# array_utils.py¶

Utils for dealing with arrays.

`openmdao.utils.array_utils.`

`abs_complex`

(x)[source]Compute the absolute value of a complex-stepped vector.

Rather than taking a Euclidian norm, simply negate the values that are less than zero.

- Parameters

xndarrayInput array.

- Returns

- ndarray
Complex-step absolute value of the array.

`openmdao.utils.array_utils.`

`array_connection_compatible`

(shape1,shape2)[source]Return True if the two arrays shapes are compatible.

Array shapes are compatible if the underlying data has the same size and is stored in the same contiguous order for the two shapes.

- Parameters

shape1tuple of intShape of the first array.

shape2tuple of intShape of the second array.

- Returns

- bool
True if the two shapes are compatible for connection, else False.

`openmdao.utils.array_utils.`

`array_viz`

(arr,prob=None,of=None,wrt=None,stream=<_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>)[source]Display the structure of a boolean array in a compact form.

If prob, of, and wrt are supplied, print the name of the response alongside each row and print the names of the design vars, aligned with each column, at the bottom.

- Parameters

arrndarrayArray being visualized.

probProblem or NoneProblem object.

oflist of str or NoneNames of response variables used in derivative calculation.

wrtlist of str or NoneNames of design variables used in derivative calculation.

streamfile-likeStream where output will be written.

`openmdao.utils.array_utils.`

`convert_neg`

(arr,size)[source]Convert any negative indices into their positive equivalent.

This only works for a 1D array.

- Parameters

arrndarrayArray having negative indices converted.

sizeintDimension of the array.

- Returns

- ndarray
The converted array.

`openmdao.utils.array_utils.`

`dv_abs_complex`

(x,x_deriv)[source]Compute the complex-step derivative of the absolute value function and its derivative.

- Parameters

xndarrayInput array, used for determining which elements to negate.

x_derivndarrayIncominng partial derivative array, may have one additional dimension.

- Returns

- ndarray
Absolute value applied to x.

- ndarray
Absolute value applied to x_deriv.

`openmdao.utils.array_utils.`

`evenly_distrib_idxs`

(num_divisions,arr_size)[source]Return evenly distributed entries for the given array size.

Given a number of divisions and the size of an array, chop the array up into pieces according to number of divisions, keeping the distribution of entries as even as possible.

- Parameters

num_divisionsintNumber of parts to divide the array into.

arr_sizeintNumber of entries in the array.

- Returns

- tuple
a tuple of (sizes, offsets), where sizes and offsets contain values for all divisions.

`openmdao.utils.array_utils.`

`get_input_idx_split`

(full_idxs,inputs,outputs,use_full_cols,is_total)[source]Split an array of indices into vec outs + ins into two arrays of indices into outs and ins.

- Parameters

full_idxsndarrayIndices into the full array (which could be outs + ins or just ins)

inputsVectorInputs vector.

outputsVectorOutputs vector.

use_full_colsboolIf True, full idxs are into the full outs + ins vector.

is_totalboolIf True, total derivatives are being computed and wrt vector is the outputs vector.

- Returns

- list of tuples
Each tuple is of the form (array, idxs).

`openmdao.utils.array_utils.`

`rand_sparsity`

(shape,density_ratio,dtype=<class 'bool'>)[source]Return a random boolean COO matrix of the given shape with given percent density.

Row and column indices are generated using random integers so some duplication is possible, resulting in a matrix with somewhat lower density than specified.

- Parameters

shapetupleDesired shape of the matrix.

density_ratiofloatApproximate ratio of nonzero to zero entries in the desired matrix.

dtypetypeSpecifies type of the values in the returned matrix.

- Returns

- coo_matrix
A COO matrix with approximately the nonzero density desired.

`openmdao.utils.array_utils.`

`shape_to_len`

(shape)[source]Compute length given a shape tuple.

For realistic-dimension arrays, looping over the shape tuple is much faster than np.prod.

- Parameters

shapetupleNumpy shape tuple.

- Returns

- int
Length of multidimensional array.

`openmdao.utils.array_utils.`

`sizes2offsets`

(size_array)[source]For a given array of sizes, return an array of offsets.

Offsets will be computed using a flattened version of size_array and then reshaped to match the shape of size_array.

- Parameters

size_arrayndarrayArray of sizes.

- Returns

- ndarray
Array of offsets.

`openmdao.utils.array_utils.`

`sparse_subinds`

(orig,inds)[source]Compute new rows or cols resulting from applying inds on top of an existing sparsity pattern.

This only comes into play when we have an approx total jacobian where some dv/resp have indices.

- Parameters

origndarrayEither row or col indices (part of a subjac sparsity pattern).

indsndarray or listSub-indices introduced when adding a desvar or response.

- Returns

- ndarray
New compressed rows or cols.

- ndarray
Mask array that can be used to update subjac value and corresponding index array to orig.

`openmdao.utils.array_utils.`

`take_nth`

(rank,size,seq)[source]Iterate returning every nth value.

Return an iterator over the sequence that returns every nth element of seq based on the given rank within a group of the given size. For example, if size = 2, a rank of 0 returns even indexed elements and a rank of 1 returns odd indexed elements.

- Parameters

rankintMPI rank of this process.

sizeintSize of the array we’re taking nth entries from.

seqiterIterator containing the values being returned.

`openmdao.utils.array_utils.`

`tile_sparse_jac`

(data,rows,cols,nrow,ncol,num_nodes)[source]Assemble arrays necessary to define a COO sparse jacobian for a vectorized component.

These arrays can also be passed to csc_matrix or csr_matrix to create CSC and CSR sparse matrices.

- Parameters

datandarrayArray of values

rowsindex arrayArray of row indices.

colsindex arrayArray of column indices.

nrowintNumber of rows in sub jacobian.

ncolintNumber of columns in sub jacobian.

num_nodesintNumber of vectorized copies to tile.

- Returns

- ndarray, ndarray, ndarray
Arrays to define a COO sparse jacobian of size num_nodes*nrow by num_nodes*ncol