Documentation for ‘block_sparse’ module¶
Documentation for the regrnd model class.

class
block_sparse.
block_sparse
(blocks, nonzero, submatrices, dtype=<type 'numpy.float32'>, row_names=None, col_names=None)[source]¶ Define a blocksparse matrix
Parameters: blocks :
list
list of [row_block_boundaries,col_block_boundaries], where each of row_block_boundaries and col_block_boundaries is a 1D
array
of integers, beginning with 0, followed by the end boundaries of each block in increasing ordernonzero :
array
boolean numpy array with number of rows equal to number of row blocks, and number of columns equal to number of col blocks. If entry [i,j] of nonzero is True, then the corresponding block is nonzero; if it is False, then the corresponding block is zero.
submatrices :
list
list of submatrices for nonzero blocks in rowmajor order; e.g., block (1,1), (1,2), (2,1), (2,2),... Each submatrix can be an
array
, ablock_sparse
matrix, or asymmetric_block_sparse
matrix.dtype : numpy data type object
Set the default data type for the submatrices. Default
float32
row_names :
array
numpy array with names of the rowblocks. Default
None
col_names :
array
numpy array with names of the colblocks. Default
None
Returns: matrix :
block_sparse
blocksparse matrix
Methods
add
(A)Matrix addition of a matrix A to current matrix dot
(A)Right multiply the current matrix with another block_sparse
matrix,symmetric_block_sparse
matrix, orarray
, A.frobenius
(A)Compute the frobenius inner product between the current matrix and matrix A get_submatrix
(block)Retrieve a particular block of the matrix get_type
(block)Retrieve the type of a particular block of the matrix norm
()Compute the frobenius norm of the current matrix qform
(y[, z])Computes quadratic form defined by current matrix and input vectors. to_dense
()Return the current matrix as a standard (dense) numpy array transpose
()Return the transpose of the blocksparse matrix 
add
(A)[source]¶ Matrix addition of a matrix A to current matrix
Parameters: A : matrix
matrix A with same dimensions as current matrix. The matrix A can be an
array
,block_sparse
matrix, orsymmetric_block_sparse
matrix. It must have the same block structure as the current matrix if the matrix is ablock_sparse
matrix orsymmetric_block_sparse
matrix.Returns: the blocksparse matrix formed by matrix addition of the current matrix to A

dot
(A)[source]¶ Right multiply the current matrix with another
block_sparse
matrix,symmetric_block_sparse
matrix, orarray
, A.Parameters: A : matrix
matrix A with compatible dimensions and block structure: i.e. the row blocks of A must match the column blocks of the current matrix, unless A is an
array
.Returns: the blocksparse matrix formed by right multiplication of the current matrix by A

frobenius
(A)[source]¶ Compute the frobenius inner product between the current matrix and matrix A
Parameters: A : matrix
matrix A with same dimensions as current matrix. The matrix A can be an
array
,block_sparse
matrix, orsymmetric_block_sparse
matrix. It must have the same block structure as the current matrix if the matrix is ablock_sparse
matrix orsymmetric_block_sparse
matrix.Returns: the frobenius inner product between the current matrix and matrix A

get_submatrix
(block)[source]¶ Retrieve a particular block of the matrix
Parameters: block :
tuple
tuple (i,j) giving the index of the block
Returns: block
either an
array
, ablock_sparse
matrix, or asymmetric_block_sparse
matrix.

get_type
(block)[source]¶ Retrieve the type of a particular block of the matrix
Parameters: block :
tuple
tuple (i,j) giving the index of the block
Returns: block type
either
array
,block_sparse
, orsymmetric_block_sparse
.

norm
()[source]¶ Compute the frobenius norm of the current matrix
Returns: the frobenius norm of the current matrix

qform
(y, z=None)[source]¶ Computes quadratic form defined by current matrix and input vectors. Let X be the current
block_sparse
matrix, and y and z column vectors. When it is defined, this computes the quadratic form y’Xz. If only y is provided, this computes the quadratic form y’Xy.Parameters: y :
array
1D numpy array of same length as number of rows of current matrix
 z :
array
1D numpy array of same length as number of rows of current matrix. Default
None
.
Returns: the value of the quadratic form y’Xz
 z :

transpose
()[source]¶ Return the transpose of the blocksparse matrix
Returns: block_sparse


class
block_sparse.
symmetric_block_sparse
(blocks, nonzero, submatrices, dtype=<type 'numpy.float32'>, row_names=None, col_names=None)[source]¶ Define a symmetric blocksparse matrix. Inherits some methods from
block_sparse
.Parameters: blocks :
array
1D numpy integer array, starting at zero, followed by block boundaries, which are the same for both rows and columns
nonzero :
array
symmetric boolean numpy array with number of rows equal to number of row blocks, which is equal to the number of col blocks. If entry [i,j] of nonzero is True, then the corresponding block is nonzero; if it is False, then the corresponding block is zero.
submatrices :
list
list of submatrices for nonzero blocks in rowmajor order, ignoring lowertriangular blocks; e.g., block (1,1), (1,2), (2,2),... Each submatrix can be a
array
, ablock_sparse
matrix, or asymmetric_block_sparse
matrix.dtype : numpy data type object
Set the default data type for the submatrices. Default
float32
row_names :
array
numpy array with names of the rowblocks. Default
None
col_names :
array
numpy array with names of the colblocks. Default
None
Returns: blocksparse matrix
Methods
add
(A)Matrix addition of a matrix A to current matrix. dot
(A)Right multiply the current matrix with another block_sparse
matrix,symmetric_block_sparse
matrix, orarray
, A.frobenius
(A)Compute the frobenius inner product between the current matrix and matrix A get_submatrix
(block)Retrieve a particular block of the matrix get_type
(block)Retrieve the type of a particular block of the matrix norm
()Compute the frobenius norm of the current matrix qform
(y[, z])Let X be the current symmetric_block_sparse
matrix, and y and z column vectors.to_dense
()Return the current matrix as a standard (dense) numpy array transpose
()Return the transpose of the symmetric blocksparse matrix 
add
(A)[source]¶ Matrix addition of a matrix A to current matrix.
Parameters: A : matrix
matrix A with same dimensions as current matrix. The matrix A can be a
array
,block_sparse
matrix, orsymmetric_block_sparse
matrix. It must have the same block structure as the current matrix if the matrix is ablock_sparse
matrix orsymmetric_block_sparse
matrix.Returns: matrix
If A is
symmetric_block_sparse
, returns asymmetric_block_sparse
matrix. Otherwise, returns ablock_sparse
matrix.

get_submatrix
(block)[source]¶ Retrieve a particular block of the matrix
Parameters: block :
tuple
tuple (i,j) giving the index of the block
Returns: block
either a
array
, ablock_sparse
matrix, or asymmetric_block_sparse
matrix.

get_type
(block)[source]¶ Retrieve the type of a particular block of the matrix
Parameters: block :
tuple
tuple (i,j) giving the index of the block
Returns: block type
either
array
,block_sparse
matrix, orsymmetric_block_sparse
matrix.

qform
(y, z=None)[source]¶ Let X be the current
symmetric_block_sparse
matrix, and y and z column vectors. When it is defined, this computes the quadratic form y’Xz. If only y is provided, this computes the quadratic form y’Xy.Parameters: y :
array
1D numpy array of same length as number of rows of current matrix
 z :
array
1D numpy array of same length as number of rows of current matrix. Default
None
.
Returns: the value of the quadratic form y’Xz
 z :


block_sparse.
matmul
(X, A)[source]¶ Matrix multiplication between
block_sparse
andsymmetric_block_sparse
matrices, as well as matrix multiplication between ablock_sparse
orsymmetric_block_sparse
matrix and anarray
.Parameters: X : matrix
The matrix X can be a
block_sparse
matrix, asymmetric_block_sparse
matrix, or aarray
.A : matrix
The matrix A can be a
block_sparse
matrix, asymmetric_block_sparse
matrix, or aarray
. Note that the number of rows of A must match the number of columns of X. Furthermore, if X and A are bothblock_sparse
orsymmetric_block_sparse
, then the column blocks of X must match the row blocks of A.Returns: the blocksparse matrix formed by matrix multiplication XA

block_sparse.
dense_to_block_sparse
(dense, blocks, symmetric, dtype=<type 'numpy.float64'>)[source]¶ Convert a standard (dense) numpy array into a
block_sparse
or asymmetric_block_sparse
matrix. Note this simply imposes a block structure onto the matrix so that it can interact with other block matrices. It does not take advantage of any sparsity in the input matrix.Parameters: dense :
array
input matrix
 blocks :
list
list of [row_block_boundaries,col_block_boundaries], where each of row_block_boundaries and col_block_boundaries is a 1D
array
of integers, beginning with 0, followed by the end boundaries of each block in increasing order symmetric :
bool
if True, returns a
symmetric_block_sparse
matrix; if False, returns ablock_sparse
matrix dtype : numpy data type
the default data type of the returned matrix
Returns: matrix
the current matrix as a
block_sparse
or asymmetric_block_sparse
matrix blocks :