Source code for openmdao.utils.array_utils

"""
Utils for dealing with arrays.
"""
import sys
from itertools import product
from copy import copy
from numbers import Integral

import numpy as np
from scipy.sparse import coo_matrix

from openmdao.core.constants import INT_DTYPE


[docs]def shape_to_len(shape): """ Compute length given a shape tuple. For realistic-dimension arrays, looping over the shape tuple is much faster than np.prod. Parameters ---------- shape : tuple Numpy shape tuple. Returns ------- int Length of multidimensional array. """ if shape is None: return None length = 1 if not isinstance(shape, Integral): for dim in shape: length *= dim return length
[docs]def evenly_distrib_idxs(num_divisions, arr_size): """ 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_divisions : int Number of parts to divide the array into. arr_size : int Number of entries in the array. Returns ------- tuple A tuple of (sizes, offsets), where sizes and offsets contain values for all divisions. """ base, leftover = divmod(arr_size, num_divisions) sizes = np.full(num_divisions, base, dtype=INT_DTYPE) # evenly distribute the remainder across size-leftover procs, # instead of giving the whole remainder to one proc sizes[:leftover] += 1 offsets = np.zeros(num_divisions, dtype=INT_DTYPE) offsets[1:] = np.cumsum(sizes)[:-1] return sizes, offsets
[docs]def take_nth(rank, size, seq): """ 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 ---------- rank : int MPI rank of this process. size : int Size of the array we're taking nth entries from. seq : iter Iterator containing the values being returned. Yields ------ generator """ assert(rank < size) it = iter(seq) while True: for proc in range(size): if rank == proc: try: yield next(it) except StopIteration: return else: try: next(it) except StopIteration: return
[docs]def convert_neg(arr, size): """ Convert any negative indices into their positive equivalent. This only works for a 1D array. Parameters ---------- arr : ndarray Array having negative indices converted. size : int Dimension of the array. Returns ------- ndarray The converted array. """ arr[arr < 0] += size return arr
[docs]def array_viz(arr, prob=None, of=None, wrt=None, stream=sys.stdout): """ 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 ---------- arr : ndarray Array being visualized. prob : Problem or None Problem object. of : list of str or None Names of response variables used in derivative calculation. wrt : list of str or None Names of design variables used in derivative calculation. stream : file-like Stream where output will be written. """ if len(arr.shape) != 2: raise RuntimeError("array_viz only works for 2d arrays.") if prob is not None: if of is None: of = prob.driver._get_ordered_nl_responses() if wrt is None: wrt = list(prob.driver._designvars) if prob is None or of is None or wrt is None: for r in range(arr.shape[0]): for c in range(arr.shape[1]): if arr[r, c]: stream.write('x') else: stream.write('.') stream.write(' %d\n' % r) else: row = 0 for res in of: for r in range(row, row + prob.driver._responses[res]['size']): col = 0 for dv in wrt: for c in range(col, col + prob.driver._designvars[dv]['size']): if arr[r, c]: stream.write('x') else: stream.write('.') col = c + 1 stream.write(' %d %s\n' % (r, res)) row = r + 1 start = 0 for name in wrt: tab = ' ' * start stream.write('%s|%s\n' % (tab, name)) start += prob.driver._designvars[name]['size']
[docs]def array_connection_compatible(shape1, shape2): """ 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 ---------- shape1 : tuple of int Shape of the first array. shape2 : tuple of int Shape of the second array. Returns ------- bool True if the two shapes are compatible for connection, else False. """ ashape1 = np.asarray(shape1, dtype=INT_DTYPE) ashape2 = np.asarray(shape2, dtype=INT_DTYPE) size1 = shape_to_len(ashape1) size2 = shape_to_len(ashape2) # Shapes are not connection-compatible if size is different if size1 != size2: return False nz1 = np.where(ashape1 > 1)[0] nz2 = np.where(ashape2 > 1)[0] if len(nz1) > 0: fundamental_shape1 = ashape1[np.min(nz1): np.max(nz1) + 1] else: fundamental_shape1 = np.ones((1,)) if len(nz2) > 0: fundamental_shape2 = ashape2[np.min(nz2): np.max(nz2) + 1] else: fundamental_shape2 = np.ones((1,)) return np.all(fundamental_shape1 == fundamental_shape2)
[docs]def tile_sparse_jac(data, rows, cols, nrow, ncol, num_nodes): """ 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 ---------- data : ndarray Array of values. rows : index array Array of row indices. cols : index array Array of column indices. nrow : int Number of rows in sub jacobian. ncol : int Number of columns in sub jacobian. num_nodes : int Number 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. """ nnz = len(rows) if np.isscalar(data): data = data * np.ones(nnz) if not np.isscalar(nrow): nrow = shape_to_len(nrow) if not np.isscalar(ncol): ncol = shape_to_len(ncol) repeat_arr = np.repeat(np.arange(num_nodes), nnz) data = np.tile(data, num_nodes) rows = np.tile(rows, num_nodes) + repeat_arr * nrow cols = np.tile(cols, num_nodes) + repeat_arr * ncol return data, rows, cols
def _global2local_offsets(global_offsets): """ Given existing global offsets, return a copy with offsets localized to each process. Parameters ---------- global_offsets : dict Arrays of global offsets keyed by vec_name and deriv direction. Returns ------- dict Arrays of local offsets keyed by vec_name and deriv direction. """ offsets = {} for type_ in global_offsets: goff = global_offsets[type_] offsets[type_] = goff.copy() if goff[0].size > 0: # adjust offsets to be local in each process offsets[type_] -= goff[:, 0].reshape((goff.shape[0], 1)) return offsets
[docs]def get_input_idx_split(full_idxs, inputs, outputs, use_full_cols, is_total): """ Split an array of indices into vec outs + ins into two arrays of indices into outs and ins. Parameters ---------- full_idxs : ndarray Indices into the full array (which could be outs + ins or just ins). inputs : Vector Inputs vector. outputs : Vector Outputs vector. use_full_cols : bool If True, full idxs are into the full outs + ins vector. is_total : bool If 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). """ assert len(full_idxs) > 0, "Empty index array passed to get_input_idx_split." full_idxs = np.asarray(full_idxs) if use_full_cols: out_size = len(outputs) out_idxs = full_idxs[full_idxs < out_size] in_idxs = full_idxs[full_idxs >= out_size] - out_size full = [(outputs, out_idxs), (inputs, in_idxs)] return [(vec, inds) for vec, inds in full if inds.size > 0] elif is_total: return [(outputs, full_idxs)] else: return [(inputs, full_idxs)]
def _flatten_src_indices(src_indices, shape_in, shape_out, size_out): """ Convert src_indices into a flat, non-negative form. Parameters ---------- src_indices : ndarray Array of src_indices. Can be flat or multi-dimensional. shape_in : tuple Shape of the input variable. shape_out : tuple Shape of the output variable. size_out : int Size of the output variable. Returns ------- ndarray The flattened src_indices. """ if len(shape_out) == 1 or shape_in == src_indices.shape: return convert_neg(src_indices.ravel(), size_out) entries = [list(range(x)) for x in shape_in] cols = np.vstack([src_indices[i] for i in product(*entries)]) dimidxs = [convert_neg(cols[:, i], shape_out[i]) for i in range(cols.shape[1])] return np.ravel_multi_index(dimidxs, shape_out)
[docs]def sizes2offsets(size_array): """ 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_array : ndarray Array of sizes. Returns ------- ndarray Array of offsets. """ offsets = np.zeros(size_array.size, dtype=size_array.dtype) offsets[1:] = np.cumsum(size_array.flat)[:-1] return offsets.reshape(size_array.shape)
[docs]def abs_complex(x): """ 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 ---------- x : ndarray Input array. Returns ------- ndarray Complex-step absolute value of the array. """ idx_neg = np.where(x < 0) x[idx_neg] = -x[idx_neg] return x
[docs]def dv_abs_complex(x, x_deriv): """ Compute the complex-step derivative of the absolute value function and its derivative. Parameters ---------- x : ndarray Input array, used for determining which elements to negate. x_deriv : ndarray Incominng partial derivative array, may have one additional dimension. Returns ------- ndarray Absolute value applied to x. ndarray Absolute value applied to x_deriv. """ idx_neg = np.where(x < 0) # Special case when x is (1, ) and x_deriv is (1, n). if len(x_deriv.shape) == 1: if idx_neg[0].size != 0: return -x, -x_deriv x[idx_neg] = -x[idx_neg] x_deriv[idx_neg] = -x_deriv[idx_neg] return x, x_deriv
[docs]def rand_sparsity(shape, density_ratio, dtype=bool): """ 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 ---------- shape : tuple Desired shape of the matrix. density_ratio : float Approximate ratio of nonzero to zero entries in the desired matrix. dtype : type Specifies type of the values in the returned matrix. Returns ------- coo_matrix A COO matrix with approximately the nonzero density desired. """ assert len(shape) == 2, f"shape must be a size 2 tuple but {shape} was given" nrows, ncols = shape nnz = int(nrows * ncols * density_ratio) data = np.ones(nnz, dtype=dtype) rows = np.random.randint(0, nrows, nnz) cols = np.random.randint(0, ncols, nnz) coo = coo_matrix((data, (rows, cols)), shape=shape) # get rid of dup rows/cols coo.sum_duplicates() return coo
[docs]def sparse_subinds(orig, inds): """ 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 ---------- orig : ndarray Either row or col indices (part of a subjac sparsity pattern). inds : ndarray or list Sub-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. """ mask = np.zeros(orig.size, dtype=bool) for i in inds: mask |= orig == i newsp = orig[mask] # replace the index with the 'compressed' index after we've masked out entries for r, i in enumerate(np.sort(inds)): newsp[newsp == i] = r return newsp, mask