draw samples from a Beta distribution. 
random.binomial (n, p[, size]) 
Draw samples from a binomial distribution. 
random.chisquare (df[, size]) 
Draw samples from a chisquare distribution. 
random.choice (a[, size, replace, p]) 
Generates a random sample from a given 1D array 
random.exponential ([scale, size]) 
Draw samples from an exponential distribution. 
random.f (dfnum, dfden[, size]) 
Draw samples from an F distribution. 
random.gamma (shape[, scale, size]) 
Draw samples from a Gamma distribution. 
random.geometric (p[, size]) 
Draw samples from the geometric distribution. 
random.gumbel ([loc, scale, size]) 
Draw samples from a Gumbel distribution. 
random.hypergeometric (ngood, nbad, nsample) 
Draw samples from a Hypergeometric distribution. 
random.laplace ([loc, scale, size]) 
Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). 
random.logistic ([loc, scale, size]) 
Draw samples from a logistic distribution. 
random.lognormal ([mean, sigma, size]) 
Draw samples from a lognormal distribution. 
random.logseries (p[, size]) 
Draw samples from a logarithmic series distribution. 
random.negative_binomial (n, p[, size]) 
Draw samples from a negative binomial distribution. 
random.noncentral_chisquare (df, nonc[, size]) 
Draw samples from a noncentral chisquare distribution. 
random.noncentral_f (dfnum, dfden, nonc[, size]) 
Draw samples from the noncentral F distribution. 
random.normal ([loc, scale, size]) 
Draw random samples from a normal (Gaussian) distribution. 
random.pareto (a[, size]) 
Draw samples from a Pareto II or Lomax distribution with specified shape. 
random.poisson ([lam, size]) 
Draw samples from a Poisson distribution. 
random.power (a[, size]) 
Draws samples in [0, 1] from a power distribution with positive exponent a  1. 
random.random ([size]) 
Return random floats in the halfopen interval [0.0, 1.0). 
random.random_sample ([size]) 
Return random floats in the halfopen interval [0.0, 1.0). 
random.rayleigh ([scale, size]) 
Draw samples from a Rayleigh distribution. 
random.standard_cauchy ([size]) 
Draw samples from a standard Cauchy distribution with mode = 0. 
random.standard_exponential ([size]) 
Draw samples from the standard exponential distribution. 
random.standard_gamma (shape[, size]) 
Draw samples from a standard Gamma distribution. 
random.standard_normal ([size]) 
Draw samples from a standard Normal distribution (mean=0, stdev=1). 
random.standard_t (df[, size]) 
Draw samples from a standard Student’s t distribution with df degrees of freedom. 
random.triangular (left, mode, right[, size]) 
Draw samples from the triangular distribution. 
random.uniform ([low, high, size]) 
Draw samples from a uniform distribution. 
random.vonmises (mu, kappa[, size]) 
Draw samples from a von Mises distribution. 
random.wald (mean, scale[, size]) 
Draw samples from a Wald, or inverse Gaussian, distribution. 
random.weibull (a[, size]) 
Draw samples from a Weibull distribution. 
random.zipf (a[, size]) 
Standard distributions 
Stats¶
stats.ttest_ind (a, b[, axis, equal_var]) 
Calculates the Ttest for the means of TWO INDEPENDENT samples of scores. 
stats.ttest_1samp (a, popmean[, axis, nan_policy]) 
Calculates the Ttest for the mean of ONE group of scores. 
stats.ttest_rel (a, b[, axis, nan_policy]) 
Calculates the Ttest on TWO RELATED samples of scores, a and b. 
stats.chisquare (f_obs[, f_exp, ddof, axis]) 
Calculates a oneway chi square test. 
stats.power_divergence (f_obs[, f_exp, ddof, …]) 
CressieRead power divergence statistic and goodness of fit test. 
stats.skew (a[, axis, bias, nan_policy]) 
Computes the skewness of a data set. 
stats.skewtest (a[, axis, nan_policy]) 
Tests whether the skew is different from the normal distribution. 
stats.kurtosis (a[, axis, fisher, bias, …]) 
Computes the kurtosis (Fisher or Pearson) of a dataset. 
stats.kurtosistest (a[, axis, nan_policy]) 
Tests whether a dataset has normal kurtosis 
stats.normaltest (a[, axis, nan_policy]) 
Tests whether a sample differs from a normal distribution. 
stats.f_oneway (*args) 
Performs a 1way ANOVA. 
stats.moment (a[, moment, axis, nan_policy]) 
Calculates the nth moment about the mean for a sample. 
Image Support¶
image.imread (filename[, imread, preprocess]) 
Read a stack of images into a dask array 
Slightly Overlapping Ghost Computations¶
ghost.ghost (x, depth, boundary) 
Share boundaries between neighboring blocks 
ghost.map_overlap (x, func, depth[, …]) 
Map a function over blocks of the array with some overlap 
Create and Store Arrays¶
from_array (x, chunks[, name, lock, asarray, …]) 
Create dask array from something that looks like an array 
from_delayed (value, shape, dtype[, name]) 
Create a dask array from a dask delayed value 
from_npy_stack (dirname[, mmap_mode]) 
Load dask array from stack of npy files 
from_zarr (url[, component, storage_options, …]) 
Load array from the zarr storage format 
store (sources, targets[, lock, regions, …]) 
Store dask arrays in arraylike objects, overwrite data in target 
to_hdf5 (filename, *args, **kwargs) 
Store arrays in HDF5 file 
to_zarr (arr, url[, component, …]) 
Save array to the zarr storage format 
to_npy_stack (dirname, x[, axis]) 
Write dask array to a stack of .npy files 
Generalized Ufuncs¶
apply_gufunc (func, signature, *args, **kwargs) 
Apply a generalized ufunc or similar python function to arrays. 
as_gufunc ([signature]) 
Decorator for dask.array.gufunc . 
gufunc (pyfunc, **kwargs) 
Binds pyfunc into dask.array.apply_gufunc when called. 
Internal functions¶
atop (func, out_ind, *args, **kwargs) 
Tensor operation: Generalized inner and outer products 
top (func, output, out_indices, …) 
Tensor operation 
Other functions¶

dask.array.
from_array
(x, chunks, name=None, lock=False, asarray=True, fancy=True, getitem=None)¶ Create dask array from something that looks like an array
Input must have a
.shape
and support numpystyle slicing.Parameters:  x : array_like
 chunks : int, tuple
How to chunk the array. Must be one of the following forms:  A blocksize like 1000.  A blockshape like (1000, 1000).  Explicit sizes of all blocks along all dimensions like
((1000, 1000, 500), (400, 400)).
1 as a blocksize indicates the size of the corresponding dimension.
 name : str, optional
The key name to use for the array. Defaults to a hash of
x
. Usename=False
to generate a random name instead of hashing (fast) lock : bool or Lock, optional
If
x
doesn’t support concurrent reads then provide a lock here, or pass in True to have dask.array create one for you. asarray : bool, optional
If True (default), then chunks will be converted to instances of
ndarray
. Set to False to pass passed chunks through unchanged. fancy : bool, optional
If
x
doesn’t support fancy indexing (e.g. indexing with lists or arrays) then set to False. Default is True.
Examples
>>> x = h5py.File('...')['/data/path'] >>> a = da.from_array(x, chunks=(1000, 1000))
If your underlying datastore does not support concurrent reads then include the
lock=True
keyword argument orlock=mylock
if you want multiple arrays to coordinate around the same lock.>>> a = da.from_array(x, chunks=(1000, 1000), lock=True)

dask.array.
from_delayed
(value, shape, dtype, name=None)¶ Create a dask array from a dask delayed value
This routine is useful for constructing dask arrays in an adhoc fashion using dask delayed, particularly when combined with stack and concatenate.
The dask array will consist of a single chunk.
Examples
>>> from dask import delayed >>> value = delayed(np.ones)(5) >>> array = from_delayed(value, (5,), float) >>> array dask.array<fromvalue, shape=(5,), dtype=float64, chunksize=(5,)> >>> array.compute() array([1., 1., 1., 1., 1.])

dask.array.
store
(sources, targets, lock=True, regions=None, compute=True, return_stored=False, **kwargs)¶ Store dask arrays in arraylike objects, overwrite data in target
This stores dask arrays into object that supports numpystyle setitem indexing. It stores values chunk by chunk so that it does not have to fill up memory. For best performance you can align the block size of the storage target with the block size of your array.
If your data fits in memory then you may prefer calling
np.array(myarray)
instead.Parameters:  sources: Array or iterable of Arrays
 targets: arraylike or Delayed or iterable of arraylikes and/or Delayeds
These should support setitem syntax
target[10:20] = ...
 lock: boolean or threading.Lock, optional
Whether or not to lock the data stores while storing. Pass True (lock each file individually), False (don’t lock) or a particular
threading.Lock
object to be shared among all writes. regions: tuple of slices or iterable of tuple of slices
Each
region
tuple inregions
should be such thattarget[region].shape = source.shape
for the corresponding source and target in sources and targets, respectively. compute: boolean, optional
If true compute immediately, return
dask.delayed.Delayed
otherwise return_stored: boolean, optional
Optionally return the stored result (default False).
Examples
>>> x = ...
>>> import h5py >>> f = h5py.File('myfile.hdf5') >>> dset = f.create_dataset('/data', shape=x.shape, ... chunks=x.chunks, ... dtype='f8')
>>> store(x, dset)
Alternatively store many arrays at the same time
>>> store([x, y, z], [dset1, dset2, dset3])

dask.array.
coarsen
(reduction, x, axes, trim_excess=False)¶ Coarsen array by applying reduction to fixed size neighborhoods
Parameters:  reduction: function
Function like np.sum, np.mean, etc…
 x: np.ndarray
Array to be coarsened
 axes: dict
Mapping of axis to coarsening factor
Examples
>>> x = np.array([1, 2, 3, 4, 5, 6]) >>> coarsen(np.sum, x, {0: 2}) array([ 3, 7, 11]) >>> coarsen(np.max, x, {0: 3}) array([3, 6])
Provide dictionary of scale per dimension
>>> x = np.arange(24).reshape((4, 6)) >>> x array([[ 0, 1, 2, 3, 4, 5], [ 6, 7, 8, 9, 10, 11], [12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23]])
>>> coarsen(np.min, x, {0: 2, 1: 3}) array([[ 0, 3], [12, 15]])
You must avoid excess elements explicitly
>>> x = np.array([1, 2, 3, 4, 5, 6, 7, 8]) >>> coarsen(np.min, x, {0: 3}, trim_excess=True) array([1, 4])

dask.array.
stack
(seq, axis=0)¶ Stack arrays along a new axis
Given a sequence of dask Arrays form a new dask Array by stacking them along a new dimension (axis=0 by default)
See also
Examples
Create slices
>>> import dask.array as da >>> import numpy as np
>>> data = [from_array(np.ones((4, 4)), chunks=(2, 2)) ... for i in range(3)]
>>> x = da.stack(data, axis=0) >>> x.shape (3, 4, 4)
>>> da.stack(data, axis=1).shape (4, 3, 4)
>>> da.stack(data, axis=1).shape (4, 4, 3)
Result is a new dask Array

dask.array.
concatenate
(seq, axis=0, allow_unknown_chunksizes=False)¶ Concatenate arrays along an existing axis
Given a sequence of dask Arrays form a new dask Array by stacking them along an existing dimension (axis=0 by default)
Parameters:  seq: list of dask.arrays
 axis: int
Dimension along which to align all of the arrays
 allow_unknown_chunksizes: bool
Allow unknown chunksizes, such as come from converting from dask dataframes. Dask.array is unable to verify that chunks line up. If data comes from differently aligned sources then this can cause unexpected results.
See also
Examples
Create slices
>>> import dask.array as da >>> import numpy as np
>>> data = [from_array(np.ones((4, 4)), chunks=(2, 2)) ... for i in range(3)]
>>> x = da.concatenate(data, axis=0) >>> x.shape (12, 4)
>>> da.concatenate(data, axis=1).shape (4, 12)
Result is a new dask Array

dask.array.
all
(a, axis=None, out=None, keepdims=False)¶ Test whether all array elements along a given axis evaluate to True.
Parameters:  a : array_like
Input array or object that can be converted to an array.
 axis : None or int or tuple of ints, optional
Axis or axes along which a logical AND reduction is performed. The default (axis = None) is to perform a logical AND over all the dimensions of the input array. axis may be negative, in which case it counts from the last to the first axis.
New in version 1.7.0.
If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before.
 out : ndarray, optional
Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if
dtype(out)
is float, the result will consist of 0.0’s and 1.0’s). See doc.ufuncs (Section “Output arguments”) for more details. keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  all : ndarray, bool
A new boolean or array is returned unless out is specified, in which case a reference to out is returned.
See also
ndarray.all
 equivalent method
any
 Test whether any element along a given axis evaluates to True.
Notes
Not a Number (NaN), positive infinity and negative infinity evaluate to True because these are not equal to zero.
Examples
>>> np.all([[True,False],[True,True]]) False
>>> np.all([[True,False],[True,True]], axis=0) array([ True, False], dtype=bool)
>>> np.all([1, 4, 5]) True
>>> np.all([1.0, np.nan]) True
>>> o=np.array([False]) >>> z=np.all([1, 4, 5], out=o) >>> id(z), id(o), z (28293632, 28293632, array([ True], dtype=bool))

dask.array.
allclose
(a, b, rtol=1e05, atol=1e08, equal_nan=False)¶ Returns True if two arrays are elementwise equal within a tolerance.
The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference atol are added together to compare against the absolute difference between a and b.
If either array contains one or more NaNs, False is returned. Infs are treated as equal if they are in the same place and of the same sign in both arrays.
Parameters:  a, b : array_like
Input arrays to compare.
 rtol : float
The relative tolerance parameter (see Notes).
 atol : float
The absolute tolerance parameter (see Notes).
 equal_nan : bool
Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array.
New in version 1.10.0.
Returns:  allclose : bool
Returns True if the two arrays are equal within the given tolerance; False otherwise.
Notes
If the following equation is elementwise True, then allclose returns True.
absolute(a  b) <= (atol + rtol * absolute(b))The above equation is not symmetric in a and b, so that allclose(a, b) might be different from allclose(b, a) in some rare cases.
Examples
>>> np.allclose([1e10,1e7], [1.00001e10,1e8]) False >>> np.allclose([1e10,1e8], [1.00001e10,1e9]) True >>> np.allclose([1e10,1e8], [1.0001e10,1e9]) False >>> np.allclose([1.0, np.nan], [1.0, np.nan]) False >>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) True

dask.array.
angle
(x, deg=0)¶ Return the angle of the complex argument.
Parameters:  z : array_like
A complex number or sequence of complex numbers.
 deg : bool, optional
Return angle in degrees if True, radians if False (default).
Returns:  angle : ndarray or scalar
The counterclockwise angle from the positive real axis on the complex plane, with dtype as numpy.float64.
See also
arctan2
,absolute
Examples
>>> np.angle([1.0, 1.0j, 1+1j]) # in radians array([ 0. , 1.57079633, 0.78539816]) >>> np.angle(1+1j, deg=True) # in degrees 45.0

dask.array.
any
(a, axis=None, out=None, keepdims=False)¶ Test whether any array element along a given axis evaluates to True.
Returns single boolean unless axis is not
None
Parameters:  a : array_like
Input array or object that can be converted to an array.
 axis : None or int or tuple of ints, optional
Axis or axes along which a logical OR reduction is performed. The default (axis = None) is to perform a logical OR over all the dimensions of the input array. axis may be negative, in which case it counts from the last to the first axis.
New in version 1.7.0.
If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before.
 out : ndarray, optional
Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if it is of type float, then it will remain so, returning 1.0 for True and 0.0 for False, regardless of the type of a). See doc.ufuncs (Section “Output arguments”) for details.
 keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  any : bool or ndarray
A new boolean or ndarray is returned unless out is specified, in which case a reference to out is returned.
See also
ndarray.any
 equivalent method
all
 Test whether all elements along a given axis evaluate to True.
Notes
Not a Number (NaN), positive infinity and negative infinity evaluate to True because these are not equal to zero.
Examples
>>> np.any([[True, False], [True, True]]) True
>>> np.any([[True, False], [False, False]], axis=0) array([ True, False], dtype=bool)
>>> np.any([1, 0, 5]) True
>>> np.any(np.nan) True
>>> o=np.array([False]) >>> z=np.any([1, 4, 5], out=o) >>> z, o (array([ True], dtype=bool), array([ True], dtype=bool)) >>> # Check now that z is a reference to o >>> z is o True >>> id(z), id(o) # identity of z and o (191614240, 191614240)

dask.array.
apply_along_axis
(func1d, axis, arr, *args, **kwargs)¶ Apply a function to 1D slices along the given axis.
Execute func1d(a, *args) where func1d operates on 1D arrays and a is a 1D slice of arr along axis.
Parameters:  func1d : function
This function should accept 1D arrays. It is applied to 1D slices of arr along the specified axis.
 axis : integer
Axis along which arr is sliced.
 arr : ndarray
Input array.
 args : any
Additional arguments to func1d.
 kwargs: any
Additional named arguments to func1d.
New in version 1.9.0.
Returns:  apply_along_axis : ndarray
The output array. The shape of outarr is identical to the shape of arr, except along the axis dimension, where the length of outarr is equal to the size of the return value of func1d. If func1d returns a scalar outarr will have one fewer dimensions than arr.
See also
apply_over_axes
 Apply a function repeatedly over multiple axes.
Examples
>>> def my_func(a): ... """Average first and last element of a 1D array""" ... return (a[0] + a[1]) * 0.5 >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]]) >>> np.apply_along_axis(my_func, 0, b) array([ 4., 5., 6.]) >>> np.apply_along_axis(my_func, 1, b) array([ 2., 5., 8.])
For a function that doesn’t return a scalar, the number of dimensions in outarr is the same as arr.
>>> b = np.array([[8,1,7], [4,3,9], [5,2,6]]) >>> np.apply_along_axis(sorted, 1, b) array([[1, 7, 8], [3, 4, 9], [2, 5, 6]])

dask.array.
apply_over_axes
(func, a, axes)¶ Apply a function repeatedly over multiple axes.
func is called as res = func(a, axis), where axis is the first element of axes. The result res of the function call must have either the same dimensions as a or one less dimension. If res has one less dimension than a, a dimension is inserted before axis. The call to func is then repeated for each axis in axes, with res as the first argument.
Parameters:  func : function
This function must take two arguments, func(a, axis).
 a : array_like
Input array.
 axes : array_like
Axes over which func is applied; the elements must be integers.
Returns:  apply_over_axis : ndarray
The output array. The number of dimensions is the same as a, but the shape can be different. This depends on whether func changes the shape of its output with respect to its input.
See also
apply_along_axis
 Apply a function to 1D slices of an array along the given axis.
Notes
This function is equivalent to tuple axis arguments to reorderable ufuncs with keepdims=True. Tuple axis arguments to ufuncs have been availabe since version 1.7.0.
Examples
>>> a = np.arange(24).reshape(2,3,4) >>> a array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]])
Sum over axes 0 and 2. The result has same number of dimensions as the original array:
>>> np.apply_over_axes(np.sum, a, [0,2]) array([[[ 60], [ 92], [124]]])
Tuple axis arguments to ufuncs are equivalent:
>>> np.sum(a, axis=(0,2), keepdims=True) array([[[ 60], [ 92], [124]]])

dask.array.
arange
(*args, **kwargs)¶ Return evenly spaced values from start to stop with step size step.
The values are halfopen [start, stop), so including start and excluding stop. This is basically the same as python’s range function but for dask arrays.
When using a noninteger step, such as 0.1, the results will often not be consistent. It is better to use linspace for these cases.
Parameters:  start : int, optional
The starting value of the sequence. The default is 0.
 stop : int
The end of the interval, this value is excluded from the interval.
 step : int, optional
The spacing between the values. The default is 1 when not specified. The last value of the sequence.
 chunks : int
The number of samples on each block. Note that the last block will have fewer samples if
len(array) % chunks != 0
.
Returns:  samples : dask array
See also

dask.array.
arccos
(x[, out])¶ Trigonometric inverse cosine, elementwise.
The inverse of cos so that, if
y = cos(x)
, thenx = arccos(y)
.Parameters:  x : array_like
xcoordinate on the unit circle. For real arguments, the domain is [1, 1].
 out : ndarray, optional
Array of the same shape as a, to store results in. See doc.ufuncs (Section “Output arguments”) for more details.
Returns:  angle : ndarray
The angle of the ray intersecting the unit circle at the given xcoordinate in radians [0, pi]. If x is a scalar then a scalar is returned, otherwise an array of the same shape as x is returned.
Notes
arccos is a multivalued function: for each x there are infinitely many numbers z such that cos(z) = x. The convention is to return the angle z whose real part lies in [0, pi].
For realvalued input data types, arccos always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, arccos is a complex analytic function that has branch cuts [inf, 1] and [1, inf] and is continuous from above on the former and from below on the latter.
The inverse cos is also known as acos or cos^1.
References
M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/
Examples
We expect the arccos of 1 to be 0, and of 1 to be pi:
>>> np.arccos([1, 1]) array([ 0. , 3.14159265])
Plot arccos:
>>> import matplotlib.pyplot as plt >>> x = np.linspace(1, 1, num=100) >>> plt.plot(x, np.arccos(x)) >>> plt.axis('tight') >>> plt.show()

dask.array.
arccosh
(x[, out])¶ Inverse hyperbolic cosine, elementwise.
Parameters:  x : array_like
Input array.
 out : ndarray, optional
Array of the same shape as x, to store results in. See doc.ufuncs (Section “Output arguments”) for details.
Returns:  arccosh : ndarray
Array of the same shape as x.
Notes
arccosh is a multivalued function: for each x there are infinitely many numbers z such that cosh(z) = x. The convention is to return the z whose imaginary part lies in [pi, pi] and the real part in
[0, inf]
.For realvalued input data types, arccosh always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, arccosh is a complex analytical function that has a branch cut [inf, 1] and is continuous from above on it.
References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arccosh Examples
>>> np.arccosh([np.e, 10.0]) array([ 1.65745445, 2.99322285]) >>> np.arccosh(1) 0.0

dask.array.
arcsin
(x[, out])¶ Inverse sine, elementwise.
Parameters:  x : array_like
ycoordinate on the unit circle.
 out : ndarray, optional
Array of the same shape as x, in which to store the results. See doc.ufuncs (Section “Output arguments”) for more details.
Returns:  angle : ndarray
The inverse sine of each element in x, in radians and in the closed interval
[pi/2, pi/2]
. If x is a scalar, a scalar is returned, otherwise an array.
Notes
arcsin is a multivalued function: for each x there are infinitely many numbers z such that \(sin(z) = x\). The convention is to return the angle z whose real part lies in [pi/2, pi/2].
For realvalued input data types, arcsin always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, arcsin is a complex analytic function that has, by convention, the branch cuts [inf, 1] and [1, inf] and is continuous from above on the former and from below on the latter.
The inverse sine is also known as asin or sin^{1}.
References
Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79ff. http://www.math.sfu.ca/~cbm/aands/
Examples
>>> np.arcsin(1) # pi/2 1.5707963267948966 >>> np.arcsin(1) # pi/2 1.5707963267948966 >>> np.arcsin(0) 0.0

dask.array.
arcsinh
(x[, out])¶ Inverse hyperbolic sine elementwise.
Parameters:  x : array_like
Input array.
 out : ndarray, optional
Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs.
Returns:  out : ndarray
Array of of the same shape as x.
Notes
arcsinh is a multivalued function: for each x there are infinitely many numbers z such that sinh(z) = x. The convention is to return the z whose imaginary part lies in [pi/2, pi/2].
For realvalued input data types, arcsinh always returns real output. For each value that cannot be expressed as a real number or infinity, it returns
nan
and sets the invalid floating point error flag.For complexvalued input, arccos is a complex analytical function that has branch cuts [1j, infj] and [1j, infj] and is continuous from the right on the former and from the left on the latter.
The inverse hyperbolic sine is also known as asinh or
sinh^1
.References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arcsinh Examples
>>> np.arcsinh(np.array([np.e, 10.0])) array([ 1.72538256, 2.99822295])

dask.array.
arctan
(x[, out])¶ Trigonometric inverse tangent, elementwise.
The inverse of tan, so that if
y = tan(x)
thenx = arctan(y)
.Parameters:  x : array_like
Input values. arctan is applied to each element of x.
Returns:  out : ndarray
Out has the same shape as x. Its real part is in
[pi/2, pi/2]
(arctan(+/inf)
returns+/pi/2
). It is a scalar if x is a scalar.
See also
Notes
arctan is a multivalued function: for each x there are infinitely many numbers z such that tan(z) = x. The convention is to return the angle z whose real part lies in [pi/2, pi/2].
For realvalued input data types, arctan always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, arctan is a complex analytic function that has [1j, infj] and [1j, infj] as branch cuts, and is continuous from the left on the former and from the right on the latter.
The inverse tangent is also known as atan or tan^{1}.
References
Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/
Examples
We expect the arctan of 0 to be 0, and of 1 to be pi/4:
>>> np.arctan([0, 1]) array([ 0. , 0.78539816])
>>> np.pi/4 0.78539816339744828
Plot arctan:
>>> import matplotlib.pyplot as plt >>> x = np.linspace(10, 10) >>> plt.plot(x, np.arctan(x)) >>> plt.axis('tight') >>> plt.show()

dask.array.
arctan2
(x1, x2[, out])¶ Elementwise arc tangent of
x1/x2
choosing the quadrant correctly.The quadrant (i.e., branch) is chosen so that
arctan2(x1, x2)
is the signed angle in radians between the ray ending at the origin and passing through the point (1,0), and the ray ending at the origin and passing through the point (x2, x1). (Note the role reversal: the “ycoordinate” is the first function parameter, the “xcoordinate” is the second.) By IEEE convention, this function is defined for x2 = +/0 and for either or both of x1 and x2 = +/inf (see Notes for specific values).This function is not defined for complexvalued arguments; for the socalled argument of complex values, use angle.
Parameters:  x1 : array_like, realvalued
ycoordinates.
 x2 : array_like, realvalued
xcoordinates. x2 must be broadcastable to match the shape of x1 or vice versa.
Returns:  angle : ndarray
Array of angles in radians, in the range
[pi, pi]
.
Notes
arctan2 is identical to the atan2 function of the underlying C library. The following special values are defined in the C standard: [1]
x1 x2 arctan2(x1,x2) +/ 0 +0 +/ 0 +/ 0 0 +/ pi > 0 +/inf +0 / +pi < 0 +/inf 0 / pi +/inf +inf +/ (pi/4) +/inf inf +/ (3*pi/4) Note that +0 and 0 are distinct floating point numbers, as are +inf and inf.
References
[1] (1, 2) ISO/IEC standard 9899:1999, “Programming language C.” Examples
Consider four points in different quadrants:
>>> x = np.array([1, +1, +1, 1]) >>> y = np.array([1, 1, +1, +1]) >>> np.arctan2(y, x) * 180 / np.pi array([135., 45., 45., 135.])
Note the order of the parameters. arctan2 is defined also when x2 = 0 and at several other special points, obtaining values in the range
[pi, pi]
:>>> np.arctan2([1., 1.], [0., 0.]) array([ 1.57079633, 1.57079633]) >>> np.arctan2([0., 0., np.inf], [+0., 0., np.inf]) array([ 0. , 3.14159265, 0.78539816])

dask.array.
arctanh
(x[, out])¶ Inverse hyperbolic tangent elementwise.
Parameters:  x : array_like
Input array.
Returns:  out : ndarray
Array of the same shape as x.
See also
emath.arctanh
Notes
arctanh is a multivalued function: for each x there are infinitely many numbers z such that tanh(z) = x. The convention is to return the z whose imaginary part lies in [pi/2, pi/2].
For realvalued input data types, arctanh always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, arctanh is a complex analytical function that has branch cuts [1, inf] and [1, inf] and is continuous from above on the former and from below on the latter.
The inverse hyperbolic tangent is also known as atanh or
tanh^1
.References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arctanh Examples
>>> np.arctanh([0, 0.5]) array([ 0. , 0.54930614])

dask.array.
argmax
(a, axis=None, out=None)¶ Returns the indices of the maximum values along an axis.
Parameters:  a : array_like
Input array.
 axis : int, optional
By default, the index is into the flattened array, otherwise along the specified axis.
 out : array, optional
If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.
Returns:  index_array : ndarray of ints
Array of indices into the array. It has the same shape as a.shape with the dimension along axis removed.
See also
ndarray.argmax
,argmin
amax
 The maximum value along a given axis.
unravel_index
 Convert a flat index into an index tuple.
Notes
In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned.
Examples
>>> a = np.arange(6).reshape(2,3) >>> a array([[0, 1, 2], [3, 4, 5]]) >>> np.argmax(a) 5 >>> np.argmax(a, axis=0) array([1, 1, 1]) >>> np.argmax(a, axis=1) array([2, 2])
>>> b = np.arange(6) >>> b[1] = 5 >>> b array([0, 5, 2, 3, 4, 5]) >>> np.argmax(b) # Only the first occurrence is returned. 1

dask.array.
argmin
(a, axis=None, out=None)¶ Returns the indices of the minimum values along an axis.
Parameters:  a : array_like
Input array.
 axis : int, optional
By default, the index is into the flattened array, otherwise along the specified axis.
 out : array, optional
If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.
Returns:  index_array : ndarray of ints
Array of indices into the array. It has the same shape as a.shape with the dimension along axis removed.
See also
ndarray.argmin
,argmax
amin
 The minimum value along a given axis.
unravel_index
 Convert a flat index into an index tuple.
Notes
In case of multiple occurrences of the minimum values, the indices corresponding to the first occurrence are returned.
Examples
>>> a = np.arange(6).reshape(2,3) >>> a array([[0, 1, 2], [3, 4, 5]]) >>> np.argmin(a) 0 >>> np.argmin(a, axis=0) array([0, 0, 0]) >>> np.argmin(a, axis=1) array([0, 0])
>>> b = np.arange(6) >>> b[4] = 0 >>> b array([0, 1, 2, 3, 0, 5]) >>> np.argmin(b) # Only the first occurrence is returned. 0

dask.array.
argtopk
(a, k, axis=1, split_every=None)¶ Extract the indices of the k largest elements from a on the given axis, and return them sorted from largest to smallest. If k is negative, extract the indices of the k smallest elements instead, and return them sorted from smallest to largest.
This assumes that
k
is small. All results will be returned in a single chunk along the given axis.Examples
>>> import dask.array as da >>> x = np.array([5, 1, 3, 6]) >>> d = da.from_array(x, chunks=2) >>> d.argtopk(2).compute() array([3, 0]) >>> d.argtopk(2).compute() array([1, 2])

dask.array.
argwhere
(a)¶ Find the indices of array elements that are nonzero, grouped by element.
Parameters:  a : array_like
Input data.
Returns:  index_array : ndarray
Indices of elements that are nonzero. Indices are grouped by element.
Notes
np.argwhere(a)
is the same asnp.transpose(np.nonzero(a))
.The output of
argwhere
is not suitable for indexing arrays. For this purpose usewhere(a)
instead.Examples
>>> x = np.arange(6).reshape(2,3) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.argwhere(x>1) array([[0, 2], [1, 0], [1, 1], [1, 2]])

dask.array.
around
(a, decimals=0, out=None)¶ Evenly round to the given number of decimals.
Parameters:  a : array_like
Input data.
 decimals : int, optional
Number of decimal places to round to (default: 0). If decimals is negative, it specifies the number of positions to the left of the decimal point.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. See doc.ufuncs (Section “Output arguments”) for details.
Returns:  rounded_array : ndarray
An array of the same type as a, containing the rounded values. Unless out was specified, a new array is created. A reference to the result is returned.
The real and imaginary parts of complex numbers are rounded separately. The result of rounding a float is a float.
Notes
For values exactly halfway between rounded decimal values, Numpy rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0, 0.5 and 0.5 round to 0.0, etc. Results may also be surprising due to the inexact representation of decimal fractions in the IEEE floating point standard [1] and errors introduced when scaling by powers of ten.
References
[1] (1, 2) “Lecture Notes on the Status of IEEE 754”, William Kahan, http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF [2] “How Futile are Mindless Assessments of Roundoff in FloatingPoint Computation?”, William Kahan, http://www.cs.berkeley.edu/~wkahan/Mindless.pdf Examples
>>> np.around([0.37, 1.64]) array([ 0., 2.]) >>> np.around([0.37, 1.64], decimals=1) array([ 0.4, 1.6]) >>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value array([ 0., 2., 2., 4., 4.]) >>> np.around([1,2,3,11], decimals=1) # ndarray of ints is returned array([ 1, 2, 3, 11]) >>> np.around([1,2,3,11], decimals=1) array([ 0, 0, 0, 10])

dask.array.
array
(object, dtype=None, copy=True, order=None, subok=False, ndmin=0)¶ Create an array.
Parameters:  object : array_like
An array, any object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence.
 dtype : datatype, optional
The desired datatype for the array. If not given, then the type will be determined as the minimum type required to hold the objects in the sequence. This argument can only be used to ‘upcast’ the array. For downcasting, use the .astype(t) method.
 copy : bool, optional
If true (default), then the object is copied. Otherwise, a copy will only be made if __array__ returns a copy, if obj is a nested sequence, or if a copy is needed to satisfy any of the other requirements (dtype, order, etc.).
 order : {‘C’, ‘F’, ‘A’}, optional
Specify the order of the array. If order is ‘C’, then the array will be in Ccontiguous order (lastindex varies the fastest). If order is ‘F’, then the returned array will be in Fortrancontiguous order (firstindex varies the fastest). If order is ‘A’ (default), then the returned array may be in any order (either C, Fortrancontiguous, or even discontiguous), unless a copy is required, in which case it will be Ccontiguous.
 subok : bool, optional
If True, then subclasses will be passedthrough, otherwise the returned array will be forced to be a baseclass array (default).
 ndmin : int, optional
Specifies the minimum number of dimensions that the resulting array should have. Ones will be prepended to the shape as needed to meet this requirement.
Returns:  out : ndarray
An array object satisfying the specified requirements.
See also
empty
,empty_like
,zeros
,zeros_like
,ones
,ones_like
,fill
Examples
>>> np.array([1, 2, 3]) array([1, 2, 3])
Upcasting:
>>> np.array([1, 2, 3.0]) array([ 1., 2., 3.])
More than one dimension:
>>> np.array([[1, 2], [3, 4]]) array([[1, 2], [3, 4]])
Minimum dimensions 2:
>>> np.array([1, 2, 3], ndmin=2) array([[1, 2, 3]])
Type provided:
>>> np.array([1, 2, 3], dtype=complex) array([ 1.+0.j, 2.+0.j, 3.+0.j])
Datatype consisting of more than one element:
>>> x = np.array([(1,2),(3,4)],dtype=[('a','<i4'),('b','<i4')]) >>> x['a'] array([1, 3])
Creating an array from subclasses:
>>> np.array(np.mat('1 2; 3 4')) array([[1, 2], [3, 4]])
>>> np.array(np.mat('1 2; 3 4'), subok=True) matrix([[1, 2], [3, 4]])

dask.array.
asanyarray
(a)¶ Convert the input to a dask array.
Subclasses of
np.ndarray
will be passed through as chunks unchanged.Parameters:  a : arraylike
Input data, in any form that can be converted to a dask array.
Returns:  out : dask array
Dask array interpretation of a.
Examples
>>> import dask.array as da >>> import numpy as np >>> x = np.arange(3) >>> da.asanyarray(x) dask.array<array, shape=(3,), dtype=int64, chunksize=(3,)>
>>> y = [[1, 2, 3], [4, 5, 6]] >>> da.asanyarray(y) dask.array<array, shape=(2, 3), dtype=int64, chunksize=(2, 3)>

dask.array.
asarray
(a)¶ Convert the input to a dask array.
Parameters:  a : arraylike
Input data, in any form that can be converted to a dask array.
Returns:  out : dask array
Dask array interpretation of a.
Examples
>>> import dask.array as da >>> import numpy as np >>> x = np.arange(3) >>> da.asarray(x) dask.array<array, shape=(3,), dtype=int64, chunksize=(3,)>
>>> y = [[1, 2, 3], [4, 5, 6]] >>> da.asarray(y) dask.array<array, shape=(2, 3), dtype=int64, chunksize=(2, 3)>

dask.array.
atleast_1d
(*arys)¶ Convert inputs to arrays with at least one dimension.
Scalar inputs are converted to 1dimensional arrays, whilst higherdimensional inputs are preserved.
Parameters:  arys1, arys2, … : array_like
One or more input arrays.
Returns:  ret : ndarray
An array, or sequence of arrays, each with
a.ndim >= 1
. Copies are made only if necessary.
See also
Examples
>>> np.atleast_1d(1.0) array([ 1.])
>>> x = np.arange(9.0).reshape(3,3) >>> np.atleast_1d(x) array([[ 0., 1., 2.], [ 3., 4., 5.], [ 6., 7., 8.]]) >>> np.atleast_1d(x) is x True
>>> np.atleast_1d(1, [3, 4]) [array([1]), array([3, 4])]

dask.array.
atleast_2d
(*arys)¶ View inputs as arrays with at least two dimensions.
Parameters:  arys1, arys2, … : array_like
One or more arraylike sequences. Nonarray inputs are converted to arrays. Arrays that already have two or more dimensions are preserved.
Returns:  res, res2, … : ndarray
An array, or tuple of arrays, each with
a.ndim >= 2
. Copies are avoided where possible, and views with two or more dimensions are returned.
See also
Examples
>>> np.atleast_2d(3.0) array([[ 3.]])
>>> x = np.arange(3.0) >>> np.atleast_2d(x) array([[ 0., 1., 2.]]) >>> np.atleast_2d(x).base is x True
>>> np.atleast_2d(1, [1, 2], [[1, 2]]) [array([[1]]), array([[1, 2]]), array([[1, 2]])]

dask.array.
atleast_3d
(*arys)¶ View inputs as arrays with at least three dimensions.
Parameters:  arys1, arys2, … : array_like
One or more arraylike sequences. Nonarray inputs are converted to arrays. Arrays that already have three or more dimensions are preserved.
Returns:  res1, res2, … : ndarray
An array, or tuple of arrays, each with
a.ndim >= 3
. Copies are avoided where possible, and views with three or more dimensions are returned. For example, a 1D array of shape(N,)
becomes a view of shape(1, N, 1)
, and a 2D array of shape(M, N)
becomes a view of shape(M, N, 1)
.
See also
Examples
>>> np.atleast_3d(3.0) array([[[ 3.]]])
>>> x = np.arange(3.0) >>> np.atleast_3d(x).shape (1, 3, 1)
>>> x = np.arange(12.0).reshape(4,3) >>> np.atleast_3d(x).shape (4, 3, 1) >>> np.atleast_3d(x).base is x True
>>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]): ... print(arr, arr.shape) ... [[[1] [2]]] (1, 2, 1) [[[1] [2]]] (1, 2, 1) [[[1 2]]] (1, 1, 2)

dask.array.
average
(a, axis=None, weights=None, returned=False)¶ Compute the weighted average along the specified axis.
Parameters:  a : array_like
Array containing data to be averaged. If a is not an array, a conversion is attempted.
 axis : int, optional
Axis along which to average a. If None, averaging is done over the flattened array.
 weights : array_like, optional
An array of weights associated with the values in a. Each value in a contributes to the average according to its associated weight. The weights array can either be 1D (in which case its length must be the size of a along the given axis) or of the same shape as a. If weights=None, then all data in a are assumed to have a weight equal to one.
 returned : bool, optional
Default is False. If True, the tuple (average, sum_of_weights) is returned, otherwise only the average is returned. If weights=None, sum_of_weights is equivalent to the number of elements over which the average is taken.
Returns:  average, [sum_of_weights] : array_type or double
Return the average along the specified axis. When returned is True, return a tuple with the average as the first element and the sum of the weights as the second element. The return type is Float if a is of integer type, otherwise it is of the same type as a. sum_of_weights is of the same type as average.
Raises:  ZeroDivisionError
When all weights along axis are zero. See numpy.ma.average for a version robust to this type of error.
 TypeError
When the length of 1D weights is not the same as the shape of a along axis.
Examples
>>> data = range(1,5) >>> data [1, 2, 3, 4] >>> np.average(data) 2.5 >>> np.average(range(1,11), weights=range(10,0,1)) 4.0
>>> data = np.arange(6).reshape((3,2)) >>> data array([[0, 1], [2, 3], [4, 5]]) >>> np.average(data, axis=1, weights=[1./4, 3./4]) array([ 0.75, 2.75, 4.75]) >>> np.average(data, weights=[1./4, 3./4]) Traceback (most recent call last): ... TypeError: Axis must be specified when shapes of a and weights differ.

dask.array.
bincount
(x, weights=None, minlength=None)¶ Count number of occurrences of each value in array of nonnegative ints.
The number of bins (of size 1) is one larger than the largest value in x. If minlength is specified, there will be at least this number of bins in the output array (though it will be longer if necessary, depending on the contents of x). Each bin gives the number of occurrences of its index value in x. If weights is specified the input array is weighted by it, i.e. if a value
n
is found at positioni
,out[n] += weight[i]
instead ofout[n] += 1
.Parameters:  x : array_like, 1 dimension, nonnegative ints
Input array.
 weights : array_like, optional
Weights, array of the same shape as x.
 minlength : int, optional
A minimum number of bins for the output array.
New in version 1.6.0.
Returns:  out : ndarray of ints
The result of binning the input array. The length of out is equal to
np.amax(x)+1
.
Raises:  ValueError
If the input is not 1dimensional, or contains elements with negative values, or if minlength is nonpositive.
 TypeError
If the type of the input is float or complex.
Examples
>>> np.bincount(np.arange(5)) array([1, 1, 1, 1, 1]) >>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7])) array([1, 3, 1, 1, 0, 0, 0, 1])
>>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23]) >>> np.bincount(x).size == np.amax(x)+1 True
The input array needs to be of integer dtype, otherwise a TypeError is raised:
>>> np.bincount(np.arange(5, dtype=np.float)) Traceback (most recent call last): File "<stdin>", line 1, in <module> TypeError: array cannot be safely cast to required type
A possible use of
bincount
is to perform sums over variablesize chunks of an array, using theweights
keyword.>>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., 0.6]) # weights >>> x = np.array([0, 1, 1, 2, 2, 2]) >>> np.bincount(x, weights=w) array([ 0.3, 0.7, 1.1])

dask.array.
bitwise_and
(x1, x2[, out])¶ Compute the bitwise AND of two arrays elementwise.
Computes the bitwise AND of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator
&
.Parameters:  x1, x2 : array_like
Only integer and boolean types are handled.
Returns:  out : array_like
Result.
See also
logical_and
,bitwise_or
,bitwise_xor
binary_repr
 Return the binary representation of the input number as a string.
Examples
The number 13 is represented by
00001101
. Likewise, 17 is represented by00010001
. The bitwise AND of 13 and 17 is therefore000000001
, or 1:>>> np.bitwise_and(13, 17) 1
>>> np.bitwise_and(14, 13) 12 >>> np.binary_repr(12) '1100' >>> np.bitwise_and([14,3], 13) array([12, 1])
>>> np.bitwise_and([11,7], [4,25]) array([0, 1]) >>> np.bitwise_and(np.array([2,5,255]), np.array([3,14,16])) array([ 2, 4, 16]) >>> np.bitwise_and([True, True], [False, True]) array([False, True], dtype=bool)

dask.array.
bitwise_not
(x[, out])¶ Compute bitwise inversion, or bitwise NOT, elementwise.
Computes the bitwise NOT of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator
~
.For signed integer inputs, the two’s complement is returned. In a two’scomplement system negative numbers are represented by the two’s complement of the absolute value. This is the most common method of representing signed integers on computers [1]. A Nbit two’scomplement system can represent every integer in the range \(2^{N1}\) to \(+2^{N1}1\).
Parameters:  x1 : array_like
Only integer and boolean types are handled.
Returns:  out : array_like
Result.
See also
bitwise_and
,bitwise_or
,bitwise_xor
,logical_not
binary_repr
 Return the binary representation of the input number as a string.
Notes
bitwise_not is an alias for invert:
>>> np.bitwise_not is np.invert True
References
[1] (1, 2) Wikipedia, “Two’s complement”, http://en.wikipedia.org/wiki/Two’s_complement Examples
We’ve seen that 13 is represented by
00001101
. The invert or bitwise NOT of 13 is then:>>> np.invert(np.array([13], dtype=uint8)) array([242], dtype=uint8) >>> np.binary_repr(x, width=8) '00001101' >>> np.binary_repr(242, width=8) '11110010'
The result depends on the bitwidth:
>>> np.invert(np.array([13], dtype=uint16)) array([65522], dtype=uint16) >>> np.binary_repr(x, width=16) '0000000000001101' >>> np.binary_repr(65522, width=16) '1111111111110010'
When using signed integer types the result is the two’s complement of the result for the unsigned type:
>>> np.invert(np.array([13], dtype=int8)) array([14], dtype=int8) >>> np.binary_repr(14, width=8) '11110010'
Booleans are accepted as well:
>>> np.invert(array([True, False])) array([False, True], dtype=bool)

dask.array.
bitwise_or
(x1, x2[, out])¶ Compute the bitwise OR of two arrays elementwise.
Computes the bitwise OR of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator

.Parameters:  x1, x2 : array_like
Only integer and boolean types are handled.
 out : ndarray, optional
Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs.
Returns:  out : array_like
Result.
See also
logical_or
,bitwise_and
,bitwise_xor
binary_repr
 Return the binary representation of the input number as a string.
Examples
The number 13 has the binaray representation
00001101
. Likewise, 16 is represented by00010000
. The bitwise OR of 13 and 16 is then000111011
, or 29:>>> np.bitwise_or(13, 16) 29 >>> np.binary_repr(29) '11101'
>>> np.bitwise_or(32, 2) 34 >>> np.bitwise_or([33, 4], 1) array([33, 5]) >>> np.bitwise_or([33, 4], [1, 2]) array([33, 6])
>>> np.bitwise_or(np.array([2, 5, 255]), np.array([4, 4, 4])) array([ 6, 5, 255]) >>> np.array([2, 5, 255])  np.array([4, 4, 4]) array([ 6, 5, 255]) >>> np.bitwise_or(np.array([2, 5, 255, 2147483647L], dtype=np.int32), ... np.array([4, 4, 4, 2147483647L], dtype=np.int32)) array([ 6, 5, 255, 2147483647]) >>> np.bitwise_or([True, True], [False, True]) array([ True, True], dtype=bool)

dask.array.
bitwise_xor
(x1, x2[, out])¶ Compute the bitwise XOR of two arrays elementwise.
Computes the bitwise XOR of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator
^
.Parameters:  x1, x2 : array_like
Only integer and boolean types are handled.
Returns:  out : array_like
Result.
See also
logical_xor
,bitwise_and
,bitwise_or
binary_repr
 Return the binary representation of the input number as a string.
Examples
The number 13 is represented by
00001101
. Likewise, 17 is represented by00010001
. The bitwise XOR of 13 and 17 is therefore00011100
, or 28:>>> np.bitwise_xor(13, 17) 28 >>> np.binary_repr(28) '11100'
>>> np.bitwise_xor(31, 5) 26 >>> np.bitwise_xor([31,3], 5) array([26, 6])
>>> np.bitwise_xor([31,3], [5,6]) array([26, 5]) >>> np.bitwise_xor([True, True], [False, True]) array([ True, False], dtype=bool)

dask.array.
block
(arrays, allow_unknown_chunksizes=False)¶ Assemble an ndarray from nested lists of blocks.
Blocks in the innermost lists are concatenated along the last dimension (1), then these are concatenated along the secondlast dimension (2), and so on until the outermost list is reached
Blocks can be of any dimension, but will not be broadcasted using the normal rules. Instead, leading axes of size 1 are inserted, to make
block.ndim
the same for all blocks. This is primarily useful for working with scalars, and means that code likeblock([v, 1])
is valid, wherev.ndim == 1
.When the nested list is two levels deep, this allows block matrices to be constructed from their components.
Parameters:  arrays : nested list of array_like or scalars (but not tuples)
If passed a single ndarray or scalar (a nested list of depth 0), this is returned unmodified (and not copied).
Elements shapes must match along the appropriate axes (without broadcasting), but leading 1s will be prepended to the shape as necessary to make the dimensions match.
 allow_unknown_chunksizes: bool
Allow unknown chunksizes, such as come from converting from dask dataframes. Dask.array is unable to verify that chunks line up. If data comes from differently aligned sources then this can cause unexpected results.
Returns:  block_array : ndarray
The array assembled from the given blocks.
The dimensionality of the output is equal to the greatest of: * the dimensionality of all the inputs * the depth to which the input list is nested
Raises:  ValueError
 If list depths are mismatched  for instance,
[[a, b], c]
is illegal, and should be spelt[[a, b], [c]]
 If lists are empty  for instance,
[[a, b], []]
 If list depths are mismatched  for instance,
See also
concatenate
 Join a sequence of arrays together.
stack
 Stack arrays in sequence along a new dimension.
hstack
 Stack arrays in sequence horizontally (column wise).
vstack
 Stack arrays in sequence vertically (row wise).
dstack
 Stack arrays in sequence depth wise (along third dimension).
vsplit
 Split array into a list of multiple subarrays vertically.
Notes
When called with only scalars,
block
is equivalent to an ndarray call. Soblock([[1, 2], [3, 4]])
is equivalent toarray([[1, 2], [3, 4]])
.This function does not enforce that the blocks lie on a fixed grid.
block([[a, b], [c, d]])
is not restricted to arrays of the form:AAAbb AAAbb cccDD
But is also allowed to produce, for some
a, b, c, d
:AAAbb AAAbb cDDDD
Since concatenation happens along the last axis first, block is _not_ capable of producing the following directly:
AAAbb cccbb cccDD
Matlab’s “square bracket stacking”,
[A, B, ...; p, q, ...]
, is equivalent toblock([[A, B, ...], [p, q, ...]])
.

dask.array.
broadcast_arrays
(*args, **kwargs)¶ Broadcast any number of arrays against each other.
Parameters:  `*args` : array_likes
The arrays to broadcast.
 subok : bool, optional
If True, then subclasses will be passedthrough, otherwise the returned arrays will be forced to be a baseclass array (default).
Returns:  broadcasted : list of arrays
These arrays are views on the original arrays. They are typically not contiguous. Furthermore, more than one element of a broadcasted array may refer to a single memory location. If you need to write to the arrays, make copies first.
Examples
>>> x = np.array([[1,2,3]]) >>> y = np.array([[1],[2],[3]]) >>> np.broadcast_arrays(x, y) [array([[1, 2, 3], [1, 2, 3], [1, 2, 3]]), array([[1, 1, 1], [2, 2, 2], [3, 3, 3]])]
Here is a useful idiom for getting contiguous copies instead of noncontiguous views.
>>> [np.array(a) for a in np.broadcast_arrays(x, y)] [array([[1, 2, 3], [1, 2, 3], [1, 2, 3]]), array([[1, 1, 1], [2, 2, 2], [3, 3, 3]])]

dask.array.
broadcast_to
(x, shape, chunks=None)¶ Broadcast an array to a new shape.
Parameters:  x : array_like
The array to broadcast.
 shape : tuple
The shape of the desired array.
 chunks : tuple, optional
If provided, then the result will use these chunks instead of the same chunks as the source array. Setting chunks explicitly as part of broadcast_to is more efficient than rechunking afterwards. Chunks are only allowed to differ from the original shape along dimensions that are new on the result or have size 1 the input array.
Returns:  broadcast : dask array
See also

dask.array.
coarsen
(reduction, x, axes, trim_excess=False) Coarsen array by applying reduction to fixed size neighborhoods
Parameters:  reduction: function
Function like np.sum, np.mean, etc…
 x: np.ndarray
Array to be coarsened
 axes: dict
Mapping of axis to coarsening factor
Examples
>>> x = np.array([1, 2, 3, 4, 5, 6]) >>> coarsen(np.sum, x, {0: 2}) array([ 3, 7, 11]) >>> coarsen(np.max, x, {0: 3}) array([3, 6])
Provide dictionary of scale per dimension
>>> x = np.arange(24).reshape((4, 6)) >>> x array([[ 0, 1, 2, 3, 4, 5], [ 6, 7, 8, 9, 10, 11], [12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23]])
>>> coarsen(np.min, x, {0: 2, 1: 3}) array([[ 0, 3], [12, 15]])
You must avoid excess elements explicitly
>>> x = np.array([1, 2, 3, 4, 5, 6, 7, 8]) >>> coarsen(np.min, x, {0: 3}, trim_excess=True) array([1, 4])

dask.array.
ceil
(x[, out])¶ Return the ceiling of the input, elementwise.
The ceil of the scalar x is the smallest integer i, such that i >= x. It is often denoted as \(\lceil x \rceil\).
Parameters:  x : array_like
Input data.
Returns:  y : ndarray or scalar
The ceiling of each element in x, with float dtype.
Examples
>>> a = np.array([1.7, 1.5, 0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.ceil(a) array([1., 1., 0., 1., 2., 2., 2.])

dask.array.
choose
(a, choices, out=None, mode='raise')¶ Construct an array from an index array and a set of arrays to choose from.
First of all, if confused or uncertain, definitely look at the Examples  in its full generality, this function is less simple than it might seem from the following code description (below ndi = numpy.lib.index_tricks):
np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)])
.But this omits some subtleties. Here is a fully general summary:
Given an “index” array (a) of integers and a sequence of n arrays (choices), a and each choice array are first broadcast, as necessary, to arrays of a common shape; calling these Ba and Bchoices[i], i = 0,…,n1 we have that, necessarily,
Ba.shape == Bchoices[i].shape
for each i. Then, a new array with shapeBa.shape
is created as follows: if
mode=raise
(the default), then, first of all, each element of a (and thus Ba) must be in the range [0, n1]; now, suppose that i (in that range) is the value at the (j0, j1, …, jm) position in Ba  then the value at the same position in the new array is the value in Bchoices[i] at that same position;  if
mode=wrap
, values in a (and thus Ba) may be any (signed) integer; modular arithmetic is used to map integers outside the range [0, n1] back into that range; and then the new array is constructed as above;  if
mode=clip
, values in a (and thus Ba) may be any (signed) integer; negative integers are mapped to 0; values greater than n1 are mapped to n1; and then the new array is constructed as above.
Parameters:  a : int array
This array must contain integers in [0, n1], where n is the number of choices, unless
mode=wrap
ormode=clip
, in which cases any integers are permissible. choices : sequence of arrays
Choice arrays. a and all of the choices must be broadcastable to the same shape. If choices is itself an array (not recommended), then its outermost dimension (i.e., the one corresponding to
choices.shape[0]
) is taken as defining the “sequence”. out : array, optional
If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.
 mode : {‘raise’ (default), ‘wrap’, ‘clip’}, optional
Specifies how indices outside [0, n1] will be treated:
 ‘raise’ : an exception is raised
 ‘wrap’ : value becomes value mod n
 ‘clip’ : values < 0 are mapped to 0, values > n1 are mapped to n1
Returns:  merged_array : array
The merged result.
Raises:  ValueError: shape mismatch
If a and each choice array are not all broadcastable to the same shape.
See also
ndarray.choose
 equivalent method
Notes
To reduce the chance of misinterpretation, even though the following “abuse” is nominally supported, choices should neither be, nor be thought of as, a single array, i.e., the outermost sequencelike container should be either a list or a tuple.
Examples
>>> choices = [[0, 1, 2, 3], [10, 11, 12, 13], ... [20, 21, 22, 23], [30, 31, 32, 33]] >>> np.choose([2, 3, 1, 0], choices ... # the first element of the result will be the first element of the ... # third (2+1) "array" in choices, namely, 20; the second element ... # will be the second element of the fourth (3+1) choice array, i.e., ... # 31, etc. ... ) array([20, 31, 12, 3]) >>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (41) array([20, 31, 12, 3]) >>> # because there are 4 choice arrays >>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4) array([20, 1, 12, 3]) >>> # i.e., 0
A couple examples illustrating how choose broadcasts:
>>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]] >>> choices = [10, 10] >>> np.choose(a, choices) array([[ 10, 10, 10], [10, 10, 10], [ 10, 10, 10]])
>>> # With thanks to Anne Archibald >>> a = np.array([0, 1]).reshape((2,1,1)) >>> c1 = np.array([1, 2, 3]).reshape((1,3,1)) >>> c2 = np.array([1, 2, 3, 4, 5]).reshape((1,1,5)) >>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2 array([[[ 1, 1, 1, 1, 1], [ 2, 2, 2, 2, 2], [ 3, 3, 3, 3, 3]], [[1, 2, 3, 4, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5]]])
 if

dask.array.
clip
(*args, **kwargs)¶ Clip (limit) the values in an array.
Given an interval, values outside the interval are clipped to the interval edges. For example, if an interval of
[0, 1]
is specified, values smaller than 0 become 0, and values larger than 1 become 1.Parameters:  a : array_like
Array containing elements to clip.
 a_min : scalar or array_like
Minimum value.
 a_max : scalar or array_like
Maximum value. If a_min or a_max are array_like, then they will be broadcasted to the shape of a.
 out : ndarray, optional
The results will be placed in this array. It may be the input array for inplace clipping. out must be of the right shape to hold the output. Its type is preserved.
Returns:  clipped_array : ndarray
An array with the elements of a, but where values < a_min are replaced with a_min, and those > a_max with a_max.
See also
numpy.doc.ufuncs
 Section “Output arguments”
Examples
>>> a = np.arange(10) >>> np.clip(a, 1, 8) array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8]) >>> a array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> np.clip(a, 3, 6, out=a) array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6]) >>> a = np.arange(10) >>> a array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> np.clip(a, [3,4,1,1,1,4,4,4,4,4], 8) array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])

dask.array.
compress
(condition, a, axis=None, out=None)¶ Return selected slices of an array along given axis.
When working along a given axis, a slice along that axis is returned in output for each index where condition evaluates to True. When working on a 1D array, compress is equivalent to extract.
Parameters:  condition : 1D array of bools
Array that selects which entries to return. If len(condition) is less than the size of a along the given axis, then output is truncated to the length of the condition array.
 a : array_like
Array from which to extract a part.
 axis : int, optional
Axis along which to take slices. If None (default), work on the flattened array.
 out : ndarray, optional
Output array. Its type is preserved and it must be of the right shape to hold the output.
Returns:  compressed_array : ndarray
A copy of a without the slices along axis for which condition is false.
See also
take
,choose
,diag
,diagonal
,select
ndarray.compress
 Equivalent method in ndarray
np.extract
 Equivalent method when working on 1D arrays
numpy.doc.ufuncs
 Section “Output arguments”
Examples
>>> a = np.array([[1, 2], [3, 4], [5, 6]]) >>> a array([[1, 2], [3, 4], [5, 6]]) >>> np.compress([0, 1], a, axis=0) array([[3, 4]]) >>> np.compress([False, True, True], a, axis=0) array([[3, 4], [5, 6]]) >>> np.compress([False, True], a, axis=1) array([[2], [4], [6]])
Working on the flattened array does not return slices along an axis but selects elements.
>>> np.compress([False, True], a) array([2])

dask.array.
concatenate
(seq, axis=0, allow_unknown_chunksizes=False) Concatenate arrays along an existing axis
Given a sequence of dask Arrays form a new dask Array by stacking them along an existing dimension (axis=0 by default)
Parameters:  seq: list of dask.arrays
 axis: int
Dimension along which to align all of the arrays
 allow_unknown_chunksizes: bool
Allow unknown chunksizes, such as come from converting from dask dataframes. Dask.array is unable to verify that chunks line up. If data comes from differently aligned sources then this can cause unexpected results.
See also
Examples
Create slices
>>> import dask.array as da >>> import numpy as np
>>> data = [from_array(np.ones((4, 4)), chunks=(2, 2)) ... for i in range(3)]
>>> x = da.concatenate(data, axis=0) >>> x.shape (12, 4)
>>> da.concatenate(data, axis=1).shape (4, 12)
Result is a new dask Array

dask.array.
conj
(x[, out])¶ Return the complex conjugate, elementwise.
The complex conjugate of a complex number is obtained by changing the sign of its imaginary part.
Parameters:  x : array_like
Input value.
Returns:  y : ndarray
The complex conjugate of x, with same dtype as y.
Examples
>>> np.conjugate(1+2j) (12j)
>>> x = np.eye(2) + 1j * np.eye(2) >>> np.conjugate(x) array([[ 1.1.j, 0.0.j], [ 0.0.j, 1.1.j]])

dask.array.
copysign
(x1, x2[, out])¶ Change the sign of x1 to that of x2, elementwise.
If both arguments are arrays or sequences, they have to be of the same length. If x2 is a scalar, its sign will be copied to all elements of x1.
Parameters:  x1 : array_like
Values to change the sign of.
 x2 : array_like
The sign of x2 is copied to x1.
 out : ndarray, optional
Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs.
Returns:  out : array_like
The values of x1 with the sign of x2.
Examples
>>> np.copysign(1.3, 1) 1.3 >>> 1/np.copysign(0, 1) inf >>> 1/np.copysign(0, 1) inf
>>> np.copysign([1, 0, 1], 1.1) array([1., 0., 1.]) >>> np.copysign([1, 0, 1], np.arange(3)1) array([1., 0., 1.])

dask.array.
corrcoef
(x, y=None, rowvar=1, bias=<class 'numpy._NoValue'>, ddof=<class 'numpy._NoValue'>)¶ Return Pearson productmoment correlation coefficients.
Please refer to the documentation for cov for more detail. The relationship between the correlation coefficient matrix, R, and the covariance matrix, C, is
\[R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } }\]The values of R are between 1 and 1, inclusive.
Parameters:  x : array_like
A 1D or 2D array containing multiple variables and observations. Each row of x represents a variable, and each column a single observation of all those variables. Also see rowvar below.
 y : array_like, optional
An additional set of variables and observations. y has the same shape as x.
 rowvar : int, optional
If rowvar is nonzero (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations.
 bias : _NoValue, optional
Has no effect, do not use.
Deprecated since version 1.10.0.
 ddof : _NoValue, optional
Has no effect, do not use.
Deprecated since version 1.10.0.
Returns:  R : ndarray
The correlation coefficient matrix of the variables.
See also
cov
 Covariance matrix
Notes
Due to floating point rounding the resulting array may not be Hermitian, the diagonal elements may not be 1, and the elements may not satisfy the inequality abs(a) <= 1. The real and imaginary parts are clipped to the interval [1, 1] in an attempt to improve on that situation but is not much help in the complex case.
This function accepts but discards arguments bias and ddof. This is for backwards compatibility with previous versions of this function. These arguments had no effect on the return values of the function and can be safely ignored in this and previous versions of numpy.

dask.array.
cos
(x[, out])¶ Cosine elementwise.
Parameters:  x : array_like
Input array in radians.
 out : ndarray, optional
Output array of same shape as x.
Returns:  y : ndarray
The corresponding cosine values.
Raises:  ValueError: invalid return array shape
if out is provided and out.shape != x.shape (See Examples)
Notes
If out is provided, the function writes the result into it, and returns a reference to out. (See Examples)
References
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972.
Examples
>>> np.cos(np.array([0, np.pi/2, np.pi])) array([ 1.00000000e+00, 6.12303177e17, 1.00000000e+00]) >>> >>> # Example of providing the optional output parameter >>> out2 = np.cos([0.1], out1) >>> out2 is out1 True >>> >>> # Example of ValueError due to provision of shape mismatched `out` >>> np.cos(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: invalid return array shape

dask.array.
cosh
(x[, out])¶ Hyperbolic cosine, elementwise.
Equivalent to
1/2 * (np.exp(x) + np.exp(x))
andnp.cos(1j*x)
.Parameters:  x : array_like
Input array.
Returns:  out : ndarray
Output array of same shape as x.
Examples
>>> np.cosh(0) 1.0
The hyperbolic cosine describes the shape of a hanging cable:
>>> import matplotlib.pyplot as plt >>> x = np.linspace(4, 4, 1000) >>> plt.plot(x, np.cosh(x)) >>> plt.show()

dask.array.
count_nonzero
(a)¶ Counts the number of nonzero values in the array
a
.Parameters:  a : array_like
The array for which to count nonzeros.
Returns:  count : int or array of int
Number of nonzero values in the array.
See also
nonzero
 Return the coordinates of all the nonzero values.
Examples
>>> np.count_nonzero(np.eye(4)) 4 >>> np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]]) 5

dask.array.
cov
(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None, aweights=None)¶ Estimate a covariance matrix, given data and weights.
Covariance indicates the level to which two variables vary together. If we examine Ndimensional samples, \(X = [x_1, x_2, ... x_N]^T\), then the covariance matrix element \(C_{ij}\) is the covariance of \(x_i\) and \(x_j\). The element \(C_{ii}\) is the variance of \(x_i\).
See the notes for an outline of the algorithm.
Parameters:  m : array_like
A 1D or 2D array containing multiple variables and observations. Each row of m represents a variable, and each column a single observation of all those variables. Also see rowvar below.
 y : array_like, optional
An additional set of variables and observations. y has the same form as that of m.
 rowvar : bool, optional
If rowvar is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations.
 bias : bool, optional
Default normalization (False) is by
(N  1)
, whereN
is the number of observations given (unbiased estimate). If bias is True, then normalization is byN
. These values can be overridden by using the keywordddof
in numpy versions >= 1.5. ddof : int, optional
If not
None
the default value implied by bias is overridden. Note thatddof=1
will return the unbiased estimate, even if both fweights and aweights are specified, andddof=0
will return the simple average. See the notes for the details. The default value isNone
.New in version 1.5.
 fweights : array_like, int, optional
1D array of integer freguency weights; the number of times each observation vector should be repeated.
New in version 1.10.
 aweights : array_like, optional
1D array of observation vector weights. These relative weights are typically large for observations considered “important” and smaller for observations considered less “important”. If
ddof=0
the array of weights can be used to assign probabilities to observation vectors.New in version 1.10.
Returns:  out : ndarray
The covariance matrix of the variables.
See also
corrcoef
 Normalized covariance matrix
Notes
Assume that the observations are in the columns of the observation array m and let
f = fweights
anda = aweights
for brevity. The steps to compute the weighted covariance are as follows:>>> w = f * a >>> v1 = np.sum(w) >>> v2 = np.sum(w * a) >>> m = np.sum(m * w, axis=1, keepdims=True) / v1 >>> cov = np.dot(m * w, m.T) * v1 / (v1**2  ddof * v2)
Note that when
a == 1
, the normalization factorv1 / (v1**2  ddof * v2)
goes over to1 / (np.sum(f)  ddof)
as it should.Examples
Consider two variables, \(x_0\) and \(x_1\), which correlate perfectly, but in opposite directions:
>>> x = np.array([[0, 2], [1, 1], [2, 0]]).T >>> x array([[0, 1, 2], [2, 1, 0]])
Note how \(x_0\) increases while \(x_1\) decreases. The covariance matrix shows this clearly:
>>> np.cov(x) array([[ 1., 1.], [1., 1.]])
Note that element \(C_{0,1}\), which shows the correlation between \(x_0\) and \(x_1\), is negative.
Further, note how x and y are combined:
>>> x = [2.1, 1, 4.3] >>> y = [3, 1.1, 0.12] >>> X = np.vstack((x,y)) >>> print(np.cov(X)) [[ 11.71 4.286 ] [ 4.286 2.14413333]] >>> print(np.cov(x, y)) [[ 11.71 4.286 ] [ 4.286 2.14413333]] >>> print(np.cov(x)) 11.71

dask.array.
cumprod
(a, axis=None, dtype=None, out=None)¶ Return the cumulative product of elements along a given axis.
Parameters:  a : array_like
Input array.
 axis : int, optional
Axis along which the cumulative product is computed. By default the input is flattened.
 dtype : dtype, optional
Type of the returned array, as well as of the accumulator in which the elements are multiplied. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used instead.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type of the resulting values will be cast if necessary.
Returns:  cumprod : ndarray
A new array holding the result is returned unless out is specified, in which case a reference to out is returned.
See also
numpy.doc.ufuncs
 Section “Output arguments”
Notes
Arithmetic is modular when using integer types, and no error is raised on overflow.
Examples
>>> a = np.array([1,2,3]) >>> np.cumprod(a) # intermediate results 1, 1*2 ... # total product 1*2*3 = 6 array([1, 2, 6]) >>> a = np.array([[1, 2, 3], [4, 5, 6]]) >>> np.cumprod(a, dtype=float) # specify type of output array([ 1., 2., 6., 24., 120., 720.])
The cumulative product for each column (i.e., over the rows) of a:
>>> np.cumprod(a, axis=0) array([[ 1, 2, 3], [ 4, 10, 18]])
The cumulative product for each row (i.e. over the columns) of a:
>>> np.cumprod(a,axis=1) array([[ 1, 2, 6], [ 4, 20, 120]])

dask.array.
cumsum
(a, axis=None, dtype=None, out=None)¶ Return the cumulative sum of the elements along a given axis.
Parameters:  a : array_like
Input array.
 axis : int, optional
Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array.
 dtype : dtype, optional
Type of the returned array and of the accumulator in which the elements are summed. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary. See doc.ufuncs (Section “Output arguments”) for more details.
Returns:  cumsum_along_axis : ndarray.
A new array holding the result is returned unless out is specified, in which case a reference to out is returned. The result has the same size as a, and the same shape as a if axis is not None or a is a 1d array.
See also
Notes
Arithmetic is modular when using integer types, and no error is raised on overflow.
Examples
>>> a = np.array([[1,2,3], [4,5,6]]) >>> a array([[1, 2, 3], [4, 5, 6]]) >>> np.cumsum(a) array([ 1, 3, 6, 10, 15, 21]) >>> np.cumsum(a, dtype=float) # specifies type of output value(s) array([ 1., 3., 6., 10., 15., 21.])
>>> np.cumsum(a,axis=0) # sum over rows for each of the 3 columns array([[1, 2, 3], [5, 7, 9]]) >>> np.cumsum(a,axis=1) # sum over columns for each of the 2 rows array([[ 1, 3, 6], [ 4, 9, 15]])

dask.array.
deg2rad
(x[, out])¶ Convert angles from degrees to radians.
Parameters:  x : array_like
Angles in degrees.
Returns:  y : ndarray
The corresponding angle in radians.
See also
rad2deg
 Convert angles from radians to degrees.
unwrap
 Remove large jumps in angle by wrapping.
Notes
New in version 1.3.0.
deg2rad(x)
isx * pi / 180
.Examples
>>> np.deg2rad(180) 3.1415926535897931

dask.array.
degrees
(x[, out])¶ Convert angles from radians to degrees.
Parameters:  x : array_like
Input array in radians.
 out : ndarray, optional
Output array of same shape as x.
Returns:  y : ndarray of floats
The corresponding degree values; if out was supplied this is a reference to it.
See also
rad2deg
 equivalent function
Examples
Convert a radian array to degrees
>>> rad = np.arange(12.)*np.pi/6 >>> np.degrees(rad) array([ 0., 30., 60., 90., 120., 150., 180., 210., 240., 270., 300., 330.])
>>> out = np.zeros((rad.shape)) >>> r = degrees(rad, out) >>> np.all(r == out) True

dask.array.
diag
(v, k=0)¶ Extract a diagonal or construct a diagonal array.
See the more detailed documentation for
numpy.diagonal
if you use this function to extract a diagonal and wish to write to the resulting array; whether it returns a copy or a view depends on what version of numpy you are using.Parameters:  v : array_like
If v is a 2D array, return a copy of its kth diagonal. If v is a 1D array, return a 2D array with v on the kth diagonal.
 k : int, optional
Diagonal in question. The default is 0. Use k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal.
Returns:  out : ndarray
The extracted diagonal or constructed diagonal array.
See also
Examples
>>> x = np.arange(9).reshape((3,3)) >>> x array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
>>> np.diag(x) array([0, 4, 8]) >>> np.diag(x, k=1) array([1, 5]) >>> np.diag(x, k=1) array([3, 7])
>>> np.diag(np.diag(x)) array([[0, 0, 0], [0, 4, 0], [0, 0, 8]])

dask.array.
diff
(a, n=1, axis=1)¶ Calculate the nth discrete difference along given axis.
The first difference is given by
out[n] = a[n+1]  a[n]
along the given axis, higher differences are calculated by using diff recursively.Parameters:  a : array_like
Input array
 n : int, optional
The number of times values are differenced.
 axis : int, optional
The axis along which the difference is taken, default is the last axis.
Returns:  diff : ndarray
The nth differences. The shape of the output is the same as a except along axis where the dimension is smaller by n.
 .
Examples
>>> x = np.array([1, 2, 4, 7, 0]) >>> np.diff(x) array([ 1, 2, 3, 7]) >>> np.diff(x, n=2) array([ 1, 1, 10])
>>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]]) >>> np.diff(x) array([[2, 3, 4], [5, 1, 2]]) >>> np.diff(x, axis=0) array([[1, 2, 0, 2]])

dask.array.
digitize
(x, bins, right=False)¶ Return the indices of the bins to which each value in input array belongs.
Each index
i
returned is such thatbins[i1] <= x < bins[i]
if bins is monotonically increasing, orbins[i1] > x >= bins[i]
if bins is monotonically decreasing. If values in x are beyond the bounds of bins, 0 orlen(bins)
is returned as appropriate. If right is True, then the right bin is closed so that the indexi
is such thatbins[i1] < x <= bins[i]
or bins[i1] >= x > bins[i]`` if bins is monotonically increasing or decreasing, respectively.Parameters:  x : array_like
Input array to be binned. Prior to Numpy 1.10.0, this array had to be 1dimensional, but can now have any shape.
 bins : array_like
Array of bins. It has to be 1dimensional and monotonic.
 right : bool, optional
Indicating whether the intervals include the right or the left bin edge. Default behavior is (right==False) indicating that the interval does not include the right edge. The left bin end is open in this case, i.e., bins[i1] <= x < bins[i] is the default behavior for monotonically increasing bins.
Returns:  out : ndarray of ints
Output array of indices, of same shape as x.
Raises:  ValueError
If bins is not monotonic.
 TypeError
If the type of the input is complex.
Notes
If values in x are such that they fall outside the bin range, attempting to index bins with the indices that digitize returns will result in an IndexError.
New in version 1.10.0.
np.digitize is implemented in terms of np.searchsorted. This means that a binary search is used to bin the values, which scales much better for larger number of bins than the previous linear search. It also removes the requirement for the input array to be 1dimensional.
Examples
>>> x = np.array([0.2, 6.4, 3.0, 1.6]) >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0]) >>> inds = np.digitize(x, bins) >>> inds array([1, 4, 3, 2]) >>> for n in range(x.size): ... print(bins[inds[n]1], "<=", x[n], "<", bins[inds[n]]) ... 0.0 <= 0.2 < 1.0 4.0 <= 6.4 < 10.0 2.5 <= 3.0 < 4.0 1.0 <= 1.6 < 2.5
>>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.]) >>> bins = np.array([0, 5, 10, 15, 20]) >>> np.digitize(x,bins,right=True) array([1, 2, 3, 4, 4]) >>> np.digitize(x,bins,right=False) array([1, 3, 3, 4, 5])

dask.array.
dot
(a, b, out=None)¶ Dot product of two arrays.
For 2D arrays it is equivalent to matrix multiplication, and for 1D arrays to inner product of vectors (without complex conjugation). For N dimensions it is a sum product over the last axis of a and the secondtolast of b:
dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])
Parameters:  a : array_like
First argument.
 b : array_like
Second argument.
 out : ndarray, optional
Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be Ccontiguous, and its dtype must be the dtype that would be returned for dot(a,b). This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible.
Returns:  output : ndarray
Returns the dot product of a and b. If a and b are both scalars or both 1D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned.
Raises:  ValueError
If the last dimension of a is not the same size as the secondtolast dimension of b.
See also
Examples
>>> np.dot(3, 4) 12
Neither argument is complexconjugated:
>>> np.dot([2j, 3j], [2j, 3j]) (13+0j)
For 2D arrays it is the matrix product:
>>> a = [[1, 0], [0, 1]] >>> b = [[4, 1], [2, 2]] >>> np.dot(a, b) array([[4, 1], [2, 2]])
>>> a = np.arange(3*4*5*6).reshape((3,4,5,6)) >>> b = np.arange(3*4*5*6)[::1].reshape((5,4,6,3)) >>> np.dot(a, b)[2,3,2,1,2,2] 499128 >>> sum(a[2,3,2,:] * b[1,2,:,2]) 499128

dask.array.
dstack
(tup)¶ Stack arrays in sequence depth wise (along third axis).
Takes a sequence of arrays and stack them along the third axis to make a single array. Rebuilds arrays divided by dsplit. This is a simple way to stack 2D arrays (images) into a single 3D array for processing.
Parameters:  tup : sequence of arrays
Arrays to stack. All of them must have the same shape along all but the third axis.
Returns:  stacked : ndarray
The array formed by stacking the given arrays.
See also
stack
 Join a sequence of arrays along a new axis.
vstack
 Stack along first axis.
hstack
 Stack along second axis.
concatenate
 Join a sequence of arrays along an existing axis.
dsplit
 Split array along third axis.
Notes
Equivalent to
np.concatenate(tup, axis=2)
.Examples
>>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.dstack((a,b)) array([[[1, 2], [2, 3], [3, 4]]])
>>> a = np.array([[1],[2],[3]]) >>> b = np.array([[2],[3],[4]]) >>> np.dstack((a,b)) array([[[1, 2]], [[2, 3]], [[3, 4]]])

dask.array.
ediff1d
(ary, to_end=None, to_begin=None)¶ The differences between consecutive elements of an array.
Parameters:  ary : array_like
If necessary, will be flattened before the differences are taken.
 to_end : array_like, optional
Number(s) to append at the end of the returned differences.
 to_begin : array_like, optional
Number(s) to prepend at the beginning of the returned differences.
Returns:  ediff1d : ndarray
The differences. Loosely, this is
ary.flat[1:]  ary.flat[:1]
.
Notes
When applied to masked arrays, this function drops the mask information if the to_begin and/or to_end parameters are used.
Examples
>>> x = np.array([1, 2, 4, 7, 0]) >>> np.ediff1d(x) array([ 1, 2, 3, 7])
>>> np.ediff1d(x, to_begin=99, to_end=np.array([88, 99])) array([99, 1, 2, 3, 7, 88, 99])
The returned array is always 1D.
>>> y = [[1, 2, 4], [1, 6, 24]] >>> np.ediff1d(y) array([ 1, 2, 3, 5, 18])

dask.array.
empty
(*args, **kwargs)¶ Blocked variant of empty
Follows the signature of empty exactly except that it also requires a keyword argument chunks=(…)
Original signature follows below. empty(shape, dtype=float, order=’C’)
Return a new array of given shape and type, without initializing entries.
Parameters:  shape : int or tuple of int
Shape of the empty array
 dtype : datatype, optional
Desired output datatype.
 order : {‘C’, ‘F’}, optional
Whether to store multidimensional data in rowmajor (Cstyle) or columnmajor (Fortranstyle) order in memory.
Returns:  out : ndarray
Array of uninitialized (arbitrary) data of the given shape, dtype, and order. Object arrays will be initialized to None.
See also
Notes
empty, unlike zeros, does not set the array values to zero, and may therefore be marginally faster. On the other hand, it requires the user to manually set all the values in the array, and should be used with caution.
Examples
>>> np.empty([2, 2]) array([[ 9.74499359e+001, 6.69583040e309], [ 2.13182611e314, 3.06959433e309]]) #random
>>> np.empty([2, 2], dtype=int) array([[1073741821, 1067949133], [ 496041986, 19249760]]) #random

dask.array.
empty_like
(a, dtype=None, chunks=None)¶ Return a new array with the same shape and type as a given array.
Parameters:  a : array_like
The shape and datatype of a define these same attributes of the returned array.
 dtype : datatype, optional
Overrides the data type of the result.
 chunks : sequence of ints
The number of samples on each block. Note that the last block will have fewer samples if
len(array) % chunks != 0
.
Returns:  out : ndarray
Array of uninitialized (arbitrary) data with the same shape and type as a.
See also
ones_like
 Return an array of ones with shape and type of input.
zeros_like
 Return an array of zeros with shape and type of input.
empty
 Return a new uninitialized array.
ones
 Return a new array setting values to one.
zeros
 Return a new array setting values to zero.
Notes
This function does not initialize the returned array; to do that use zeros_like or ones_like instead. It may be marginally faster than the functions that do set the array values.

dask.array.
einsum
(subscripts, *operands, out=None, dtype=None, order='K', casting='safe')¶ Evaluates the Einstein summation convention on the operands.
Using the Einstein summation convention, many common multidimensional array operations can be represented in a simple fashion. This function provides a way to compute such summations. The best way to understand this function is to try the examples below, which show how many common NumPy functions can be implemented as calls to einsum.
Parameters:  subscripts : str
Specifies the subscripts for summation.
 operands : list of array_like
These are the arrays for the operation.
 out : ndarray, optional
If provided, the calculation is done into this array.
 dtype : datatype, optional
If provided, forces the calculation to use the data type specified. Note that you may have to also give a more liberal casting parameter to allow the conversions.
 order : {‘C’, ‘F’, ‘A’, ‘K’}, optional
Controls the memory layout of the output. ‘C’ means it should be C contiguous. ‘F’ means it should be Fortran contiguous, ‘A’ means it should be ‘F’ if the inputs are all ‘F’, ‘C’ otherwise. ‘K’ means it should be as close to the layout as the inputs as is possible, including arbitrarily permuted axes. Default is ‘K’.
 casting : {‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional
Controls what kind of data casting may occur. Setting this to ‘unsafe’ is not recommended, as it can adversely affect accumulations.
 ‘no’ means the data types should not be cast at all.
 ‘equiv’ means only byteorder changes are allowed.
 ‘safe’ means only casts which can preserve values are allowed.
 ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.
 ‘unsafe’ means any data conversions may be done.
Returns:  output : ndarray
The calculation based on the Einstein summation convention.
Notes
New in version 1.6.0.
The subscripts string is a commaseparated list of subscript labels, where each label refers to a dimension of the corresponding operand. Repeated subscripts labels in one operand take the diagonal. For example,
np.einsum('ii', a)
is equivalent tonp.trace(a)
.Whenever a label is repeated, it is summed, so
np.einsum('i,i', a, b)
is equivalent tonp.inner(a,b)
. If a label appears only once, it is not summed, sonp.einsum('i', a)
produces a view ofa
with no changes.The order of labels in the output is by default alphabetical. This means that
np.einsum('ij', a)
doesn’t affect a 2D array, whilenp.einsum('ji', a)
takes its transpose.The output can be controlled by specifying output subscript labels as well. This specifies the label order, and allows summing to be disallowed or forced when desired. The call
np.einsum('i>', a)
is likenp.sum(a, axis=1)
, andnp.einsum('ii>i', a)
is likenp.diag(a)
. The difference is that einsum does not allow broadcasting by default.To enable and control broadcasting, use an ellipsis. Default NumPystyle broadcasting is done by adding an ellipsis to the left of each term, like
np.einsum('...ii>...i', a)
. To take the trace along the first and last axes, you can donp.einsum('i...i', a)
, or to do a matrixmatrix product with the leftmost indices instead of rightmost, you can donp.einsum('ij...,jk...>ik...', a, b)
.When there is only one operand, no axes are summed, and no output parameter is provided, a view into the operand is returned instead of a new array. Thus, taking the diagonal as
np.einsum('ii>i', a)
produces a view.An alternative way to provide the subscripts and operands is as
einsum(op0, sublist0, op1, sublist1, ..., [sublistout])
. The examples below have corresponding einsum calls with the two parameter methods.New in version 1.10.0.
Views returned from einsum are now writeable whenever the input array is writeable. For example,
np.einsum('ijk...>kji...', a)
will now have the same effect asnp.swapaxes(a, 0, 2)
andnp.einsum('ii>i', a)
will return a writeable view of the diagonal of a 2D array.Examples
>>> a = np.arange(25).reshape(5,5) >>> b = np.arange(5) >>> c = np.arange(6).reshape(2,3)
>>> np.einsum('ii', a) 60 >>> np.einsum(a, [0,0]) 60 >>> np.trace(a) 60
>>> np.einsum('ii>i', a) array([ 0, 6, 12, 18, 24]) >>> np.einsum(a, [0,0], [0]) array([ 0, 6, 12, 18, 24]) >>> np.diag(a) array([ 0, 6, 12, 18, 24])
>>> np.einsum('ij,j', a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum(a, [0,1], b, [1]) array([ 30, 80, 130, 180, 230]) >>> np.dot(a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum('...j,j', a, b) array([ 30, 80, 130, 180, 230])
>>> np.einsum('ji', c) array([[0, 3], [1, 4], [2, 5]]) >>> np.einsum(c, [1,0]) array([[0, 3], [1, 4], [2, 5]]) >>> c.T array([[0, 3], [1, 4], [2, 5]])
>>> np.einsum('..., ...', 3, c) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.einsum(3, [Ellipsis], c, [Ellipsis]) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.multiply(3, c) array([[ 0, 3, 6], [ 9, 12, 15]])
>>> np.einsum('i,i', b, b) 30 >>> np.einsum(b, [0], b, [0]) 30 >>> np.inner(b,b) 30
>>> np.einsum('i,j', np.arange(2)+1, b) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.einsum(np.arange(2)+1, [0], b, [1]) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.outer(np.arange(2)+1, b) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]])
>>> np.einsum('i...>...', a) array([50, 55, 60, 65, 70]) >>> np.einsum(a, [0,Ellipsis], [Ellipsis]) array([50, 55, 60, 65, 70]) >>> np.sum(a, axis=0) array([50, 55, 60, 65, 70])
>>> a = np.arange(60.).reshape(3,4,5) >>> b = np.arange(24.).reshape(4,3,2) >>> np.einsum('ijk,jil>kl', a, b) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3]) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> np.tensordot(a,b, axes=([1,0],[0,1])) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]])
>>> a = np.arange(6).reshape((3,2)) >>> b = np.arange(12).reshape((4,3)) >>> np.einsum('ki,jk>ij', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]]) >>> np.einsum('ki,...k>i...', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]]) >>> np.einsum('k...,jk', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]])
>>> # since version 1.10.0 >>> a = np.zeros((3, 3)) >>> np.einsum('ii>i', a)[:] = 1 >>> a array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])

dask.array.
exp
(x[, out])¶ Calculate the exponential of all elements in the input array.
Parameters:  x : array_like
Input values.
Returns:  out : ndarray
Output array, elementwise exponential of x.
See also
expm1
 Calculate
exp(x)  1
for all elements in the array. exp2
 Calculate
2**x
for all elements in the array.
Notes
The irrational number
e
is also known as Euler’s number. It is approximately 2.718281, and is the base of the natural logarithm,ln
(this means that, if \(x = \ln y = \log_e y\), then \(e^x = y\). For real input,exp(x)
is always positive.For complex arguments,
x = a + ib
, we can write \(e^x = e^a e^{ib}\). The first term, \(e^a\), is already known (it is the real argument, described above). The second term, \(e^{ib}\), is \(\cos b + i \sin b\), a function with magnitude 1 and a periodic phase.References
[1] Wikipedia, “Exponential function”, http://en.wikipedia.org/wiki/Exponential_function [2] M. Abramovitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” Dover, 1964, p. 69, http://www.math.sfu.ca/~cbm/aands/page_69.htm Examples
Plot the magnitude and phase of
exp(x)
in the complex plane:>>> import matplotlib.pyplot as plt
>>> x = np.linspace(2*np.pi, 2*np.pi, 100) >>> xx = x + 1j * x[:, np.newaxis] # a + ib over complex plane >>> out = np.exp(xx)
>>> plt.subplot(121) >>> plt.imshow(np.abs(out), ... extent=[2*np.pi, 2*np.pi, 2*np.pi, 2*np.pi]) >>> plt.title('Magnitude of exp(x)')
>>> plt.subplot(122) >>> plt.imshow(np.angle(out), ... extent=[2*np.pi, 2*np.pi, 2*np.pi, 2*np.pi]) >>> plt.title('Phase (angle) of exp(x)') >>> plt.show()

dask.array.
expm1
(x[, out])¶ Calculate
exp(x)  1
for all elements in the array.Parameters:  x : array_like
Input values.
Returns:  out : ndarray
Elementwise exponential minus one:
out = exp(x)  1
.
See also
log1p
log(1 + x)
, the inverse of expm1.
Notes
This function provides greater precision than
exp(x)  1
for small values ofx
.Examples
The true value of
exp(1e10)  1
is1.00000000005e10
to about 32 significant digits. This example shows the superiority of expm1 in this case.>>> np.expm1(1e10) 1.00000000005e10 >>> np.exp(1e10)  1 1.000000082740371e10

dask.array.
eye
(N, chunks, M=None, k=0, dtype=<class 'float'>)¶ Return a 2D Array with ones on the diagonal and zeros elsewhere.
Parameters:  N : int
Number of rows in the output.
 chunks: int
chunk size of resulting blocks
 M : int, optional
Number of columns in the output. If None, defaults to N.
 k : int, optional
Index of the diagonal: 0 (the default) refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal.
 dtype : datatype, optional
Datatype of the returned array.
Returns:  I : Array of shape (N,M)
An array where all elements are equal to zero, except for the kth diagonal, whose values are equal to one.

dask.array.
fabs
(x[, out])¶ Compute the absolute values elementwise.
This function returns the absolute values (positive magnitude) of the data in x. Complex values are not handled, use absolute to find the absolute values of complex data.
Parameters:  x : array_like
The array of numbers for which the absolute values are required. If x is a scalar, the result y will also be a scalar.
 out : ndarray, optional
Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs.
Returns:  y : ndarray or scalar
The absolute values of x, the returned values are always floats.
See also
absolute
 Absolute values including complex types.
Examples
>>> np.fabs(1) 1.0 >>> np.fabs([1.2, 1.2]) array([ 1.2, 1.2])

dask.array.
fix
(*args, **kwargs)¶ Round to nearest integer towards zero.
Round an array of floats elementwise to nearest integer towards zero. The rounded values are returned as floats.
Parameters:  x : array_like
An array of floats to be rounded
 y : ndarray, optional
Output array
Returns:  out : ndarray of floats
The array of rounded numbers
Examples
>>> np.fix(3.14) 3.0 >>> np.fix(3) 3.0 >>> np.fix([2.1, 2.9, 2.1, 2.9]) array([ 2., 2., 2., 2.])

dask.array.
flatnonzero
(a)¶ Return indices that are nonzero in the flattened version of a.
This is equivalent to a.ravel().nonzero()[0].
Parameters:  a : ndarray
Input array.
Returns:  res : ndarray
Output array, containing the indices of the elements of a.ravel() that are nonzero.
See also
Examples
>>> x = np.arange(2, 3) >>> x array([2, 1, 0, 1, 2]) >>> np.flatnonzero(x) array([0, 1, 3, 4])
Use the indices of the nonzero elements as an index array to extract these elements:
>>> x.ravel()[np.flatnonzero(x)] array([2, 1, 1, 2])

dask.array.
flip
(m, axis)¶ Reverse element order along axis.
Parameters:  axis : int
Axis to reverse element order of.
Returns:  reversed array : ndarray

dask.array.
flipud
(m)¶ Flip array in the up/down direction.
Flip the entries in each column in the up/down direction. Rows are preserved, but appear in a different order than before.
Parameters:  m : array_like
Input array.
Returns:  out : array_like
A view of m with the rows reversed. Since a view is returned, this operation is \(\mathcal O(1)\).
See also
fliplr
 Flip array in the left/right direction.
rot90
 Rotate array counterclockwise.
Notes
Equivalent to
A[::1,...]
. Does not require the array to be twodimensional.Examples
>>> A = np.diag([1.0, 2, 3]) >>> A array([[ 1., 0., 0.], [ 0., 2., 0.], [ 0., 0., 3.]]) >>> np.flipud(A) array([[ 0., 0., 3.], [ 0., 2., 0.], [ 1., 0., 0.]])
>>> A = np.random.randn(2,3,5) >>> np.all(np.flipud(A)==A[::1,...]) True
>>> np.flipud([1,2]) array([2, 1])

dask.array.
fliplr
(m)¶ Flip array in the left/right direction.
Flip the entries in each row in the left/right direction. Columns are preserved, but appear in a different order than before.
Parameters:  m : array_like
Input array, must be at least 2D.
Returns:  f : ndarray
A view of m with the columns reversed. Since a view is returned, this operation is \(\mathcal O(1)\).
See also
flipud
 Flip array in the up/down direction.
rot90
 Rotate array counterclockwise.
Notes
Equivalent to A[:,::1]. Requires the array to be at least 2D.
Examples
>>> A = np.diag([1.,2.,3.]) >>> A array([[ 1., 0., 0.], [ 0., 2., 0.], [ 0., 0., 3.]]) >>> np.fliplr(A) array([[ 0., 0., 1.], [ 0., 2., 0.], [ 3., 0., 0.]])
>>> A = np.random.randn(2,3,5) >>> np.all(np.fliplr(A)==A[:,::1,...]) True

dask.array.
floor
(x[, out])¶ Return the floor of the input, elementwise.
The floor of the scalar x is the largest integer i, such that i <= x. It is often denoted as \(\lfloor x \rfloor\).
Parameters:  x : array_like
Input data.
Returns:  y : ndarray or scalar
The floor of each element in x.
Notes
Some spreadsheet programs calculate the “floortowardszero”, in other words
floor(2.5) == 2
. NumPy instead uses the definition of floor where floor(2.5) == 3.Examples
>>> a = np.array([1.7, 1.5, 0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.floor(a) array([2., 2., 1., 0., 1., 1., 2.])

dask.array.
fmax
(x1, x2[, out])¶ Elementwise maximum of array elements.
Compare two arrays and returns a new array containing the elementwise maxima. If one of the elements being compared is a NaN, then the nonnan element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are ignored when possible.
Parameters:  x1, x2 : array_like
The arrays holding the elements to be compared. They must have the same shape.
Returns:  y : ndarray or scalar
The maximum of x1 and x2, elementwise. Returns scalar if both x1 and x2 are scalars.
See also
Notes
New in version 1.3.0.
The fmax is equivalent to
np.where(x1 >= x2, x1, x2)
when neither x1 nor x2 are NaNs, but it is faster and does proper broadcasting.Examples
>>> np.fmax([2, 3, 4], [1, 5, 2]) array([ 2., 5., 4.])
>>> np.fmax(np.eye(2), [0.5, 2]) array([[ 1. , 2. ], [ 0.5, 2. ]])
>>> np.fmax([np.nan, 0, np.nan],[0, np.nan, np.nan]) array([ 0., 0., NaN])

dask.array.
fmin
(x1, x2[, out])¶ Elementwise minimum of array elements.
Compare two arrays and returns a new array containing the elementwise minima. If one of the elements being compared is a NaN, then the nonnan element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are ignored when possible.
Parameters:  x1, x2 : array_like
The arrays holding the elements to be compared. They must have the same shape.
Returns:  y : ndarray or scalar
The minimum of x1 and x2, elementwise. Returns scalar if both x1 and x2 are scalars.
See also
Notes
New in version 1.3.0.
The fmin is equivalent to
np.where(x1 <= x2, x1, x2)
when neither x1 nor x2 are NaNs, but it is faster and does proper broadcasting.Examples
>>> np.fmin([2, 3, 4], [1, 5, 2]) array([2, 5, 4])
>>> np.fmin(np.eye(2), [0.5, 2]) array([[ 1. , 2. ], [ 0.5, 2. ]])
>>> np.fmin([np.nan, 0, np.nan],[0, np.nan, np.nan]) array([ 0., 0., NaN])

dask.array.
fmod
(x1, x2[, out])¶ Return the elementwise remainder of division.
This is the NumPy implementation of the C library function fmod, the remainder has the same sign as the dividend x1. It is equivalent to the Matlab(TM)
rem
function and should not be confused with the Python modulus operatorx1 % x2
.Parameters:  x1 : array_like
Dividend.
 x2 : array_like
Divisor.
Returns:  y : array_like
The remainder of the division of x1 by x2.
See also
remainder
 Equivalent to the Python
%
operator.
divide
Notes
The result of the modulo operation for negative dividend and divisors is bound by conventions. For fmod, the sign of result is the sign of the dividend, while for remainder the sign of the result is the sign of the divisor. The fmod function is equivalent to the Matlab(TM)
rem
function.Examples
>>> np.fmod([3, 2, 1, 1, 2, 3], 2) array([1, 0, 1, 1, 0, 1]) >>> np.remainder([3, 2, 1, 1, 2, 3], 2) array([1, 0, 1, 1, 0, 1])
>>> np.fmod([5, 3], [2, 2.]) array([ 1., 1.]) >>> a = np.arange(3, 3).reshape(3, 2) >>> a array([[3, 2], [1, 0], [ 1, 2]]) >>> np.fmod(a, [2,2]) array([[1, 0], [1, 0], [ 1, 0]])

dask.array.
frexp
(x[, out1, out2])¶ Decompose the elements of x into mantissa and twos exponent.
Returns (mantissa, exponent), where x = mantissa * 2**exponent`. The mantissa is lies in the open interval(1, 1), while the twos exponent is a signed integer.
Parameters:  x : array_like
Array of numbers to be decomposed.
 out1 : ndarray, optional
Output array for the mantissa. Must have the same shape as x.
 out2 : ndarray, optional
Output array for the exponent. Must have the same shape as x.
Returns:  (mantissa, exponent) : tuple of ndarrays, (float, int)
mantissa is a float array with values between 1 and 1. exponent is an int array which represents the exponent of 2.
See also
ldexp
 Compute
y = x1 * 2**x2
, the inverse of frexp.
Notes
Complex dtypes are not supported, they will raise a TypeError.
Examples
>>> x = np.arange(9) >>> y1, y2 = np.frexp(x) >>> y1 array([ 0. , 0.5 , 0.5 , 0.75 , 0.5 , 0.625, 0.75 , 0.875, 0.5 ]) >>> y2 array([0, 1, 2, 2, 3, 3, 3, 3, 4]) >>> y1 * 2**y2 array([ 0., 1., 2., 3., 4., 5., 6., 7., 8.])

dask.array.
fromfunction
(function, shape, **kwargs)¶ Construct an array by executing a function over each coordinate.
The resulting array therefore has a value
fn(x, y, z)
at coordinate(x, y, z)
.Parameters:  function : callable
The function is called with N parameters, where N is the rank of shape. Each parameter represents the coordinates of the array varying along a specific axis. For example, if shape were
(2, 2)
, then the parameters in turn be (0, 0), (0, 1), (1, 0), (1, 1). shape : (N,) tuple of ints
Shape of the output array, which also determines the shape of the coordinate arrays passed to function.
 dtype : datatype, optional
Datatype of the coordinate arrays passed to function. By default, dtype is float.
Returns:  fromfunction : any
The result of the call to function is passed back directly. Therefore the shape of fromfunction is completely determined by function. If function returns a scalar value, the shape of fromfunction would match the shape parameter.
Notes
Keywords other than dtype are passed to function.
Examples
>>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int) array([[ True, False, False], [False, True, False], [False, False, True]], dtype=bool)
>>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int) array([[0, 1, 2], [1, 2, 3], [2, 3, 4]])

dask.array.
frompyfunc
(func, nin, nout)¶ Takes an arbitrary Python function and returns a Numpy ufunc.
Can be used, for example, to add broadcasting to a builtin Python function (see Examples section).
Parameters:  func : Python function object
An arbitrary Python function.
 nin : int
The number of input arguments.
 nout : int
The number of objects returned by func.
Returns:  out : ufunc
Returns a Numpy universal function (
ufunc
) object.
Notes
The returned ufunc always returns PyObject arrays.
Examples
Use frompyfunc to add broadcasting to the Python function
oct
:>>> oct_array = np.frompyfunc(oct, 1, 1) >>> oct_array(np.array((10, 30, 100))) array([012, 036, 0144], dtype=object) >>> np.array((oct(10), oct(30), oct(100))) # for comparison array(['012', '036', '0144'], dtype='S4')

dask.array.
full
(*args, **kwargs)¶ Blocked variant of full
Follows the signature of full exactly except that it also requires a keyword argument chunks=(…)
Original signature follows below.
Return a new array of given shape and type, filled with fill_value.
Parameters:  shape : int or sequence of ints
Shape of the new array, e.g.,
(2, 3)
or2
. fill_value : scalar
Fill value.
 dtype : datatype, optional
The desired datatype for the array, e.g., np.int8. Default is float, but will change to np.array(fill_value).dtype in a future release.
 order : {‘C’, ‘F’}, optional
Whether to store multidimensional data in C or Fortrancontiguous (row or columnwise) order in memory.
Returns:  out : ndarray
Array of fill_value with the given shape, dtype, and order.
See also
zeros_like
 Return an array of zeros with shape and type of input.
ones_like
 Return an array of ones with shape and type of input.
empty_like
 Return an empty array with shape and type of input.
full_like
 Fill an array with shape and type of input.
zeros
 Return a new array setting values to zero.
ones
 Return a new array setting values to one.
empty
 Return a new uninitialized array.
Examples
>>> np.full((2, 2), np.inf) array([[ inf, inf], [ inf, inf]]) >>> np.full((2, 2), 10, dtype=np.int) array([[10, 10], [10, 10]])

dask.array.
full_like
(a, fill_value, dtype=None, chunks=None)¶ Return a full array with the same shape and type as a given array.
Parameters:  a : array_like
The shape and datatype of a define these same attributes of the returned array.
 fill_value : scalar
Fill value.
 dtype : datatype, optional
Overrides the data type of the result.
 chunks : sequence of ints
The number of samples on each block. Note that the last block will have fewer samples if
len(array) % chunks != 0
.
Returns:  out : ndarray
Array of fill_value with the same shape and type as a.
See also
zeros_like
 Return an array of zeros with shape and type of input.
ones_like
 Return an array of ones with shape and type of input.
empty_like
 Return an empty array with shape and type of input.
zeros
 Return a new array setting values to zero.
ones
 Return a new array setting values to one.
empty
 Return a new uninitialized array.
full
 Fill a new array.

dask.array.
gradient
(f, *varargs, **kwargs)¶ Return the gradient of an Ndimensional array.
The gradient is computed using second order accurate central differences in the interior and either first differences or second order accurate onesides (forward or backwards) differences at the boundaries. The returned gradient hence has the same shape as the input array.
Parameters:  f : array_like
An Ndimensional array containing samples of a scalar function.
 varargs : scalar or list of scalar, optional
N scalars specifying the sample distances for each dimension, i.e. dx, dy, dz, … Default distance: 1. single scalar specifies sample distance for all dimensions. if axis is given, the number of varargs must equal the number of axes.
 edge_order : {1, 2}, optional
Gradient is calculated using N^{th} order accurate differences at the boundaries. Default: 1.
New in version 1.9.1.
 axis : None or int or tuple of ints, optional
Gradient is calculated only along the given axis or axes The default (axis = None) is to calculate the gradient for all the axes of the input array. axis may be negative, in which case it counts from the last to the first axis.
New in version 1.11.0.
Returns:  gradient : list of ndarray
Each element of list has the same shape as f giving the derivative of f with respect to each dimension.
Examples
>>> x = np.array([1, 2, 4, 7, 11, 16], dtype=np.float) >>> np.gradient(x) array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ]) >>> np.gradient(x, 2) array([ 0.5 , 0.75, 1.25, 1.75, 2.25, 2.5 ])
For two dimensional arrays, the return will be two arrays ordered by axis. In this example the first array stands for the gradient in rows and the second one in columns direction:
>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float)) [array([[ 2., 2., 1.], [ 2., 2., 1.]]), array([[ 1. , 2.5, 4. ], [ 1. , 1. , 1. ]])]
>>> x = np.array([0, 1, 2, 3, 4]) >>> dx = np.gradient(x) >>> y = x**2 >>> np.gradient(y, dx, edge_order=2) array([0., 2., 4., 6., 8.])
The axis keyword can be used to specify a subset of axes of which the gradient is calculated >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=np.float), axis=0) array([[ 2., 2., 1.],
[ 2., 2., 1.]])

dask.array.
histogram
(a, bins=None, range=None, normed=False, weights=None, density=None)¶ Blocked variant of
numpy.histogram()
.Follows the signature of
numpy.histogram()
exactly with the following exceptions: Either an iterable specifying the
bins
or the number ofbins
and arange
argument is required as computingmin
andmax
over blocked arrays is an expensive operation that must be performed explicitly. weights
must be a dask.array.Array with the same block structure asa
.
Examples
Using number of bins and range:
>>> import dask.array as da >>> import numpy as np >>> x = da.from_array(np.arange(10000), chunks=10) >>> h, bins = da.histogram(x, bins=10, range=[0, 10000]) >>> bins array([ 0., 1000., 2000., 3000., 4000., 5000., 6000., 7000., 8000., 9000., 10000.]) >>> h.compute() array([1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000])
Explicitly specifying the bins:
>>> h, bins = da.histogram(x, bins=np.array([0, 5000, 10000])) >>> bins array([ 0, 5000, 10000]) >>> h.compute() array([5000, 5000])
 Either an iterable specifying the

dask.array.
hstack
(tup)¶ Stack arrays in sequence horizontally (column wise).
Take a sequence of arrays and stack them horizontally to make a single array. Rebuild arrays divided by hsplit.
Parameters:  tup : sequence of ndarrays
All arrays must have the same shape along all but the second axis.
Returns:  stacked : ndarray
The array formed by stacking the given arrays.
See also
stack
 Join a sequence of arrays along a new axis.
vstack
 Stack arrays in sequence vertically (row wise).
dstack
 Stack arrays in sequence depth wise (along third axis).
concatenate
 Join a sequence of arrays along an existing axis.
hsplit
 Split array along second axis.
Notes
Equivalent to
np.concatenate(tup, axis=1)
Examples
>>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.hstack((a,b)) array([1, 2, 3, 2, 3, 4]) >>> a = np.array([[1],[2],[3]]) >>> b = np.array([[2],[3],[4]]) >>> np.hstack((a,b)) array([[1, 2], [2, 3], [3, 4]])

dask.array.
hypot
(x1, x2[, out])¶ Given the “legs” of a right triangle, return its hypotenuse.
Equivalent to
sqrt(x1**2 + x2**2)
, elementwise. If x1 or x2 is scalar_like (i.e., unambiguously castable to a scalar type), it is broadcast for use with each element of the other argument. (See Examples)Parameters:  x1, x2 : array_like
Leg of the triangle(s).
 out : ndarray, optional
Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs.
Returns:  z : ndarray
The hypotenuse of the triangle(s).
Examples
>>> np.hypot(3*np.ones((3, 3)), 4*np.ones((3, 3))) array([[ 5., 5., 5.], [ 5., 5., 5.], [ 5., 5., 5.]])
Example showing broadcast of scalar_like argument:
>>> np.hypot(3*np.ones((3, 3)), [4]) array([[ 5., 5., 5.], [ 5., 5., 5.], [ 5., 5., 5.]])

dask.array.
imag
(*args, **kwargs)¶ Return the imaginary part of the elements of the array.
Parameters:  val : array_like
Input array.
Returns:  out : ndarray
Output array. If val is real, the type of val is used for the output. If val has complex elements, the returned type is float.
Examples
>>> a = np.array([1+2j, 3+4j, 5+6j]) >>> a.imag array([ 2., 4., 6.]) >>> a.imag = np.array([8, 10, 12]) >>> a array([ 1. +8.j, 3.+10.j, 5.+12.j])

dask.array.
indices
(dimensions, dtype=<class 'int'>, chunks=None)¶ Implements NumPy’s
indices
for Dask Arrays.Generates a grid of indices covering the dimensions provided.
The final array has the shape
(len(dimensions), *dimensions)
. The chunks are used to specify the chunking for axis 1 up tolen(dimensions)
. The 0th axis always has chunks of length 1.Parameters:  dimensions : sequence of ints
The shape of the index grid.
 dtype : dtype, optional
Type to use for the array. Default is
int
. chunks : sequence of ints
The number of samples on each block. Note that the last block will have fewer samples if
len(array) % chunks != 0
.
Returns:  grid : dask array

dask.array.
insert
(arr, obj, values, axis=None)¶ Insert values along the given axis before the given indices.
Parameters:  arr : array_like
Input array.
 obj : int, slice or sequence of ints
Object that defines the index or indices before which values is inserted.
New in version 1.8.0.
Support for multiple insertions when obj is a single scalar or a sequence with one element (similar to calling insert multiple times).
 values : array_like
Values to insert into arr. If the type of values is different from that of arr, values is converted to the type of arr. values should be shaped so that
arr[...,obj,...] = values
is legal. axis : int, optional
Axis along which to insert values. If axis is None then arr is flattened first.
Returns:  out : ndarray
A copy of arr with values inserted. Note that insert does not occur inplace: a new array is returned. If axis is None, out is a flattened array.
See also
append
 Append elements at the end of an array.
concatenate
 Join a sequence of arrays along an existing axis.
delete
 Delete elements from an array.
Notes
Note that for higher dimensional inserts obj=0 behaves very different from obj=[0] just like arr[:,0,:] = values is different from arr[:,[0],:] = values.
Examples
>>> a = np.array([[1, 1], [2, 2], [3, 3]]) >>> a array([[1, 1], [2, 2], [3, 3]]) >>> np.insert(a, 1, 5) array([1, 5, 1, 2, 2, 3, 3]) >>> np.insert(a, 1, 5, axis=1) array([[1, 5, 1], [2, 5, 2], [3, 5, 3]])
Difference between sequence and scalars:
>>> np.insert(a, [1], [[1],[2],[3]], axis=1) array([[1, 1, 1], [2, 2, 2], [3, 3, 3]]) >>> np.array_equal(np.insert(a, 1, [1, 2, 3], axis=1), ... np.insert(a, [1], [[1],[2],[3]], axis=1)) True
>>> b = a.flatten() >>> b array([1, 1, 2, 2, 3, 3]) >>> np.insert(b, [2, 2], [5, 6]) array([1, 1, 5, 6, 2, 2, 3, 3])
>>> np.insert(b, slice(2, 4), [5, 6]) array([1, 1, 5, 2, 6, 2, 3, 3])
>>> np.insert(b, [2, 2], [7.13, False]) # type casting array([1, 1, 7, 0, 2, 2, 3, 3])
>>> x = np.arange(8).reshape(2, 4) >>> idx = (1, 3) >>> np.insert(x, idx, 999, axis=1) array([[ 0, 999, 1, 2, 999, 3], [ 4, 999, 5, 6, 999, 7]])

dask.array.
isclose
(a, b, rtol=1e05, atol=1e08, equal_nan=False)¶ Returns a boolean array where two arrays are elementwise equal within a tolerance.
The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference atol are added together to compare against the absolute difference between a and b.
Parameters:  a, b : array_like
Input arrays to compare.
 rtol : float
The relative tolerance parameter (see Notes).
 atol : float
The absolute tolerance parameter (see Notes).
 equal_nan : bool
Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array.
Returns:  y : array_like
Returns a boolean array of where a and b are equal within the given tolerance. If both a and b are scalars, returns a single boolean value.
See also
Notes
New in version 1.7.0.
For finite values, isclose uses the following equation to test whether two floating point values are equivalent.
absolute(a  b) <= (atol + rtol * absolute(b))The above equation is not symmetric in a and b, so that isclose(a, b) might be different from isclose(b, a) in some rare cases.
Examples
>>> np.isclose([1e10,1e7], [1.00001e10,1e8]) array([True, False]) >>> np.isclose([1e10,1e8], [1.00001e10,1e9]) array([True, True]) >>> np.isclose([1e10,1e8], [1.0001e10,1e9]) array([False, True]) >>> np.isclose([1.0, np.nan], [1.0, np.nan]) array([True, False]) >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) array([True, True])

dask.array.
iscomplex
(*args, **kwargs)¶ Returns a bool array, where True if input element is complex.
What is tested is whether the input has a nonzero imaginary part, not if the input type is complex.
Parameters:  x : array_like
Input array.
Returns:  out : ndarray of bools
Output array.
Examples
>>> np.iscomplex([1+1j, 1+0j, 4.5, 3, 2, 2j]) array([ True, False, False, False, False, True], dtype=bool)

dask.array.
isfinite
(x[, out])¶ Test elementwise for finiteness (not infinity or not Not a Number).
The result is returned as a boolean array.
Parameters:  x : array_like
Input values.
 out : ndarray, optional
Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs.
Returns:  y : ndarray, bool
For scalar input, the result is a new boolean with value True if the input is finite; otherwise the value is False (input is either positive infinity, negative infinity or Not a Number).
For array input, the result is a boolean array with the same dimensions as the input and the values are True if the corresponding element of the input is finite; otherwise the values are False (element is either positive infinity, negative infinity or Not a Number).
Notes
Not a Number, positive infinity and negative infinity are considered to be nonfinite.
Numpy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Also that positive infinity is not equivalent to negative infinity. But infinity is equivalent to positive infinity. Errors result if the second argument is also supplied when x is a scalar input, or if first and second arguments have different shapes.
Examples
>>> np.isfinite(1) True >>> np.isfinite(0) True >>> np.isfinite(np.nan) False >>> np.isfinite(np.inf) False >>> np.isfinite(np.NINF) False >>> np.isfinite([np.log(1.),1.,np.log(0)]) array([False, True, False], dtype=bool)
>>> x = np.array([np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isfinite(x, y) array([0, 1, 0]) >>> y array([0, 1, 0])

dask.array.
isin
(element, test_elements, assume_unique=False, invert=False)¶

dask.array.
isinf
(x[, out])¶ Test elementwise for positive or negative infinity.
Returns a boolean array of the same shape as x, True where
x == +/inf
, otherwise False.Parameters:  x : array_like
Input values
 out : array_like, optional
An array with the same shape as x to store the result.
Returns:  y : bool (scalar) or boolean ndarray
For scalar input, the result is a new boolean with value True if the input is positive or negative infinity; otherwise the value is False.
For array input, the result is a boolean array with the same shape as the input and the values are True where the corresponding element of the input is positive or negative infinity; elsewhere the values are False. If a second argument was supplied the result is stored there. If the type of that array is a numeric type the result is represented as zeros and ones, if the type is boolean then as False and True, respectively. The return value y is then a reference to that array.
Notes
Numpy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754).
Errors result if the second argument is supplied when the first argument is a scalar, or if the first and second arguments have different shapes.
Examples
>>> np.isinf(np.inf) True >>> np.isinf(np.nan) False >>> np.isinf(np.NINF) True >>> np.isinf([np.inf, np.inf, 1.0, np.nan]) array([ True, True, False, False], dtype=bool)
>>> x = np.array([np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isinf(x, y) array([1, 0, 1]) >>> y array([1, 0, 1])

dask.array.
isneginf
(*args, **kwargs)¶ Test elementwise for negative infinity, return result as bool array.
Parameters:  x : array_like
The input array.
 y : array_like, optional
A boolean array with the same shape and type as x to store the result.
Returns:  y : ndarray
A boolean array with the same dimensions as the input. If second argument is not supplied then a numpy boolean array is returned with values True where the corresponding element of the input is negative infinity and values False where the element of the input is not negative infinity.
If a second argument is supplied the result is stored there. If the type of that array is a numeric type the result is represented as zeros and ones, if the type is boolean then as False and True. The return value y is then a reference to that array.
Notes
Numpy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754).
Errors result if the second argument is also supplied when x is a scalar input, or if first and second arguments have different shapes.
Examples
>>> np.isneginf(np.NINF) array(True, dtype=bool) >>> np.isneginf(np.inf) array(False, dtype=bool) >>> np.isneginf(np.PINF) array(False, dtype=bool) >>> np.isneginf([np.inf, 0., np.inf]) array([ True, False, False], dtype=bool)
>>> x = np.array([np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isneginf(x, y) array([1, 0, 0]) >>> y array([1, 0, 0])

dask.array.
isnan
(x[, out])¶ Test elementwise for NaN and return result as a boolean array.
Parameters:  x : array_like
Input array.
Returns:  y : ndarray or bool
For scalar input, the result is a new boolean with value True if the input is NaN; otherwise the value is False.
For array input, the result is a boolean array of the same dimensions as the input and the values are True if the corresponding element of the input is NaN; otherwise the values are False.
Notes
Numpy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity.
Examples
>>> np.isnan(np.nan) True >>> np.isnan(np.inf) False >>> np.isnan([np.log(1.),1.,np.log(0)]) array([ True, False, False], dtype=bool)

dask.array.
isnull
(values)¶ pandas.isnull for dask arrays

dask.array.
isposinf
(*args, **kwargs)¶ Test elementwise for positive infinity, return result as bool array.
Parameters:  x : array_like
The input array.
 y : array_like, optional
A boolean array with the same shape as x to store the result.
Returns:  y : ndarray
A boolean array with the same dimensions as the input. If second argument is not supplied then a boolean array is returned with values True where the corresponding element of the input is positive infinity and values False where the element of the input is not positive infinity.
If a second argument is supplied the result is stored there. If the type of that array is a numeric type the result is represented as zeros and ones, if the type is boolean then as False and True. The return value y is then a reference to that array.
Notes
Numpy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754).
Errors result if the second argument is also supplied when x is a scalar input, or if first and second arguments have different shapes.
Examples
>>> np.isposinf(np.PINF) array(True, dtype=bool) >>> np.isposinf(np.inf) array(True, dtype=bool) >>> np.isposinf(np.NINF) array(False, dtype=bool) >>> np.isposinf([np.inf, 0., np.inf]) array([False, False, True], dtype=bool)
>>> x = np.array([np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isposinf(x, y) array([0, 0, 1]) >>> y array([0, 0, 1])

dask.array.
isreal
(*args, **kwargs)¶ Returns a bool array, where True if input element is real.
If element has complex type with zero complex part, the return value for that element is True.
Parameters:  x : array_like
Input array.
Returns:  out : ndarray, bool
Boolean array of same shape as x.
Examples
>>> np.isreal([1+1j, 1+0j, 4.5, 3, 2, 2j]) array([False, True, True, True, True, False], dtype=bool)

dask.array.
ldexp
(x1, x2[, out])¶ Returns x1 * 2**x2, elementwise.
The mantissas x1 and twos exponents x2 are used to construct floating point numbers
x1 * 2**x2
.Parameters:  x1 : array_like
Array of multipliers.
 x2 : array_like, int
Array of twos exponents.
 out : ndarray, optional
Output array for the result.
Returns:  y : ndarray or scalar
The result of
x1 * 2**x2
.
See also
frexp
 Return (y1, y2) from
x = y1 * 2**y2
, inverse to ldexp.
Notes
Complex dtypes are not supported, they will raise a TypeError.
ldexp is useful as the inverse of frexp, if used by itself it is more clear to simply use the expression
x1 * 2**x2
.Examples
>>> np.ldexp(5, np.arange(4)) array([ 5., 10., 20., 40.], dtype=float32)
>>> x = np.arange(6) >>> np.ldexp(*np.frexp(x)) array([ 0., 1., 2., 3., 4., 5.])

dask.array.
linspace
(start, stop, num=50, chunks=None, dtype=None)¶ Return num evenly spaced values over the closed interval [start, stop].
TODO: implement the endpoint, restep, and dtype keyword args
Parameters:  start : scalar
The starting value of the sequence.
 stop : scalar
The last value of the sequence.
 num : int, optional
Number of samples to include in the returned dask array, including the endpoints.
 chunks : int
The number of samples on each block. Note that the last block will have fewer samples if num % blocksize != 0
Returns:  samples : dask array
See also

dask.array.
log
(x[, out])¶ Natural logarithm, elementwise.
The natural logarithm log is the inverse of the exponential function, so that log(exp(x)) = x. The natural logarithm is logarithm in base e.
Parameters:  x : array_like
Input value.
Returns:  y : ndarray
The natural logarithm of x, elementwise.
Notes
Logarithm is a multivalued function: for each x there is an infinite number of z such that exp(z) = x. The convention is to return the z whose imaginary part lies in [pi, pi].
For realvalued input data types, log always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, log is a complex analytical function that has a branch cut [inf, 0] and is continuous from above on it. log handles the floatingpoint negative zero as an infinitesimal negative number, conforming to the C99 standard.
References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Logarithm”. http://en.wikipedia.org/wiki/Logarithm Examples
>>> np.log([1, np.e, np.e**2, 0]) array([ 0., 1., 2., Inf])

dask.array.
log10
(x[, out])¶ Return the base 10 logarithm of the input array, elementwise.
Parameters:  x : array_like
Input values.
Returns:  y : ndarray
The logarithm to the base 10 of x, elementwise. NaNs are returned where x is negative.
See also
emath.log10
Notes
Logarithm is a multivalued function: for each x there is an infinite number of z such that 10**z = x. The convention is to return the z whose imaginary part lies in [pi, pi].
For realvalued input data types, log10 always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, log10 is a complex analytical function that has a branch cut [inf, 0] and is continuous from above on it. log10 handles the floatingpoint negative zero as an infinitesimal negative number, conforming to the C99 standard.
References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Logarithm”. http://en.wikipedia.org/wiki/Logarithm Examples
>>> np.log10([1e15, 3.]) array([15., NaN])

dask.array.
log1p
(x[, out])¶ Return the natural logarithm of one plus the input array, elementwise.
Calculates
log(1 + x)
.Parameters:  x : array_like
Input values.
Returns:  y : ndarray
Natural logarithm of 1 + x, elementwise.
See also
expm1
exp(x)  1
, the inverse of log1p.
Notes
For realvalued input, log1p is accurate also for x so small that 1 + x == 1 in floatingpoint accuracy.
Logarithm is a multivalued function: for each x there is an infinite number of z such that exp(z) = 1 + x. The convention is to return the z whose imaginary part lies in [pi, pi].
For realvalued input data types, log1p always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, log1p is a complex analytical function that has a branch cut [inf, 1] and is continuous from above on it. log1p handles the floatingpoint negative zero as an infinitesimal negative number, conforming to the C99 standard.
References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Logarithm”. http://en.wikipedia.org/wiki/Logarithm Examples
>>> np.log1p(1e99) 1e99 >>> np.log(1 + 1e99) 0.0

dask.array.
log2
(x[, out])¶ Base2 logarithm of x.
Parameters:  x : array_like
Input values.
Returns:  y : ndarray
Base2 logarithm of x.
Notes
New in version 1.3.0.
Logarithm is a multivalued function: for each x there is an infinite number of z such that 2**z = x. The convention is to return the z whose imaginary part lies in [pi, pi].
For realvalued input data types, log2 always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, log2 is a complex analytical function that has a branch cut [inf, 0] and is continuous from above on it. log2 handles the floatingpoint negative zero as an infinitesimal negative number, conforming to the C99 standard.
Examples
>>> x = np.array([0, 1, 2, 2**4]) >>> np.log2(x) array([Inf, 0., 1., 4.])
>>> xi = np.array([0+1.j, 1, 2+0.j, 4.j]) >>> np.log2(xi) array([ 0.+2.26618007j, 0.+0.j , 1.+0.j , 2.+2.26618007j])

dask.array.
logaddexp
(x1, x2[, out])¶ Logarithm of the sum of exponentiations of the inputs.
Calculates
log(exp(x1) + exp(x2))
. This function is useful in statistics where the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers. In such cases the logarithm of the calculated probability is stored. This function allows adding probabilities stored in such a fashion.Parameters:  x1, x2 : array_like
Input values.
Returns:  result : ndarray
Logarithm of
exp(x1) + exp(x2)
.
See also
logaddexp2
 Logarithm of the sum of exponentiations of inputs in base 2.
Notes
New in version 1.3.0.
Examples
>>> prob1 = np.log(1e50) >>> prob2 = np.log(2.5e50) >>> prob12 = np.logaddexp(prob1, prob2) >>> prob12 113.87649168120691 >>> np.exp(prob12) 3.5000000000000057e50

dask.array.
logaddexp2
(x1, x2[, out])¶ Logarithm of the sum of exponentiations of the inputs in base2.
Calculates
log2(2**x1 + 2**x2)
. This function is useful in machine learning when the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers. In such cases the base2 logarithm of the calculated probability can be used instead. This function allows adding probabilities stored in such a fashion.Parameters:  x1, x2 : array_like
Input values.
 out : ndarray, optional
Array to store results in.
Returns:  result : ndarray
Base2 logarithm of
2**x1 + 2**x2
.
See also
logaddexp
 Logarithm of the sum of exponentiations of the inputs.
Notes
New in version 1.3.0.
Examples
>>> prob1 = np.log2(1e50) >>> prob2 = np.log2(2.5e50) >>> prob12 = np.logaddexp2(prob1, prob2) >>> prob1, prob2, prob12 (166.09640474436813, 164.77447664948076, 164.28904982231052) >>> 2**prob12 3.4999999999999914e50

dask.array.
logical_and
(x1, x2[, out])¶ Compute the truth value of x1 AND x2 elementwise.
Parameters:  x1, x2 : array_like
Input arrays. x1 and x2 must be of the same shape.
Returns:  y : ndarray or bool
Boolean result with the same shape as x1 and x2 of the logical AND operation on corresponding elements of x1 and x2.
See also
Examples
>>> np.logical_and(True, False) False >>> np.logical_and([True, False], [False, False]) array([False, False], dtype=bool)
>>> x = np.arange(5) >>> np.logical_and(x>1, x<4) array([False, False, True, True, False], dtype=bool)

dask.array.
logical_not
(x[, out])¶ Compute the truth value of NOT x elementwise.
Parameters:  x : array_like
Logical NOT is applied to the elements of x.
Returns:  y : bool or ndarray of bool
Boolean result with the same shape as x of the NOT operation on elements of x.
See also
Examples
>>> np.logical_not(3) False >>> np.logical_not([True, False, 0, 1]) array([False, True, True, False], dtype=bool)
>>> x = np.arange(5) >>> np.logical_not(x<3) array([False, False, False, True, True], dtype=bool)

dask.array.
logical_or
(x1, x2[, out])¶ Compute the truth value of x1 OR x2 elementwise.
Parameters:  x1, x2 : array_like
Logical OR is applied to the elements of x1 and x2. They have to be of the same shape.
Returns:  y : ndarray or bool
Boolean result with the same shape as x1 and x2 of the logical OR operation on elements of x1 and x2.
See also
Examples
>>> np.logical_or(True, False) True >>> np.logical_or([True, False], [False, False]) array([ True, False], dtype=bool)
>>> x = np.arange(5) >>> np.logical_or(x < 1, x > 3) array([ True, False, False, False, True], dtype=bool)

dask.array.
logical_xor
(x1, x2[, out])¶ Compute the truth value of x1 XOR x2, elementwise.
Parameters:  x1, x2 : array_like
Logical XOR is applied to the elements of x1 and x2. They must be broadcastable to the same shape.
Returns:  y : bool or ndarray of bool
Boolean result of the logical XOR operation applied to the elements of x1 and x2; the shape is determined by whether or not broadcasting of one or both arrays was required.
See also
Examples
>>> np.logical_xor(True, False) True >>> np.logical_xor([True, True, False, False], [True, False, True, False]) array([False, True, True, False], dtype=bool)
>>> x = np.arange(5) >>> np.logical_xor(x < 1, x > 3) array([ True, False, False, False, True], dtype=bool)
Simple example showing support of broadcasting
>>> np.logical_xor(0, np.eye(2)) array([[ True, False], [False, True]], dtype=bool)

dask.array.
matmul
(a, b, out=None)¶ Matrix product of two arrays.
The behavior depends on the arguments in the following way.
 If both arguments are 2D they are multiplied like conventional matrices.
 If either argument is ND, N > 2, it is treated as a stack of matrices residing in the last two indexes and broadcast accordingly.
 If the first argument is 1D, it is promoted to a matrix by prepending a 1 to its dimensions. After matrix multiplication the prepended 1 is removed.
 If the second argument is 1D, it is promoted to a matrix by appending a 1 to its dimensions. After matrix multiplication the appended 1 is removed.
Multiplication by a scalar is not allowed, use
*
instead. Note that multiplying a stack of matrices with a vector will result in a stack of vectors, but matmul will not recognize it as such.matmul
differs fromdot
in two important ways. Multiplication by scalars is not allowed.
 Stacks of matrices are broadcast together as if the matrices were elements.
Warning
This function is preliminary and included in Numpy 1.10 for testing and documentation. Its semantics will not change, but the number and order of the optional arguments will.
New in version 1.10.0.
Parameters:  a : array_like
First argument.
 b : array_like
Second argument.
 out : ndarray, optional
Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be Ccontiguous, and its dtype must be the dtype that would be returned for dot(a,b). This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible.
Returns:  output : ndarray
Returns the dot product of a and b. If a and b are both 1D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned.
Raises:  ValueError
If the last dimension of a is not the same size as the secondtolast dimension of b.
If scalar value is passed.
See also
Notes
The matmul function implements the semantics of the @ operator introduced in Python 3.5 following PEP465.
Examples
For 2D arrays it is the matrix product:
>>> a = [[1, 0], [0, 1]] >>> b = [[4, 1], [2, 2]] >>> np.matmul(a, b) array([[4, 1], [2, 2]])
For 2D mixed with 1D, the result is the usual.
>>> a = [[1, 0], [0, 1]] >>> b = [1, 2] >>> np.matmul(a, b) array([1, 2]) >>> np.matmul(b, a) array([1, 2])
Broadcasting is conventional for stacks of arrays
>>> a = np.arange(2*2*4).reshape((2,2,4)) >>> b = np.arange(2*2*4).reshape((2,4,2)) >>> np.matmul(a,b).shape (2, 2, 2) >>> np.matmul(a,b)[0,1,1] 98 >>> sum(a[0,1,:] * b[0,:,1]) 98
Vector, vector returns the scalar inner product, but neither argument is complexconjugated:
>>> np.matmul([2j, 3j], [2j, 3j]) (13+0j)
Scalar multiplication raises an error.
>>> np.matmul([1,2], 3) Traceback (most recent call last): ... ValueError: Scalar operands are not allowed, use '*' instead

dask.array.
max
(a, axis=None, out=None, keepdims=False)¶ Return the maximum of an array or maximum along an axis.
Parameters:  a : array_like
Input data.
 axis : None or int or tuple of ints, optional
Axis or axes along which to operate. By default, flattened input is used.
If this is a tuple of ints, the maximum is selected over multiple axes, instead of a single axis or all the axes as before.
 out : ndarray, optional
Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See doc.ufuncs (Section “Output arguments”) for more details.
 keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  amax : ndarray or scalar
Maximum of a. If axis is None, the result is a scalar value. If axis is given, the result is an array of dimension
a.ndim  1
.
See also
amin
 The minimum value of an array along a given axis, propagating any NaNs.
nanmax
 The maximum value of an array along a given axis, ignoring any NaNs.
maximum
 Elementwise maximum of two arrays, propagating any NaNs.
fmax
 Elementwise maximum of two arrays, ignoring any NaNs.
argmax
 Return the indices of the maximum values.
Notes
NaN values are propagated, that is if at least one item is NaN, the corresponding max value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmax.
Don’t use amax for elementwise comparison of 2 arrays; when
a.shape[0]
is 2,maximum(a[0], a[1])
is faster thanamax(a, axis=0)
.Examples
>>> a = np.arange(4).reshape((2,2)) >>> a array([[0, 1], [2, 3]]) >>> np.amax(a) # Maximum of the flattened array 3 >>> np.amax(a, axis=0) # Maxima along the first axis array([2, 3]) >>> np.amax(a, axis=1) # Maxima along the second axis array([1, 3])
>>> b = np.arange(5, dtype=np.float) >>> b[2] = np.NaN >>> np.amax(b) nan >>> np.nanmax(b) 4.0

dask.array.
maximum
(x1, x2[, out])¶ Elementwise maximum of array elements.
Compare two arrays and returns a new array containing the elementwise maxima. If one of the elements being compared is a NaN, then that element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are propagated.
Parameters:  x1, x2 : array_like
The arrays holding the elements to be compared. They must have the same shape, or shapes that can be broadcast to a single shape.
Returns:  y : ndarray or scalar
The maximum of x1 and x2, elementwise. Returns scalar if both x1 and x2 are scalars.
See also
Notes
The maximum is equivalent to
np.where(x1 >= x2, x1, x2)
when neither x1 nor x2 are nans, but it is faster and does proper broadcasting.Examples
>>> np.maximum([2, 3, 4], [1, 5, 2]) array([2, 5, 4])
>>> np.maximum(np.eye(2), [0.5, 2]) # broadcasting array([[ 1. , 2. ], [ 0.5, 2. ]])
>>> np.maximum([np.nan, 0, np.nan], [0, np.nan, np.nan]) array([ NaN, NaN, NaN]) >>> np.maximum(np.Inf, 1) inf

dask.array.
mean
(a, axis=None, dtype=None, out=None, keepdims=False)¶ Compute the arithmetic mean along the specified axis.
Returns the average of the array elements. The average is taken over the flattened array by default, otherwise over the specified axis. float64 intermediate and return values are used for integer inputs.
Parameters:  a : array_like
Array containing numbers whose mean is desired. If a is not an array, a conversion is attempted.
 axis : None or int or tuple of ints, optional
Axis or axes along which the means are computed. The default is to compute the mean of the flattened array.
If this is a tuple of ints, a mean is performed over multiple axes, instead of a single axis or all the axes as before.
 dtype : datatype, optional
Type to use in computing the mean. For integer inputs, the default is float64; for floating point inputs, it is the same as the input dtype.
 out : ndarray, optional
Alternate output array in which to place the result. The default is
None
; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See doc.ufuncs for details. keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  m : ndarray, see dtype parameter above
If out=None, returns a new array containing the mean values, otherwise a reference to the output array is returned.
Notes
The arithmetic mean is the sum of the elements along the axis divided by the number of elements.
Note that for floatingpoint input, the mean is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higherprecision accumulator using the dtype keyword can alleviate this issue.
Examples
>>> a = np.array([[1, 2], [3, 4]]) >>> np.mean(a) 2.5 >>> np.mean(a, axis=0) array([ 2., 3.]) >>> np.mean(a, axis=1) array([ 1.5, 3.5])
In single precision, mean can be inaccurate:
>>> a = np.zeros((2, 512*512), dtype=np.float32) >>> a[0, :] = 1.0 >>> a[1, :] = 0.1 >>> np.mean(a) 0.546875
Computing the mean in float64 is more accurate:
>>> np.mean(a, dtype=np.float64) 0.55000000074505806

dask.array.
meshgrid
(*xi, **kwargs)¶ Return coordinate matrices from coordinate vectors.
Make ND coordinate arrays for vectorized evaluations of ND scalar/vector fields over ND grids, given onedimensional coordinate arrays x1, x2,…, xn.
Changed in version 1.9: 1D and 0D cases are allowed.
Parameters:  x1, x2,…, xn : array_like
1D arrays representing the coordinates of a grid.
 indexing : {‘xy’, ‘ij’}, optional
Cartesian (‘xy’, default) or matrix (‘ij’) indexing of output. See Notes for more details.
New in version 1.7.0.
 sparse : bool, optional
If True a sparse grid is returned in order to conserve memory. Default is False.
New in version 1.7.0.
 copy : bool, optional
If False, a view into the original arrays are returned in order to conserve memory. Default is True. Please note that
sparse=False, copy=False
will likely return noncontiguous arrays. Furthermore, more than one element of a broadcast array may refer to a single memory location. If you need to write to the arrays, make copies first.New in version 1.7.0.
Returns:  X1, X2,…, XN : ndarray
For vectors x1, x2,…, ‘xn’ with lengths
Ni=len(xi)
, return(N1, N2, N3,...Nn)
shaped arrays if indexing=’ij’ or(N2, N1, N3,...Nn)
shaped arrays if indexing=’xy’ with the elements of xi repeated to fill the matrix along the first dimension for x1, the second for x2 and so on.
See also
index_tricks.mgrid
 Construct a multidimensional “meshgrid” using indexing notation.
index_tricks.ogrid
 Construct an open multidimensional “meshgrid” using indexing notation.
Notes
This function supports both indexing conventions through the indexing keyword argument. Giving the string ‘ij’ returns a meshgrid with matrix indexing, while ‘xy’ returns a meshgrid with Cartesian indexing. In the 2D case with inputs of length M and N, the outputs are of shape (N, M) for ‘xy’ indexing and (M, N) for ‘ij’ indexing. In the 3D case with inputs of length M, N and P, outputs are of shape (N, M, P) for ‘xy’ indexing and (M, N, P) for ‘ij’ indexing. The difference is illustrated by the following code snippet:
xv, yv = meshgrid(x, y, sparse=False, indexing='ij') for i in range(nx): for j in range(ny): # treat xv[i,j], yv[i,j] xv, yv = meshgrid(x, y, sparse=False, indexing='xy') for i in range(nx): for j in range(ny): # treat xv[j,i], yv[j,i]
In the 1D and 0D case, the indexing and sparse keywords have no effect.
Examples
>>> nx, ny = (3, 2) >>> x = np.linspace(0, 1, nx) >>> y = np.linspace(0, 1, ny) >>> xv, yv = meshgrid(x, y) >>> xv array([[ 0. , 0.5, 1. ], [ 0. , 0.5, 1. ]]) >>> yv array([[ 0., 0., 0.], [ 1., 1., 1.]]) >>> xv, yv = meshgrid(x, y, sparse=True) # make sparse output arrays >>> xv array([[ 0. , 0.5, 1. ]]) >>> yv array([[ 0.], [ 1.]])
meshgrid is very useful to evaluate functions on a grid.
>>> x = np.arange(5, 5, 0.1) >>> y = np.arange(5, 5, 0.1) >>> xx, yy = meshgrid(x, y, sparse=True) >>> z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2) >>> h = plt.contourf(x,y,z)

dask.array.
min
(a, axis=None, out=None, keepdims=False)¶ Return the minimum of an array or minimum along an axis.
Parameters:  a : array_like
Input data.
 axis : None or int or tuple of ints, optional
Axis or axes along which to operate. By default, flattened input is used.
If this is a tuple of ints, the minimum is selected over multiple axes, instead of a single axis or all the axes as before.
 out : ndarray, optional
Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See doc.ufuncs (Section “Output arguments”) for more details.
 keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  amin : ndarray or scalar
Minimum of a. If axis is None, the result is a scalar value. If axis is given, the result is an array of dimension
a.ndim  1
.
See also
amax
 The maximum value of an array along a given axis, propagating any NaNs.
nanmin
 The minimum value of an array along a given axis, ignoring any NaNs.
minimum
 Elementwise minimum of two arrays, propagating any NaNs.
fmin
 Elementwise minimum of two arrays, ignoring any NaNs.
argmin
 Return the indices of the minimum values.
Notes
NaN values are propagated, that is if at least one item is NaN, the corresponding min value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmin.
Don’t use amin for elementwise comparison of 2 arrays; when
a.shape[0]
is 2,minimum(a[0], a[1])
is faster thanamin(a, axis=0)
.Examples
>>> a = np.arange(4).reshape((2,2)) >>> a array([[0, 1], [2, 3]]) >>> np.amin(a) # Minimum of the flattened array 0 >>> np.amin(a, axis=0) # Minima along the first axis array([0, 1]) >>> np.amin(a, axis=1) # Minima along the second axis array([0, 2])
>>> b = np.arange(5, dtype=np.float) >>> b[2] = np.NaN >>> np.amin(b) nan >>> np.nanmin(b) 0.0

dask.array.
minimum
(x1, x2[, out])¶ Elementwise minimum of array elements.
Compare two arrays and returns a new array containing the elementwise minima. If one of the elements being compared is a NaN, then that element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are propagated.
Parameters:  x1, x2 : array_like
The arrays holding the elements to be compared. They must have the same shape, or shapes that can be broadcast to a single shape.
Returns:  y : ndarray or scalar
The minimum of x1 and x2, elementwise. Returns scalar if both x1 and x2 are scalars.
See also
Notes
The minimum is equivalent to
np.where(x1 <= x2, x1, x2)
when neither x1 nor x2 are NaNs, but it is faster and does proper broadcasting.Examples
>>> np.minimum([2, 3, 4], [1, 5, 2]) array([1, 3, 2])
>>> np.minimum(np.eye(2), [0.5, 2]) # broadcasting array([[ 0.5, 0. ], [ 0. , 1. ]])
>>> np.minimum([np.nan, 0, np.nan],[0, np.nan, np.nan]) array([ NaN, NaN, NaN]) >>> np.minimum(np.Inf, 1) inf

dask.array.
modf
(x[, out1, out2])¶ Return the fractional and integral parts of an array, elementwise.
The fractional and integral parts are negative if the given number is negative.
Parameters:  x : array_like
Input array.
Returns:  y1 : ndarray
Fractional part of x.
 y2 : ndarray
Integral part of x.
Notes
For integer input the return values are floats.
Examples
>>> np.modf([0, 3.5]) (array([ 0. , 0.5]), array([ 0., 3.])) >>> np.modf(0.5) (0.5, 0)

dask.array.
moment
(a, order, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None, out=None)¶

dask.array.
nanargmax
(x, axis, **kwargs)¶

dask.array.
nanargmin
(x, axis, **kwargs)¶

dask.array.
nancumprod
(a, axis=None, dtype=None, out=None)¶ Return the cumulative product of array elements over a given axis treating Not a Numbers (NaNs) as one. The cumulative product does not change when NaNs are encountered and leading NaNs are replaced by ones.
Ones are returned for slices that are allNaN or empty.
New in version 1.12.0.
Parameters:  a : array_like
Input array.
 axis : int, optional
Axis along which the cumulative product is computed. By default the input is flattened.
 dtype : dtype, optional
Type of the returned array, as well as of the accumulator in which the elements are multiplied. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used instead.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type of the resulting values will be cast if necessary.
Returns:  nancumprod : ndarray
A new array holding the result is returned unless out is specified, in which case it is returned.
See also
numpy.cumprod()
 Cumulative product across array propagating NaNs.
isnan
 Show which elements are NaN.
Examples
>>> np.nancumprod(1) array([1]) >>> np.nancumprod([1]) array([1]) >>> np.nancumprod([1, np.nan]) array([ 1., 1.]) >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nancumprod(a) array([ 1., 2., 6., 6.]) >>> np.nancumprod(a, axis=0) array([[ 1., 2.], [ 3., 2.]]) >>> np.nancumprod(a, axis=1) array([[ 1., 2.], [ 3., 3.]])

dask.array.
nancumsum
(a, axis=None, dtype=None, out=None)¶ Return the cumulative sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. The cumulative sum does not change when NaNs are encountered and leading NaNs are replaced by zeros.
Zeros are returned for slices that are allNaN or empty.
New in version 1.12.0.
Parameters:  a : array_like
Input array.
 axis : int, optional
Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array.
 dtype : dtype, optional
Type of the returned array and of the accumulator in which the elements are summed. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary. See doc.ufuncs (Section “Output arguments”) for more details.
Returns:  nancumsum : ndarray.
A new array holding the result is returned unless out is specified, in which it is returned. The result has the same size as a, and the same shape as a if axis is not None or a is a 1d array.
See also
numpy.cumsum()
 Cumulative sum across array propagating NaNs.
isnan
 Show which elements are NaN.
Examples
>>> np.nancumsum(1) array([1]) >>> np.nancumsum([1]) array([1]) >>> np.nancumsum([1, np.nan]) array([ 1., 1.]) >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nancumsum(a) array([ 1., 3., 6., 6.]) >>> np.nancumsum(a, axis=0) array([[ 1., 2.], [ 4., 2.]]) >>> np.nancumsum(a, axis=1) array([[ 1., 3.], [ 3., 3.]])

dask.array.
nanmax
(a, axis=None, out=None, keepdims=False)¶ Return the maximum of an array or maximum along an axis, ignoring any NaNs. When allNaN slices are encountered a
RuntimeWarning
is raised and NaN is returned for that slice.Parameters:  a : array_like
Array containing numbers whose maximum is desired. If a is not an array, a conversion is attempted.
 axis : int, optional
Axis along which the maximum is computed. The default is to compute the maximum of the flattened array.
 out : ndarray, optional
Alternate output array in which to place the result. The default is
None
; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See doc.ufuncs for details.New in version 1.8.0.
 keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original a.
New in version 1.8.0.
Returns:  nanmax : ndarray
An array with the same shape as a, with the specified axis removed. If a is a 0d array, or if axis is None, an ndarray scalar is returned. The same dtype as a is returned.
See also
nanmin
 The minimum value of an array along a given axis, ignoring any NaNs.
amax
 The maximum value of an array along a given axis, propagating any NaNs.
fmax
 Elementwise maximum of two arrays, ignoring any NaNs.
maximum
 Elementwise maximum of two arrays, propagating any NaNs.
isnan
 Shows which elements are Not a Number (NaN).
isfinite
 Shows which elements are neither NaN nor infinity.
Notes
Numpy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Positive infinity is treated as a very large number and negative infinity is treated as a very small (i.e. negative) number.
If the input has a integer type the function is equivalent to np.max.
Examples
>>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nanmax(a) 3.0 >>> np.nanmax(a, axis=0) array([ 3., 2.]) >>> np.nanmax(a, axis=1) array([ 2., 3.])
When positive infinity and negative infinity are present:
>>> np.nanmax([1, 2, np.nan, np.NINF]) 2.0 >>> np.nanmax([1, 2, np.nan, np.inf]) inf

dask.array.
nanmean
(a, axis=None, dtype=None, out=None, keepdims=False)¶ Compute the arithmetic mean along the specified axis, ignoring NaNs.
Returns the average of the array elements. The average is taken over the flattened array by default, otherwise over the specified axis. float64 intermediate and return values are used for integer inputs.
For allNaN slices, NaN is returned and a RuntimeWarning is raised.
New in version 1.8.0.
Parameters:  a : array_like
Array containing numbers whose mean is desired. If a is not an array, a conversion is attempted.
 axis : int, optional
Axis along which the means are computed. The default is to compute the mean of the flattened array.
 dtype : datatype, optional
Type to use in computing the mean. For integer inputs, the default is float64; for inexact inputs, it is the same as the input dtype.
 out : ndarray, optional
Alternate output array in which to place the result. The default is
None
; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See doc.ufuncs for details. keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  m : ndarray, see dtype parameter above
If out=None, returns a new array containing the mean values, otherwise a reference to the output array is returned. Nan is returned for slices that contain only NaNs.
Notes
The arithmetic mean is the sum of the nonNaN elements along the axis divided by the number of nonNaN elements.
Note that for floatingpoint input, the mean is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32. Specifying a higherprecision accumulator using the dtype keyword can alleviate this issue.
Examples
>>> a = np.array([[1, np.nan], [3, 4]]) >>> np.nanmean(a) 2.6666666666666665 >>> np.nanmean(a, axis=0) array([ 2., 4.]) >>> np.nanmean(a, axis=1) array([ 1., 3.5])

dask.array.
nanmin
(a, axis=None, out=None, keepdims=False)¶ Return minimum of an array or minimum along an axis, ignoring any NaNs. When allNaN slices are encountered a
RuntimeWarning
is raised and Nan is returned for that slice.Parameters:  a : array_like
Array containing numbers whose minimum is desired. If a is not an array, a conversion is attempted.
 axis : int, optional
Axis along which the minimum is computed. The default is to compute the minimum of the flattened array.
 out : ndarray, optional
Alternate output array in which to place the result. The default is
None
; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See doc.ufuncs for details.New in version 1.8.0.
 keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original a.
New in version 1.8.0.
Returns:  nanmin : ndarray
An array with the same shape as a, with the specified axis removed. If a is a 0d array, or if axis is None, an ndarray scalar is returned. The same dtype as a is returned.
See also
nanmax
 The maximum value of an array along a given axis, ignoring any NaNs.
amin
 The minimum value of an array along a given axis, propagating any NaNs.
fmin
 Elementwise minimum of two arrays, ignoring any NaNs.
minimum
 Elementwise minimum of two arrays, propagating any NaNs.
isnan
 Shows which elements are Not a Number (NaN).
isfinite
 Shows which elements are neither NaN nor infinity.
Notes
Numpy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Positive infinity is treated as a very large number and negative infinity is treated as a very small (i.e. negative) number.
If the input has a integer type the function is equivalent to np.min.
Examples
>>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nanmin(a) 1.0 >>> np.nanmin(a, axis=0) array([ 1., 2.]) >>> np.nanmin(a, axis=1) array([ 1., 3.])
When positive infinity and negative infinity are present:
>>> np.nanmin([1, 2, np.nan, np.inf]) 1.0 >>> np.nanmin([1, 2, np.nan, np.NINF]) inf

dask.array.
nanprod
(a, axis=None, dtype=None, out=None, keepdims=0)¶ Return the product of array elements over a given axis treating Not a Numbers (NaNs) as zero.
One is returned for slices that are allNaN or empty.
New in version 1.10.0.
Parameters:  a : array_like
Array containing numbers whose sum is desired. If a is not an array, a conversion is attempted.
 axis : int, optional
Axis along which the product is computed. The default is to compute the product of the flattened array.
 dtype : datatype, optional
The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of a is used. An exception is when a has an integer type with less precision than the platform (u)intp. In that case, the default will be either (u)int32 or (u)int64 depending on whether the platform is 32 or 64 bits. For inexact inputs, dtype must be inexact.
 out : ndarray, optional
Alternate output array in which to place the result. The default is
None
. If provided, it must have the same shape as the expected output, but the type will be cast if necessary. See doc.ufuncs for details. The casting of NaN to integer can yield unexpected results. keepdims : bool, optional
If True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  y : ndarray or numpy scalar
See also
numpy.prod
 Product across array propagating NaNs.
isnan
 Show which elements are NaN.
Notes
Numpy integer arithmetic is modular. If the size of a product exceeds the size of an integer accumulator, its value will wrap around and the result will be incorrect. Specifying
dtype=double
can alleviate that problem.Examples
>>> np.nanprod(1) 1 >>> np.nanprod([1]) 1 >>> np.nanprod([1, np.nan]) 1.0 >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nanprod(a) 6.0 >>> np.nanprod(a, axis=0) array([ 3., 2.])

dask.array.
nanstd
(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)¶ Compute the standard deviation along the specified axis, while ignoring NaNs.
Returns the standard deviation, a measure of the spread of a distribution, of the nonNaN array elements. The standard deviation is computed for the flattened array by default, otherwise over the specified axis.
For allNaN slices or slices with zero degrees of freedom, NaN is returned and a RuntimeWarning is raised.
New in version 1.8.0.
Parameters:  a : array_like
Calculate the standard deviation of the nonNaN values.
 axis : int, optional
Axis along which the standard deviation is computed. The default is to compute the standard deviation of the flattened array.
 dtype : dtype, optional
Type to use in computing the standard deviation. For arrays of integer type the default is float64, for arrays of float types it is the same as the array type.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape as the expected output but the type (of the calculated values) will be cast if necessary.
 ddof : int, optional
Means Delta Degrees of Freedom. The divisor used in calculations is
N  ddof
, whereN
represents the number of nonNaN elements. By default ddof is zero. keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  standard_deviation : ndarray, see dtype parameter above.
If out is None, return a new array containing the standard deviation, otherwise return a reference to the output array. If ddof is >= the number of nonNaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN.
Notes
The standard deviation is the square root of the average of the squared deviations from the mean:
std = sqrt(mean(abs(x  x.mean())**2))
.The average squared deviation is normally calculated as
x.sum() / N
, whereN = len(x)
. If, however, ddof is specified, the divisorN  ddof
is used instead. In standard statistical practice,ddof=1
provides an unbiased estimator of the variance of the infinite population.ddof=0
provides a maximum likelihood estimate of the variance for normally distributed variables. The standard deviation computed in this function is the square root of the estimated variance, so even withddof=1
, it will not be an unbiased estimate of the standard deviation per se.Note that, for complex numbers, std takes the absolute value before squaring, so that the result is always real and nonnegative.
For floatingpoint input, the std is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higheraccuracy accumulator using the dtype keyword can alleviate this issue.
Examples
>>> a = np.array([[1, np.nan], [3, 4]]) >>> np.nanstd(a) 1.247219128924647 >>> np.nanstd(a, axis=0) array([ 1., 0.]) >>> np.nanstd(a, axis=1) array([ 0., 0.5])

dask.array.
nansum
(a, axis=None, dtype=None, out=None, keepdims=0)¶ Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero.
In Numpy versions <= 1.8 Nan is returned for slices that are allNaN or empty. In later versions zero is returned.
Parameters:  a : array_like
Array containing numbers whose sum is desired. If a is not an array, a conversion is attempted.
 axis : int, optional
Axis along which the sum is computed. The default is to compute the sum of the flattened array.
 dtype : datatype, optional
The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of a is used. An exception is when a has an integer type with less precision than the platform (u)intp. In that case, the default will be either (u)int32 or (u)int64 depending on whether the platform is 32 or 64 bits. For inexact inputs, dtype must be inexact.
New in version 1.8.0.
 out : ndarray, optional
Alternate output array in which to place the result. The default is
None
. If provided, it must have the same shape as the expected output, but the type will be cast if necessary. See doc.ufuncs for details. The casting of NaN to integer can yield unexpected results.New in version 1.8.0.
 keepdims : bool, optional
If True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
New in version 1.8.0.
Returns:  y : ndarray or numpy scalar
See also
Notes
If both positive and negative infinity are present, the sum will be Not A Number (NaN).
Numpy integer arithmetic is modular. If the size of a sum exceeds the size of an integer accumulator, its value will wrap around and the result will be incorrect. Specifying
dtype=double
can alleviate that problem.Examples
>>> np.nansum(1) 1 >>> np.nansum([1]) 1 >>> np.nansum([1, np.nan]) 1.0 >>> a = np.array([[1, 1], [1, np.nan]]) >>> np.nansum(a) 3.0 >>> np.nansum(a, axis=0) array([ 2., 1.]) >>> np.nansum([1, np.nan, np.inf]) inf >>> np.nansum([1, np.nan, np.NINF]) inf >>> np.nansum([1, np.nan, np.inf, np.inf]) # both +/ infinity present nan

dask.array.
nanvar
(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)¶ Compute the variance along the specified axis, while ignoring NaNs.
Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis.
For allNaN slices or slices with zero degrees of freedom, NaN is returned and a RuntimeWarning is raised.
New in version 1.8.0.
Parameters:  a : array_like
Array containing numbers whose variance is desired. If a is not an array, a conversion is attempted.
 axis : int, optional
Axis along which the variance is computed. The default is to compute the variance of the flattened array.
 dtype : datatype, optional
Type to use in computing the variance. For arrays of integer type the default is float32; for arrays of float types it is the same as the array type.
 out : ndarray, optional
Alternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary.
 ddof : int, optional
“Delta Degrees of Freedom”: the divisor used in the calculation is
N  ddof
, whereN
represents the number of nonNaN elements. By default ddof is zero. keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  variance : ndarray, see dtype parameter above
If out is None, return a new array containing the variance, otherwise return a reference to the output array. If ddof is >= the number of nonNaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN.
See also
numpy.doc.ufuncs
 Section “Output arguments”
Notes
The variance is the average of the squared deviations from the mean, i.e.,
var = mean(abs(x  x.mean())**2)
.The mean is normally calculated as
x.sum() / N
, whereN = len(x)
. If, however, ddof is specified, the divisorN  ddof
is used instead. In standard statistical practice,ddof=1
provides an unbiased estimator of the variance of a hypothetical infinite population.ddof=0
provides a maximum likelihood estimate of the variance for normally distributed variables.Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative.
For floatingpoint input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higheraccuracy accumulator using the
dtype
keyword can alleviate this issue.Examples
>>> a = np.array([[1, np.nan], [3, 4]]) >>> np.var(a) 1.5555555555555554 >>> np.nanvar(a, axis=0) array([ 1., 0.]) >>> np.nanvar(a, axis=1) array([ 0., 0.25])

dask.array.
nan_to_num
(*args, **kwargs)¶ Replace nan with zero and inf with finite numbers.
Returns an array or scalar replacing Not a Number (NaN) with zero, (positive) infinity with a very large number and negative infinity with a very small (or negative) number.
Parameters:  x : array_like
Input data.
Returns:  out : ndarray
New Array with the same shape as x and dtype of the element in x with the greatest precision. If x is inexact, then NaN is replaced by zero, and infinity (infinity) is replaced by the largest (smallest or most negative) floating point value that fits in the output dtype. If x is not inexact, then a copy of x is returned.
See also
Notes
Numpy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity.
Examples
>>> np.set_printoptions(precision=8) >>> x = np.array([np.inf, np.inf, np.nan, 128, 128]) >>> np.nan_to_num(x) array([ 1.79769313e+308, 1.79769313e+308, 0.00000000e+000, 1.28000000e+002, 1.28000000e+002])

dask.array.
nextafter
(x1, x2[, out])¶ Return the next floatingpoint value after x1 towards x2, elementwise.
Parameters:  x1 : array_like
Values to find the next representable value of.
 x2 : array_like
The direction where to look for the next representable value of x1.
 out : ndarray, optional
Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs.
Returns:  out : array_like
The next representable values of x1 in the direction of x2.
Examples
>>> eps = np.finfo(np.float64).eps >>> np.nextafter(1, 2) == eps + 1 True >>> np.nextafter([1, 2], [2, 1]) == [eps + 1, 2  eps] array([ True, True], dtype=bool)

dask.array.
nonzero
(a)¶ Return the indices of the elements that are nonzero.
Returns a tuple of arrays, one for each dimension of a, containing the indices of the nonzero elements in that dimension. The values in a are always tested and returned in rowmajor, Cstyle order. The corresponding nonzero values can be obtained with:
a[nonzero(a)]
To group the indices by element, rather than dimension, use:
transpose(nonzero(a))
The result of this is always a 2D array, with a row for each nonzero element.
Parameters:  a : array_like
Input array.
Returns:  tuple_of_arrays : tuple
Indices of elements that are nonzero.
See also
flatnonzero
 Return indices that are nonzero in the flattened version of the input array.
ndarray.nonzero
 Equivalent ndarray method.
count_nonzero
 Counts the number of nonzero elements in the input array.
Examples
>>> x = np.eye(3) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> np.nonzero(x) (array([0, 1, 2]), array([0, 1, 2]))
>>> x[np.nonzero(x)] array([ 1., 1., 1.]) >>> np.transpose(np.nonzero(x)) array([[0, 0], [1, 1], [2, 2]])
A common use for
nonzero
is to find the indices of an array, where a condition is True. Given an array a, the condition a > 3 is a boolean array and since False is interpreted as 0, np.nonzero(a > 3) yields the indices of the a where the condition is true.>>> a = np.array([[1,2,3],[4,5,6],[7,8,9]]) >>> a > 3 array([[False, False, False], [ True, True, True], [ True, True, True]], dtype=bool) >>> np.nonzero(a > 3) (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
The
nonzero
method of the boolean array can also be called.>>> (a > 3).nonzero() (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))

dask.array.
notnull
(values)¶ pandas.notnull for dask arrays

dask.array.
ones
(*args, **kwargs)¶ Blocked variant of ones
Follows the signature of ones exactly except that it also requires a keyword argument chunks=(…)
Original signature follows below.
Return a new array of given shape and type, filled with ones.
Parameters:  shape : int or sequence of ints
Shape of the new array, e.g.,
(2, 3)
or2
. dtype : datatype, optional
The desired datatype for the array, e.g., numpy.int8. Default is numpy.float64.
 order : {‘C’, ‘F’}, optional
Whether to store multidimensional data in C or Fortrancontiguous (row or columnwise) order in memory.
Returns:  out : ndarray
Array of ones with the given shape, dtype, and order.
Examples
>>> np.ones(5) array([ 1., 1., 1., 1., 1.])
>>> np.ones((5,), dtype=np.int) array([1, 1, 1, 1, 1])
>>> np.ones((2, 1)) array([[ 1.], [ 1.]])
>>> s = (2,2) >>> np.ones(s) array([[ 1., 1.], [ 1., 1.]])

dask.array.
ones_like
(a, dtype=None, chunks=None)¶ Return an array of ones with the same shape and type as a given array.
Parameters:  a : array_like
The shape and datatype of a define these same attributes of the returned array.
 dtype : datatype, optional
Overrides the data type of the result.
 chunks : sequence of ints
The number of samples on each block. Note that the last block will have fewer samples if
len(array) % chunks != 0
.
Returns:  out : ndarray
Array of ones with the same shape and type as a.
See also
zeros_like
 Return an array of zeros with shape and type of input.
empty_like
 Return an empty array with shape and type of input.
zeros
 Return a new array setting values to zero.
ones
 Return a new array setting values to one.
empty
 Return a new uninitialized array.

dask.array.
outer
(a, b, out=None)¶ Compute the outer product of two vectors.
Given two vectors,
a = [a0, a1, ..., aM]
andb = [b0, b1, ..., bN]
, the outer product [1] is:[[a0*b0 a0*b1 ... a0*bN ] [a1*b0 . [ ... . [aM*b0 aM*bN ]]
Parameters:  a : (M,) array_like
First input vector. Input is flattened if not already 1dimensional.
 b : (N,) array_like
Second input vector. Input is flattened if not already 1dimensional.
 out : (M, N) ndarray, optional
A location where the result is stored
New in version 1.9.0.
Returns:  out : (M, N) ndarray
out[i, j] = a[i] * b[j]
See also
inner
,einsum
References
[1] (1, 2) : G. H. Golub and C. F. van Loan, Matrix Computations, 3rd ed., Baltimore, MD, Johns Hopkins University Press, 1996, pg. 8. Examples
Make a (very coarse) grid for computing a Mandelbrot set:
>>> rl = np.outer(np.ones((5,)), np.linspace(2, 2, 5)) >>> rl array([[2., 1., 0., 1., 2.], [2., 1., 0., 1., 2.], [2., 1., 0., 1., 2.], [2., 1., 0., 1., 2.], [2., 1., 0., 1., 2.]]) >>> im = np.outer(1j*np.linspace(2, 2, 5), np.ones((5,))) >>> im array([[ 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j], [ 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j], [ 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [ 0.1.j, 0.1.j, 0.1.j, 0.1.j, 0.1.j], [ 0.2.j, 0.2.j, 0.2.j, 0.2.j, 0.2.j]]) >>> grid = rl + im >>> grid array([[2.+2.j, 1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j], [2.+1.j, 1.+1.j, 0.+1.j, 1.+1.j, 2.+1.j], [2.+0.j, 1.+0.j, 0.+0.j, 1.+0.j, 2.+0.j], [2.1.j, 1.1.j, 0.1.j, 1.1.j, 2.1.j], [2.2.j, 1.2.j, 0.2.j, 1.2.j, 2.2.j]])
An example using a “vector” of letters:
>>> x = np.array(['a', 'b', 'c'], dtype=object) >>> np.outer(x, [1, 2, 3]) array([[a, aa, aaa], [b, bb, bbb], [c, cc, ccc]], dtype=object)

dask.array.
pad
(array, pad_width, mode, **kwargs)¶ Pads an array.
Parameters:  array : array_like of rank N
Input array
 pad_width : {sequence, array_like, int}
Number of values padded to the edges of each axis. ((before_1, after_1), … (before_N, after_N)) unique pad widths for each axis. ((before, after),) yields same before and after pad for each axis. (pad,) or int is a shortcut for before = after = pad width for all axes.
 mode : str or function
One of the following string values or a user supplied function.
 ‘constant’
Pads with a constant value.
 ‘edge’
Pads with the edge values of array.
 ‘linear_ramp’
Pads with the linear ramp between end_value and the array edge value.
 ‘maximum’
Pads with the maximum value of all or part of the vector along each axis.
 ‘mean’
Pads with the mean value of all or part of the vector along each axis.
 ‘median’
Pads with the median value of all or part of the vector along each axis.
 ‘minimum’
Pads with the minimum value of all or part of the vector along each axis.
 ‘reflect’
Pads with the reflection of the vector mirrored on the first and last values of the vector along each axis.
 ‘symmetric’
Pads with the reflection of the vector mirrored along the edge of the array.
 ‘wrap’
Pads with the wrap of the vector along the axis. The first values are used to pad the end and the end values are used to pad the beginning.
 <function>
Padding function, see Notes.
 stat_length : sequence or int, optional
Used in ‘maximum’, ‘mean’, ‘median’, and ‘minimum’. Number of values at edge of each axis used to calculate the statistic value.
((before_1, after_1), … (before_N, after_N)) unique statistic lengths for each axis.
((before, after),) yields same before and after statistic lengths for each axis.
(stat_length,) or int is a shortcut for before = after = statistic length for all axes.
Default is
None
, to use the entire axis. constant_values : sequence or int, optional
Used in ‘constant’. The values to set the padded values for each axis.
((before_1, after_1), … (before_N, after_N)) unique pad constants for each axis.
((before, after),) yields same before and after constants for each axis.
(constant,) or int is a shortcut for before = after = constant for all axes.
Default is 0.
 end_values : sequence or int, optional
Used in ‘linear_ramp’. The values used for the ending value of the linear_ramp and that will form the edge of the padded array.
((before_1, after_1), … (before_N, after_N)) unique end values for each axis.
((before, after),) yields same before and after end values for each axis.
(constant,) or int is a shortcut for before = after = end value for all axes.
Default is 0.
 reflect_type : {‘even’, ‘odd’}, optional
Used in ‘reflect’, and ‘symmetric’. The ‘even’ style is the default with an unaltered reflection around the edge value. For the ‘odd’ style, the extented part of the array is created by subtracting the reflected values from two times the edge value.
Returns:  pad : ndarray
Padded array of rank equal to array with shape increased according to pad_width.
Notes
New in version 1.7.0.
For an array with rank greater than 1, some of the padding of later axes is calculated from padding of previous axes. This is easiest to think about with a rank 2 array where the corners of the padded array are calculated by using padded values from the first axis.
The padding function, if used, should return a rank 1 array equal in length to the vector argument with padded values replaced. It has the following signature:
padding_func(vector, iaxis_pad_width, iaxis, **kwargs)
where
 vector : ndarray
 A rank 1 array already padded with zeros. Padded values are vector[:pad_tuple[0]] and vector[pad_tuple[1]:].
 iaxis_pad_width : tuple
 A 2tuple of ints, iaxis_pad_width[0] represents the number of values padded at the beginning of vector where iaxis_pad_width[1] represents the number of values padded at the end of vector.
 iaxis : int
 The axis currently being calculated.
 kwargs : misc
 Any keyword arguments the function requires.
Examples
>>> a = [1, 2, 3, 4, 5] >>> np.lib.pad(a, (2,3), 'constant', constant_values=(4, 6)) array([4, 4, 1, 2, 3, 4, 5, 6, 6, 6])
>>> np.lib.pad(a, (2, 3), 'edge') array([1, 1, 1, 2, 3, 4, 5, 5, 5, 5])
>>> np.lib.pad(a, (2, 3), 'linear_ramp', end_values=(5, 4)) array([ 5, 3, 1, 2, 3, 4, 5, 2, 1, 4])
>>> np.lib.pad(a, (2,), 'maximum') array([5, 5, 1, 2, 3, 4, 5, 5, 5])
>>> np.lib.pad(a, (2,), 'mean') array([3, 3, 1, 2, 3, 4, 5, 3, 3])
>>> np.lib.pad(a, (2,), 'median') array([3, 3, 1, 2, 3, 4, 5, 3, 3])
>>> a = [[1, 2], [3, 4]] >>> np.lib.pad(a, ((3, 2), (2, 3)), 'minimum') array([[1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [3, 3, 3, 4, 3, 3, 3], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1]])
>>> a = [1, 2, 3, 4, 5] >>> np.lib.pad(a, (2, 3), 'reflect') array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2])
>>> np.lib.pad(a, (2, 3), 'reflect', reflect_type='odd') array([1, 0, 1, 2, 3, 4, 5, 6, 7, 8])
>>> np.lib.pad(a, (2, 3), 'symmetric') array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3])
>>> np.lib.pad(a, (2, 3), 'symmetric', reflect_type='odd') array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7])
>>> np.lib.pad(a, (2, 3), 'wrap') array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3])
>>> def padwithtens(vector, pad_width, iaxis, kwargs): ... vector[:pad_width[0]] = 10 ... vector[pad_width[1]:] = 10 ... return vector
>>> a = np.arange(6) >>> a = a.reshape((2, 3))
>>> np.lib.pad(a, 2, padwithtens) array([[10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10], [10, 10, 0, 1, 2, 10, 10], [10, 10, 3, 4, 5, 10, 10], [10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10]])

dask.array.
percentile
(a, q, interpolation='linear')¶ Approximate percentile of 1D array
See
numpy.percentile()
for more information

dask.array.
piecewise
(x, condlist, funclist, *args, **kw)¶ Evaluate a piecewisedefined function.
Given a set of conditions and corresponding functions, evaluate each function on the input data wherever its condition is true.
Parameters:  x : ndarray
The input domain.
 condlist : list of bool arrays
Each boolean array corresponds to a function in funclist. Wherever condlist[i] is True, funclist[i](x) is used as the output value.
Each boolean array in condlist selects a piece of x, and should therefore be of the same shape as x.
The length of condlist must correspond to that of funclist. If one extra function is given, i.e. if
len(funclist)  len(condlist) == 1
, then that extra function is the default value, used wherever all conditions are false. funclist : list of callables, f(x,*args,**kw), or scalars
Each function is evaluated over x wherever its corresponding condition is True. It should take an array as input and give an array or a scalar value as output. If, instead of a callable, a scalar is provided then a constant function (
lambda x: scalar
) is assumed. args : tuple, optional
Any further arguments given to piecewise are passed to the functions upon execution, i.e., if called
piecewise(..., ..., 1, 'a')
, then each function is called asf(x, 1, 'a')
. kw : dict, optional
Keyword arguments used in calling piecewise are passed to the functions upon execution, i.e., if called
piecewise(..., ..., lambda=1)
, then each function is called asf(x, lambda=1)
.
Returns:  out : ndarray
The output is the same shape and type as x and is found by calling the functions in funclist on the appropriate portions of x, as defined by the boolean arrays in condlist. Portions not covered by any condition have a default value of 0.
Notes
This is similar to choose or select, except that functions are evaluated on elements of x that satisfy the corresponding condition from condlist.
The result is:
 funclist[0](x[condlist[0]]) out = funclist[1](x[condlist[1]]) ... funclist[n2](x[condlist[n2]]) 
Examples
Define the sigma function, which is 1 for
x < 0
and +1 forx >= 0
.>>> x = np.linspace(2.5, 2.5, 6) >>> np.piecewise(x, [x < 0, x >= 0], [1, 1]) array([1., 1., 1., 1., 1., 1.])
Define the absolute value, which is
x
forx <0
andx
forx >= 0
.>>> np.piecewise(x, [x < 0, x >= 0], [lambda x: x, lambda x: x]) array([ 2.5, 1.5, 0.5, 0.5, 1.5, 2.5])

dask.array.
prod
(a, axis=None, dtype=None, out=None, keepdims=False)¶ Return the product of array elements over a given axis.
Parameters:  a : array_like
Input data.
 axis : None or int or tuple of ints, optional
Axis or axes along which a product is performed. The default, axis=None, will calculate the product of all the elements in the input array. If axis is negative it counts from the last to the first axis.
New in version 1.7.0.
If axis is a tuple of ints, a product is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before.
 dtype : dtype, optional
The type of the returned array, as well as of the accumulator in which the elements are multiplied. The dtype of a is used by default unless a has an integer dtype of less precision than the default platform integer. In that case, if a is signed then the platform integer is used while if a is unsigned then an unsigned integer of the same precision as the platform integer is used.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary.
 keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.
Returns:  product_along_axis : ndarray, see dtype parameter above.
An array shaped as a but with the specified axis removed. Returns a reference to out if specified.
See also
ndarray.prod
 equivalent method
numpy.doc.ufuncs
 Section “Output arguments”
Notes
Arithmetic is modular when using integer types, and no error is raised on overflow. That means that, on a 32bit platform:
>>> x = np.array([536870910, 536870910, 536870910, 536870910]) >>> np.prod(x) #random 16
The product of an empty array is the neutral element 1:
>>> np.prod([]) 1.0
Examples
By default, calculate the product of all elements:
>>> np.prod([1.,2.]) 2.0
Even when the input array is twodimensional:
>>> np.prod([[1.,2.],[3.,4.]]) 24.0
But we can also specify the axis over which to multiply:
>>> np.prod([[1.,2.],[3.,4.]], axis=1) array([ 2., 12.])
If the type of x is unsigned, then the output type is the unsigned platform integer:
>>> x = np.array([1, 2, 3], dtype=np.uint8) >>> np.prod(x).dtype == np.uint True
If x is of a signed integer type, then the output type is the default platform integer:
>>> x = np.array([1, 2, 3], dtype=np.int8) >>> np.prod(x).dtype == np.int True

dask.array.
ptp
(a, axis=None, out=None)¶ Range of values (maximum  minimum) along an axis.
The name of the function comes from the acronym for ‘peak to peak’.
Parameters:  a : array_like
Input values.
 axis : int, optional
Axis along which to find the peaks. By default, flatten the array.
 out : array_like
Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type of the output values will be cast if necessary.
Returns:  ptp : ndarray
A new array holding the result, unless out was specified, in which case a reference to out is returned.
Examples
>>> x = np.arange(4).reshape((2,2)) >>> x array([[0, 1], [2, 3]])
>>> np.ptp(x, axis=0) array([2, 2])
>>> np.ptp(x, axis=1) array([1, 1])

dask.array.
rad2deg
(x[, out])¶ Convert angles from radians to degrees.
Parameters:  x : array_like
Angle in radians.
 out : ndarray, optional
Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs.
Returns:  y : ndarray
The corresponding angle in degrees.
See also
deg2rad
 Convert angles from degrees to radians.
unwrap
 Remove large jumps in angle by wrapping.
Notes
New in version 1.3.0.
rad2deg(x) is
180 * x / pi
.Examples
>>> np.rad2deg(np.pi/2) 90.0

dask.array.
radians
(x[, out])¶ Convert angles from degrees to radians.
Parameters:  x : array_like
Input array in degrees.
 out : ndarray, optional
Output array of same shape as x.
Returns:  y : ndarray
The corresponding radian values.
See also
deg2rad
 equivalent function
Examples
Convert a degree array to radians
>>> deg = np.arange(12.) * 30. >>> np.radians(deg) array([ 0. , 0.52359878, 1.04719755, 1.57079633, 2.0943951 , 2.61799388, 3.14159265, 3.66519143, 4.1887902 , 4.71238898, 5.23598776, 5.75958653])
>>> out = np.zeros((deg.shape)) >>> ret = np.radians(deg, out) >>> ret is out True

dask.array.
ravel
(a, order='C')¶ Return a contiguous flattened array.
A 1D array, containing the elements of the input, is returned. A copy is made only if needed.
As of NumPy 1.10, the returned array will have the same type as the input array. (for example, a masked array will be returned for a masked array input)
Parameters:  a : array_like
Input array. The elements in a are read in the order specified by order, and packed as a 1D array.
 order : {‘C’,’F’, ‘A’, ‘K’}, optional
The elements of a are read using this index order. ‘C’ means to index the elements in rowmajor, Cstyle order, with the last axis index changing fastest, back to the first axis index changing slowest. ‘F’ means to index the elements in columnmajor, Fortranstyle order, with the first index changing fastest, and the last index changing slowest. Note that the ‘C’ and ‘F’ options take no account of the memory layout of the underlying array, and only refer to the order of axis indexing. ‘A’ means to read the elements in Fortranlike index order if a is Fortran contiguous in memory, Clike order otherwise. ‘K’ means to read the elements in the order they occur in memory, except for reversing the data when strides are negative. By default, ‘C’ index order is used.
Returns:  y : array_like
If a is a matrix, y is a 1D ndarray, otherwise y is an array of the same subtype as a. The shape of the returned array is
(a.size,)
. Matrices are special cased for backward compatibility.
See also
ndarray.flat
 1D iterator over an array.
ndarray.flatten
 1D array copy of the elements of an array in rowmajor order.
ndarray.reshape
 Change the shape of an array without changing its data.
Notes
In rowmajor, Cstyle order, in two dimensions, the row index varies the slowest, and the column index the quickest. This can be generalized to multiple dimensions, where rowmajor order implies that the index along the first axis varies slowest, and the index along the last quickest. The opposite holds for columnmajor, Fortranstyle index ordering.
When a view is desired in as many cases as possible,
arr.reshape(1)
may be preferable.Examples
It is equivalent to
reshape(1, order=order)
.>>> x = np.array([[1, 2, 3], [4, 5, 6]]) >>> print(np.ravel(x)) [1 2 3 4 5 6]
>>> print(x.reshape(1)) [1 2 3 4 5 6]
>>> print(np.ravel(x, order='F')) [1 4 2 5 3 6]
When
order
is ‘A’, it will preserve the array’s ‘C’ or ‘F’ ordering:>>> print(np.ravel(x.T)) [1 4 2 5 3 6] >>> print(np.ravel(x.T, order='A')) [1 2 3 4 5 6]
When
order
is ‘K’, it will preserve orderings that are neither ‘C’ nor ‘F’, but won’t reverse axes:>>> a = np.arange(3)[::1]; a array([2, 1, 0]) >>> a.ravel(order='C') array([2, 1, 0]) >>> a.ravel(order='K') array([2, 1, 0])
>>> a = np.arange(12).reshape(2,3,2).swapaxes(1,2); a array([[[ 0, 2, 4], [ 1, 3, 5]], [[ 6, 8, 10], [ 7, 9, 11]]]) >>> a.ravel(order='C') array([ 0, 2, 4, 1, 3, 5, 6, 8, 10, 7, 9, 11]) >>> a.ravel(order='K') array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])

dask.array.
real
(*args, **kwargs)¶ Return the real part of the elements of the array.
Parameters:  val : array_like
Input array.
Returns:  out : ndarray
Output array. If val is real, the type of val is used for the output. If val has complex elements, the returned type is float.
Examples
>>> a = np.array([1+2j, 3+4j, 5+6j]) >>> a.real array([ 1., 3., 5.]) >>> a.real = 9 >>> a array([ 9.+2.j, 9.+4.j, 9.+6.j]) >>> a.real = np.array([9, 8, 7]) >>> a array([ 9.+2.j, 8.+4.j, 7.+6.j])

dask.array.
rechunk
(x, chunks, threshold=None, block_size_limit=None)¶ Convert blocks in dask array x for new chunks.
Parameters:  x: dask array
Array to be rechunked.
 chunks: int, tuple or dict
The new block dimensions to create. 1 indicates the full size of the corresponding dimension.
 threshold: int
The graph growth factor under which we don’t bother introducing an intermediate step.
 block_size_limit: int
The maximum block size (in bytes) we want to produce Defaults to the configuration value
array.chunksize
Examples
>>> import dask.array as da >>> x = da.ones((1000, 1000), chunks=(100, 100))
Specify uniform chunk sizes with a tuple
>>> y = x.rechunk((1000, 10))
Or chunk only specific dimensions with a dictionary
>>> y = x.rechunk({0: 1000})
Use the value
1
to specify that you want a single chunk along a dimension or the value"auto"
to specify that dask can freely rechunk a dimension to attain blocks of a uniform block size>>> y = x.rechunk({0: 1, 1: 'auto'}, block_size_limit=1e8)

dask.array.
repeat
(a, repeats, axis=None)¶ Repeat elements of an array.
Parameters:  a : array_like
Input array.
 repeats : int or array of ints
The number of repetitions for each element. repeats is broadcasted to fit the shape of the given axis.
 axis : int, optional
The axis along which to repeat values. By default, use the flattened input array, and return a flat output array.
Returns:  repeated_array : ndarray
Output array which has the same shape as a, except along the given axis.
See also
tile
 Tile an array.
Examples
>>> x = np.array([[1,2],[3,4]]) >>> np.repeat(x, 2) array([1, 1, 2, 2, 3, 3, 4, 4]) >>> np.repeat(x, 3, axis=1) array([[1, 1, 1, 2, 2, 2], [3, 3, 3, 4, 4, 4]]) >>> np.repeat(x, [1, 2], axis=0) array([[1, 2], [3, 4], [3, 4]])

dask.array.
reshape
(x, shape)¶ Reshape array to new shape
This is a parallelized version of the
np.reshape
function with the following limitations: It assumes that the array is stored in Corder
 It only allows for reshapings that collapse or merge dimensions like
(1, 2, 3, 4) > (1, 6, 4)
or(64,) > (4, 4, 4)
When communication is necessary this algorithm depends on the logic within rechunk. It endeavors to keep chunk sizes roughly the same when possible.
See also

dask.array.
result_type
(*arrays_and_dtypes)¶ Returns the type that results from applying the NumPy type promotion rules to the arguments.
Type promotion in NumPy works similarly to the rules in languages like C++, with some slight differences. When both scalars and arrays are used, the array’s type takes precedence and the actual value of the scalar is taken into account.
For example, calculating 3*a, where a is an array of 32bit floats, intuitively should result in a 32bit float output. If the 3 is a 32bit integer, the NumPy rules indicate it can’t convert losslessly into a 32bit float, so a 64bit float should be the result type. By examining the value of the constant, ‘3’, we see that it fits in an 8bit integer, which can be cast losslessly into the 32bit float.
Parameters:  arrays_and_dtypes : list of arrays and dtypes
The operands of some operation whose result type is needed.
Returns:  out : dtype
The result type.
See also
dtype
,promote_types
,min_scalar_type
,can_cast
Notes
New in version 1.6.0.
The specific algorithm used is as follows.
Categories are determined by first checking which of boolean, integer (int/uint), or floating point (float/complex) the maximum kind of all the arrays and the scalars are.
If there are only scalars or the maximum category of the scalars is higher than the maximum category of the arrays, the data types are combined with
promote_types()
to produce the return value.Otherwise, min_scalar_type is called on each array, and the resulting data types are all combined with
promote_types()
to produce the return value.The set of int values is not a subset of the uint values for types with the same number of bits, something not reflected in
min_scalar_type()
, but handled as a special case in result_type.Examples
>>> np.result_type(3, np.arange(7, dtype='i1')) dtype('int8')
>>> np.result_type('i4', 'c8') dtype('complex128')
>>> np.result_type(3.0, 2) dtype('float64')

dask.array.
rint
(x[, out])¶ Round elements of the array to the nearest integer.
Parameters:  x : array_like
Input array.
Returns:  out : ndarray or scalar
Output array is same shape and type as x.
Examples
>>> a = np.array([1.7, 1.5, 0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.rint(a) array([2., 2., 0., 0., 2., 2., 2.])

dask.array.
roll
(a, shift, axis=None)¶ Roll array elements along a given axis.
Elements that roll beyond the last position are reintroduced at the first.
Parameters:  a : array_like
Input array.
 shift : int
The number of places by which elements are shifted.
 axis : int, optional
The axis along which elements are shifted. By default, the array is flattened before shifting, after which the original shape is restored.
Returns:  res : ndarray
Output array, with the same shape as a.
See also
rollaxis
 Roll the specified axis backwards, until it lies in a given position.
Examples
>>> x = np.arange(10) >>> np.roll(x, 2) array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7])
>>> x2 = np.reshape(x, (2,5)) >>> x2 array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]) >>> np.roll(x2, 1) array([[9, 0, 1, 2, 3], [4, 5, 6, 7, 8]]) >>> np.roll(x2, 1, axis=0) array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]) >>> np.roll(x2, 1, axis=1) array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]])

dask.array.
round
(a, decimals=0, out=None)¶ Round an array to the given number of decimals.
Refer to around for full documentation.
See also
around
 equivalent function

dask.array.
sign
(x[, out])¶ Returns an elementwise indication of the sign of a number.
The sign function returns
1 if x < 0, 0 if x==0, 1 if x > 0
. nan is returned for nan inputs.For complex inputs, the sign function returns
sign(x.real) + 0j if x.real != 0 else sign(x.imag) + 0j
.complex(nan, 0) is returned for complex nan inputs.
Parameters:  x : array_like
Input values.
Returns:  y : ndarray
The sign of x.
Notes
There is more than one definition of sign in common use for complex numbers. The definition used here is equivalent to \(x/\sqrt{x*x}\) which is different from a common alternative, \(x/x\).
Examples
>>> np.sign([5., 4.5]) array([1., 1.]) >>> np.sign(0) 0 >>> np.sign(52j) (1+0j)

dask.array.
signbit
(x[, out])¶ Returns elementwise True where signbit is set (less than zero).
Parameters:  x : array_like
The input value(s).
 out : ndarray, optional
Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs.
Returns:  result : ndarray of bool
Output array, or reference to out if that was supplied.
Examples
>>> np.signbit(1.2) True >>> np.signbit(np.array([1, 2.3, 2.1])) array([False, True, False], dtype=bool)

dask.array.
sin
(x[, out])¶ Trigonometric sine, elementwise.
Parameters:  x : array_like
Angle, in radians (\(2 \pi\) rad equals 360 degrees).
Returns:  y : array_like
The sine of each element of x.
Notes
The sine is one of the fundamental functions of trigonometry (the mathematical study of triangles). Consider a circle of radius 1 centered on the origin. A ray comes in from the \(+x\) axis, makes an angle at the origin (measured counterclockwise from that axis), and departs from the origin. The \(y\) coordinate of the outgoing ray’s intersection with the unit circle is the sine of that angle. It ranges from 1 for \(x=3\pi / 2\) to +1 for \(\pi / 2.\) The function has zeroes where the angle is a multiple of \(\pi\). Sines of angles between \(\pi\) and \(2\pi\) are negative. The numerous properties of the sine and related functions are included in any standard trigonometry text.
Examples
Print sine of one angle:
>>> np.sin(np.pi/2.) 1.0
Print sines of an array of angles given in degrees:
>>> np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180. ) array([ 0. , 0.5 , 0.70710678, 0.8660254 , 1. ])
Plot the sine function:
>>> import matplotlib.pylab as plt >>> x = np.linspace(np.pi, np.pi, 201) >>> plt.plot(x, np.sin(x)) >>> plt.xlabel('Angle [rad]') >>> plt.ylabel('sin(x)') >>> plt.axis('tight') >>> plt.show()

dask.array.
sinh
(x[, out])¶ Hyperbolic sine, elementwise.
Equivalent to
1/2 * (np.exp(x)  np.exp(x))
or1j * np.sin(1j*x)
.Parameters:  x : array_like
Input array.
 out : ndarray, optional
Output array of same shape as x.
Returns:  y : ndarray
The corresponding hyperbolic sine values.
Raises:  ValueError: invalid return array shape
if out is provided and out.shape != x.shape (See Examples)
Notes
If out is provided, the function writes the result into it, and returns a reference to out. (See Examples)
References
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972, pg. 83.
Examples
>>> np.sinh(0) 0.0 >>> np.sinh(np.pi*1j/2) 1j >>> np.sinh(np.pi*1j) # (exact value is 0) 1.2246063538223773e016j >>> # Discrepancy due to vagaries of floating point arithmetic.
>>> # Example of providing the optional output parameter >>> out2 = np.sinh([0.1], out1) >>> out2 is out1 True
>>> # Example of ValueError due to provision of shape mismatched `out` >>> np.sinh(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: invalid return array shape

dask.array.
sqrt
(x[, out])¶ Return the positive squareroot of an array, elementwise.
Parameters:  x : array_like
The values whose squareroots are required.
 out : ndarray, optional
Alternate array object in which to put the result; if provided, it must have the same shape as x
Returns:  y : ndarray
An array of the same shape as x, containing the positive squareroot of each element in x. If any element in x is complex, a complex array is returned (and the squareroots of negative reals are calculated). If all of the elements in x are real, so is y, with negative elements returning
nan
. If out was provided, y is a reference to it.
See also
lib.scimath.sqrt
 A version which returns complex numbers when given negative reals.
Notes
sqrt has–consistent with common convention–as its branch cut the real “interval” [inf, 0), and is continuous from above on it. A branch cut is a curve in the complex plane across which a given complex function fails to be continuous.
Examples
>>> np.sqrt([1,4,9]) array([ 1., 2., 3.])
>>> np.sqrt([4, 1, 3+4J]) array([ 2.+0.j, 0.+1.j, 1.+2.j])
>>> np.sqrt([4, 1, numpy.inf]) array([ 2., NaN, Inf])

dask.array.
square
(x[, out])¶ Return the elementwise square of the input.
Parameters:  x : array_like
Input data.
Returns:  out : ndarray
Elementwise x*x, of the same shape and dtype as x. Returns scalar if x is a scalar.
See also
numpy.linalg.matrix_power
,sqrt
,power
Examples
>>> np.square([1j, 1]) array([1.0.j, 1.+0.j])

dask.array.
squeeze
(a, axis=None)¶ Remove singledimensional entries from the shape of an array.
Parameters:  a : array_like
Input data.
 axis : None or int or tuple of ints, optional
New in version 1.7.0.
Selects a subset of the singledimensional entries in the shape. If an axis is selected with shape entry greater than one, an error is raised.
Returns:  squeezed : ndarray
The input array, but with all or a subset of the dimensions of length 1 removed. This is always a itself or a view into a.
Examples
>>> x = np.array([[[0], [1], [2]]]) >>> x.shape (1, 3, 1) >>> np.squeeze(x).shape (3,) >>> np.squeeze(x, axis=(2,)).shape (1, 3)

dask.array.
stack
(seq, axis=0) Stack arrays along a new axis
Given a sequence of dask Arrays form a new dask Array by stacking them along a new dimension (axis=0 by default)
See also
Examples
Create slices
>>> import dask.array as da >>> import numpy as np
>>> data = [from_array(np.ones((4, 4)), chunks=(2, 2)) ... for i in range(3)]
>>> x = da.stack(data, axis=0) >>> x.shape (3, 4, 4)
>>> da.stack(data, axis=1).shape (4, 3, 4)
>>> da.stack(data, axis=1).shape (4, 4, 3)
Result is a new dask Array

dask.array.
std
(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)¶ Compute the standard deviation along the specified axis.
Returns the standard deviation, a measure of the spread of a distribution, of the array elements. The standard deviation is computed for the flattened array by default, otherwise over the specified axis.
Parameters:  a : array_like
Calculate the standard deviation of these values.
 axis : None or int or tuple of ints, optional
Axis or axes along which the standard deviation is computed. The default is to compute the standard deviation of the flattened array.
If this is a tuple of ints, a standard deviation is performed over multiple axes, instead of a single axis or all the axes as before.
 dtype : dtype, optional
Type to use in computing the standard deviation. For arrays of integer type the default is float64, for arrays of float types it is the same as the array type.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape as the expected output but the type (of the calculated values) will be cast if necessary.
 ddof : int, optional
Means Delta Degrees of Freedom. The divisor used in calculations is
N  ddof
, whereN
represents the number of elements. By default ddof is zero. keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  standard_deviation : ndarray, see dtype parameter above.
If out is None, return a new array containing the standard deviation, otherwise return a reference to the output array.
Notes
The standard deviation is the square root of the average of the squared deviations from the mean, i.e.,
std = sqrt(mean(abs(x  x.mean())**2))
.The average squared deviation is normally calculated as
x.sum() / N
, whereN = len(x)
. If, however, ddof is specified, the divisorN  ddof
is used instead. In standard statistical practice,ddof=1
provides an unbiased estimator of the variance of the infinite population.ddof=0
provides a maximum likelihood estimate of the variance for normally distributed variables. The standard deviation computed in this function is the square root of the estimated variance, so even withddof=1
, it will not be an unbiased estimate of the standard deviation per se.Note that, for complex numbers, std takes the absolute value before squaring, so that the result is always real and nonnegative.
For floatingpoint input, the std is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higheraccuracy accumulator using the dtype keyword can alleviate this issue.
Examples
>>> a = np.array([[1, 2], [3, 4]]) >>> np.std(a) 1.1180339887498949 >>> np.std(a, axis=0) array([ 1., 1.]) >>> np.std(a, axis=1) array([ 0.5, 0.5])
In single precision, std() can be inaccurate:
>>> a = np.zeros((2, 512*512), dtype=np.float32) >>> a[0, :] = 1.0 >>> a[1, :] = 0.1 >>> np.std(a) 0.45000005
Computing the standard deviation in float64 is more accurate:
>>> np.std(a, dtype=np.float64) 0.44999999925494177

dask.array.
sum
(a, axis=None, dtype=None, out=None, keepdims=False)¶ Sum of array elements over a given axis.
Parameters:  a : array_like
Elements to sum.
 axis : None or int or tuple of ints, optional
Axis or axes along which a sum is performed. The default, axis=None, will sum all of the elements of the input array. If axis is negative it counts from the last to the first axis.
New in version 1.7.0.
If axis is a tuple of ints, a sum is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before.
 dtype : dtype, optional
The type of the returned array and of the accumulator in which the elements are summed. The dtype of a is used by default unless a has an integer dtype of less precision than the default platform integer. In that case, if a is signed then the platform integer is used while if a is unsigned then an unsigned integer of the same precision as the platform integer is used.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary.
 keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.
Returns:  sum_along_axis : ndarray
An array with the same shape as a, with the specified axis removed. If a is a 0d array, or if axis is None, a scalar is returned. If an output array is specified, a reference to out is returned.
See also
ndarray.sum
 Equivalent method.
cumsum
 Cumulative sum of array elements.
trapz
 Integration of array values using the composite trapezoidal rule.
Notes
Arithmetic is modular when using integer types, and no error is raised on overflow.
The sum of an empty array is the neutral element 0:
>>> np.sum([]) 0.0
Examples
>>> np.sum([0.5, 1.5]) 2.0 >>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32) 1 >>> np.sum([[0, 1], [0, 5]]) 6 >>> np.sum([[0, 1], [0, 5]], axis=0) array([0, 6]) >>> np.sum([[0, 1], [0, 5]], axis=1) array([1, 5])
If the accumulator is too small, overflow occurs:
>>> np.ones(128, dtype=np.int8).sum(dtype=np.int8) 128

dask.array.
take
(a, indices, axis=None, out=None, mode='raise')¶ Take elements from an array along an axis.
This function does the same thing as “fancy” indexing (indexing arrays using arrays); however, it can be easier to use if you need elements along a given axis.
Parameters:  a : array_like
The source array.
 indices : array_like
The indices of the values to extract.
New in version 1.8.0.
Also allow scalars for indices.
 axis : int, optional
The axis over which to select values. By default, the flattened input array is used.
 out : ndarray, optional
If provided, the result will be placed in this array. It should be of the appropriate shape and dtype.
 mode : {‘raise’, ‘wrap’, ‘clip’}, optional
Specifies how outofbounds indices will behave.
 ‘raise’ – raise an error (default)
 ‘wrap’ – wrap around
 ‘clip’ – clip to the range
‘clip’ mode means that all indices that are too large are replaced by the index that addresses the last element along that axis. Note that this disables indexing with negative numbers.
Returns:  subarray : ndarray
The returned array has the same type as a.
See also
compress
 Take elements using a boolean mask
ndarray.take
 equivalent method
Examples
>>> a = [4, 3, 5, 7, 6, 8] >>> indices = [0, 1, 4] >>> np.take(a, indices) array([4, 3, 6])
In this example if a is an ndarray, “fancy” indexing can be used.
>>> a = np.array(a) >>> a[indices] array([4, 3, 6])
If indices is not one dimensional, the output also has these dimensions.
>>> np.take(a, [[0, 1], [2, 3]]) array([[4, 3], [5, 7]])

dask.array.
tan
(x[, out])¶ Compute tangent elementwise.
Equivalent to
np.sin(x)/np.cos(x)
elementwise.Parameters:  x : array_like
Input array.
 out : ndarray, optional
Output array of same shape as x.
Returns:  y : ndarray
The corresponding tangent values.
Raises:  ValueError: invalid return array shape
if out is provided and out.shape != x.shape (See Examples)
Notes
If out is provided, the function writes the result into it, and returns a reference to out. (See Examples)
References
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972.
Examples
>>> from math import pi >>> np.tan(np.array([pi,pi/2,pi])) array([ 1.22460635e16, 1.63317787e+16, 1.22460635e16]) >>> >>> # Example of providing the optional output parameter illustrating >>> # that what is returned is a reference to said parameter >>> out2 = np.cos([0.1], out1) >>> out2 is out1 True >>> >>> # Example of ValueError due to provision of shape mismatched `out` >>> np.cos(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: invalid return array shape

dask.array.
tanh
(x[, out])¶ Compute hyperbolic tangent elementwise.
Equivalent to
np.sinh(x)/np.cosh(x)
or1j * np.tan(1j*x)
.Parameters:  x : array_like
Input array.
 out : ndarray, optional
Output array of same shape as x.
Returns:  y : ndarray
The corresponding hyperbolic tangent values.
Raises:  ValueError: invalid return array shape
if out is provided and out.shape != x.shape (See Examples)
Notes
If out is provided, the function writes the result into it, and returns a reference to out. (See Examples)
References
[1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972, pg. 83. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Hyperbolic function”, http://en.wikipedia.org/wiki/Hyperbolic_function Examples
>>> np.tanh((0, np.pi*1j, np.pi*1j/2)) array([ 0. +0.00000000e+00j, 0. 1.22460635e16j, 0. +1.63317787e+16j])
>>> # Example of providing the optional output parameter illustrating >>> # that what is returned is a reference to said parameter >>> out2 = np.tanh([0.1], out1) >>> out2 is out1 True
>>> # Example of ValueError due to provision of shape mismatched `out` >>> np.tanh(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: invalid return array shape

dask.array.
tensordot
(a, b, axes=2)¶ Compute tensor dot product along specified axes for arrays >= 1D.
Given two tensors (arrays of dimension greater than or equal to one), a and b, and an array_like object containing two array_like objects,
(a_axes, b_axes)
, sum the products of a’s and b’s elements (components) over the axes specified bya_axes
andb_axes
. The third argument can be a single nonnegative integer_like scalar,N
; if it is such, then the lastN
dimensions of a and the firstN
dimensions of b are summed over.Parameters:  a, b : array_like, len(shape) >= 1
Tensors to “dot”.
 axes : int or (2,) array_like
 integer_like If an int N, sum over the last N axes of a and the first N axes of b in order. The sizes of the corresponding axes must match.
 (2,) array_like Or, a list of axes to be summed over, first sequence applying to a, second to b. Both elements array_like must be of the same length.
Notes
 Three common use cases are:
axes = 0
: tensor product $aotimes b$axes = 1
: tensor dot product $acdot b$axes = 2
: (default) tensor double contraction $a:b$
When axes is integer_like, the sequence for evaluation will be: first the Nth axis in a and 0th axis in b, and the 1th axis in a and Nth axis in b last.
When there is more than one axis to sum over  and they are not the last (first) axes of a (b)  the argument axes should consist of two sequences of the same length, with the first axis to sum over given first in both sequences, the second axis second, and so forth.
Examples
A “traditional” example:
>>> a = np.arange(60.).reshape(3,4,5) >>> b = np.arange(24.).reshape(4,3,2) >>> c = np.tensordot(a,b, axes=([1,0],[0,1])) >>> c.shape (5, 2) >>> c array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> # A slower but equivalent way of computing the same... >>> d = np.zeros((5,2)) >>> for i in range(5): ... for j in range(2): ... for k in range(3): ... for n in range(4): ... d[i,j] += a[k,n,i] * b[n,k,j] >>> c == d array([[ True, True], [ True, True], [ True, True], [ True, True], [ True, True]], dtype=bool)
An extended example taking advantage of the overloading of + and *:
>>> a = np.array(range(1, 9)) >>> a.shape = (2, 2, 2) >>> A = np.array(('a', 'b', 'c', 'd'), dtype=object) >>> A.shape = (2, 2) >>> a; A array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]) array([[a, b], [c, d]], dtype=object)
>>> np.tensordot(a, A) # third argument default is 2 for doublecontraction array([abbcccdddd, aaaaabbbbbbcccccccdddddddd], dtype=object)
>>> np.tensordot(a, A, 1) array([[[acc, bdd], [aaacccc, bbbdddd]], [[aaaaacccccc, bbbbbdddddd], [aaaaaaacccccccc, bbbbbbbdddddddd]]], dtype=object)
>>> np.tensordot(a, A, 0) # tensor product (result too long to incl.) array([[[[[a, b], [c, d]], ...
>>> np.tensordot(a, A, (0, 1)) array([[[abbbbb, cddddd], [aabbbbbb, ccdddddd]], [[aaabbbbbbb, cccddddddd], [aaaabbbbbbbb, ccccdddddddd]]], dtype=object)
>>> np.tensordot(a, A, (2, 1)) array([[[abb, cdd], [aaabbbb, cccdddd]], [[aaaaabbbbbb, cccccdddddd], [aaaaaaabbbbbbbb, cccccccdddddddd]]], dtype=object)
>>> np.tensordot(a, A, ((0, 1), (0, 1))) array([abbbcccccddddddd, aabbbbccccccdddddddd], dtype=object)
>>> np.tensordot(a, A, ((2, 1), (1, 0))) array([acccbbdddd, aaaaacccccccbbbbbbdddddddd], dtype=object)

dask.array.
tile
(A, reps)¶ Construct an array by repeating A the number of times given by reps.
If reps has length
d
, the result will have dimension ofmax(d, A.ndim)
.If
A.ndim < d
, A is promoted to be ddimensional by prepending new axes. So a shape (3,) array is promoted to (1, 3) for 2D replication, or shape (1, 1, 3) for 3D replication. If this is not the desired behavior, promote A to ddimensions manually before calling this function.If
A.ndim > d
, reps is promoted to A.ndim by prepending 1’s to it. Thus for an A of shape (2, 3, 4, 5), a reps of (2, 2) is treated as (1, 1, 2, 2).Note : Although tile may be used for broadcasting, it is strongly recommended to use numpy’s broadcasting operations and functions.
Parameters:  A : array_like
The input array.
 reps : array_like
The number of repetitions of A along each axis.
Returns:  c : ndarray
The tiled output array.
See also
repeat
 Repeat elements of an array.
broadcast_to
 Broadcast an array to a new shape
Examples
>>> a = np.array([0, 1, 2]) >>> np.tile(a, 2) array([0, 1, 2, 0, 1, 2]) >>> np.tile(a, (2, 2)) array([[0, 1, 2, 0, 1, 2], [0, 1, 2, 0, 1, 2]]) >>> np.tile(a, (2, 1, 2)) array([[[0, 1, 2, 0, 1, 2]], [[0, 1, 2, 0, 1, 2]]])
>>> b = np.array([[1, 2], [3, 4]]) >>> np.tile(b, 2) array([[1, 2, 1, 2], [3, 4, 3, 4]]) >>> np.tile(b, (2, 1)) array([[1, 2], [3, 4], [1, 2], [3, 4]])
>>> c = np.array([1,2,3,4]) >>> np.tile(c,(4,1)) array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]])

dask.array.
topk
(a, k, axis=1, split_every=None)¶ Extract the k largest elements from a on the given axis, and return them sorted from largest to smallest. If k is negative, extract the k smallest elements instead, and return them sorted from smallest to largest.
This assumes that
k
is small. All results will be returned in a single chunk along the given axis.Examples
>>> import dask.array as da >>> x = np.array([5, 1, 3, 6]) >>> d = da.from_array(x, chunks=2) >>> d.topk(2).compute() array([6, 5]) >>> d.topk(2).compute() array([1, 3])

dask.array.
transpose
(a, axes=None)¶ Permute the dimensions of an array.
Parameters:  a : array_like
Input array.
 axes : list of ints, optional
By default, reverse the dimensions, otherwise permute the axes according to the values given.
Returns:  p : ndarray
a with its axes permuted. A view is returned whenever possible.
See also
moveaxis
,argsort
Notes
Use transpose(a, argsort(axes)) to invert the transposition of tensors when using the axes keyword argument.
Transposing a 1D array returns an unchanged view of the original array.
Examples
>>> x = np.arange(4).reshape((2,2)) >>> x array([[0, 1], [2, 3]])
>>> np.transpose(x) array([[0, 2], [1, 3]])
>>> x = np.ones((1, 2, 3)) >>> np.transpose(x, (1, 0, 2)).shape (2, 1, 3)

dask.array.
tril
(m, k=0)¶ Lower triangle of an array with elements above the kth diagonal zeroed.
Parameters:  m : array_like, shape (M, M)
Input array.
 k : int, optional
Diagonal above which to zero elements. k = 0 (the default) is the main diagonal, k < 0 is below it and k > 0 is above.
Returns:  tril : ndarray, shape (M, M)
Lower triangle of m, of same shape and datatype as m.
See also
triu
 upper triangle of an array

dask.array.
triu
(m, k=0)¶ Upper triangle of an array with elements above the kth diagonal zeroed.
Parameters:  m : array_like, shape (M, N)
Input array.
 k : int, optional
Diagonal above which to zero elements. k = 0 (the default) is the main diagonal, k < 0 is below it and k > 0 is above.
Returns:  triu : ndarray, shape (M, N)
Upper triangle of m, of same shape and datatype as m.
See also
tril
 lower triangle of an array

dask.array.
trunc
(x[, out])¶ Return the truncated value of the input, elementwise.
The truncated value of the scalar x is the nearest integer i which is closer to zero than x is. In short, the fractional part of the signed number x is discarded.
Parameters:  x : array_like
Input data.
Returns:  y : ndarray or scalar
The truncated value of each element in x.
Notes
New in version 1.3.0.
Examples
>>> a = np.array([1.7, 1.5, 0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.trunc(a) array([1., 1., 0., 0., 1., 1., 2.])

dask.array.
unique
(ar, return_index=False, return_inverse=False, return_counts=False)¶ Find the unique elements of an array.
Returns the sorted unique elements of an array. There are three optional outputs in addition to the unique elements: the indices of the input array that give the unique values, the indices of the unique array that reconstruct the input array, and the number of times each unique value comes up in the input array.
Parameters:  ar : array_like
Input array. This will be flattened if it is not already 1D.
 return_index : bool, optional
If True, also return the indices of ar that result in the unique array.
 return_inverse : bool, optional
If True, also return the indices of the unique array that can be used to reconstruct ar.
 return_counts : bool, optional
If True, also return the number of times each unique value comes up in ar.
New in version 1.9.0.
Returns:  unique : ndarray
The sorted unique values.
 unique_indices : ndarray, optional
The indices of the first occurrences of the unique values in the (flattened) original array. Only provided if return_index is True.
 unique_inverse : ndarray, optional
The indices to reconstruct the (flattened) original array from the unique array. Only provided if return_inverse is True.
 unique_counts : ndarray, optional
The number of times each of the unique values comes up in the original array. Only provided if return_counts is True.
New in version 1.9.0.
See also
numpy.lib.arraysetops
 Module with a number of other functions for performing set operations on arrays.
Examples
>>> np.unique([1, 1, 2, 2, 3, 3]) array([1, 2, 3]) >>> a = np.array([[1, 1], [2, 3]]) >>> np.unique(a) array([1, 2, 3])
Return the indices of the original array that give the unique values:
>>> a = np.array(['a', 'b', 'b', 'c', 'a']) >>> u, indices = np.unique(a, return_index=True) >>> u array(['a', 'b', 'c'], dtype='S1') >>> indices array([0, 1, 3]) >>> a[indices] array(['a', 'b', 'c'], dtype='S1')
Reconstruct the input array from the unique values:
>>> a = np.array([1, 2, 6, 4, 2, 3, 2]) >>> u, indices = np.unique(a, return_inverse=True) >>> u array([1, 2, 3, 4, 6]) >>> indices array([0, 1, 4, 3, 1, 2, 1]) >>> u[indices] array([1, 2, 6, 4, 2, 3, 2])

dask.array.
var
(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)¶ Compute the variance along the specified axis.
Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis.
Parameters:  a : array_like
Array containing numbers whose variance is desired. If a is not an array, a conversion is attempted.
 axis : None or int or tuple of ints, optional
Axis or axes along which the variance is computed. The default is to compute the variance of the flattened array.
If this is a tuple of ints, a variance is performed over multiple axes, instead of a single axis or all the axes as before.
 dtype : datatype, optional
Type to use in computing the variance. For arrays of integer type the default is float32; for arrays of float types it is the same as the array type.
 out : ndarray, optional
Alternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary.
 ddof : int, optional
“Delta Degrees of Freedom”: the divisor used in the calculation is
N  ddof
, whereN
represents the number of elements. By default ddof is zero. keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.
Returns:  variance : ndarray, see dtype parameter above
If
out=None
, returns a new array containing the variance; otherwise, a reference to the output array is returned.
Notes
The variance is the average of the squared deviations from the mean, i.e.,
var = mean(abs(x  x.mean())**2)
.The mean is normally calculated as
x.sum() / N
, whereN = len(x)
. If, however, ddof is specified, the divisorN  ddof
is used instead. In standard statistical practice,ddof=1
provides an unbiased estimator of the variance of a hypothetical infinite population.ddof=0
provides a maximum likelihood estimate of the variance for normally distributed variables.Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative.
For floatingpoint input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higheraccuracy accumulator using the
dtype
keyword can alleviate this issue.Examples
>>> a = np.array([[1, 2], [3, 4]]) >>> np.var(a) 1.25 >>> np.var(a, axis=0) array([ 1., 1.]) >>> np.var(a, axis=1) array([ 0.25, 0.25])
In single precision, var() can be inaccurate:
>>> a = np.zeros((2, 512*512), dtype=np.float32) >>> a[0, :] = 1.0 >>> a[1, :] = 0.1 >>> np.var(a) 0.20250003
Computing the variance in float64 is more accurate:
>>> np.var(a, dtype=np.float64) 0.20249999932944759 >>> ((10.55)**2 + (0.10.55)**2)/2 0.2025

dask.array.
vdot
(a, b)¶ Return the dot product of two vectors.
The vdot(a, b) function handles complex numbers differently than dot(a, b). If the first argument is complex the complex conjugate of the first argument is used for the calculation of the dot product.
Note that vdot handles multidimensional arrays differently than dot: it does not perform a matrix product, but flattens input arguments to 1D vectors first. Consequently, it should only be used for vectors.
Parameters:  a : array_like
If a is complex the complex conjugate is taken before calculation of the dot product.
 b : array_like
Second argument to