newDMat rows cols

Construct new DMat with rows rows and cols columns.

withDMat mat f

Apply f to a mat.

withNewDMat rows cols f

Apply f to a new DMat with rows rows and cols columns.

d_mat_init mat rows cols

Initialises a matrix with the given number of rows and columns for use.

d_mat_clear mat

Clears the given matrix.

d_mat_set mat1 mat2

Sets mat1 to a copy of mat2. The dimensions of mat1 and mat2 must be the same.

d_mat_swap mat1 mat2

Swaps two matrices. The dimensions of mat1 and mat2 are allowed to be different.

d_mat_swap_entrywise mat1 mat2

Swaps two matrices by swapping the individual entries rather than swapping the contents of the structs.

d_mat_entry mat i j

Returns the entry of mat at row \(i\) and column \(j\). Both \(i\) and \(j\) must not exceed the dimensions of the matrix. This function is implemented as a macro.

d_mat_get_entry mat i j

Returns the entry of mat at row \(i\) and column \(j\). Both \(i\) and \(j\) must not exceed the dimensions of the matrix.

d_mat_entry_ptr mat i j

Returns a pointer to the entry of mat at row \(i\) and column \(j\). Both \(i\) and \(j\) must not exceed the dimensions of the matrix.

d_mat_zero mat

Sets all entries of mat to 0.

d_mat_one mat

Sets mat to the unit matrix, having ones on the main diagonal and zeroes elsewhere. If mat is nonsquare, it is set to the truncation of a unit matrix.

d_mat_randtest mat state minexp maxexp

Sets the entries of mat to random signed numbers with exponents between minexp and maxexp or zero.

d_mat_get_str mat

Returns a string representation of the given matrix.

d_mat_fprint file mat

Prints the given matrix to the stream stdout.

d_mat_print mat

Prints the given matrix to the stream stdout.

d_mat_equal mat1 mat2

Returns a non-zero value if mat1 and mat2 have the same dimensions and entries, and zero otherwise.

d_mat_approx_equal mat1 mat2 eps

Returns a non-zero value if mat1 and mat2 have the same dimensions and entries within eps of each other, and zero otherwise.

d_mat_is_zero mat

Returns a non-zero value if all entries mat are zero, and otherwise returns zero.

d_mat_is_approx_zero mat eps

Returns a non-zero value if all entries mat are zero to within eps and otherwise returns zero.

d_mat_is_empty mat

Returns a non-zero value if the number of rows or the number of columns in mat is zero, and otherwise returns zero.

d_mat_is_square mat

Returns a non-zero value if the number of rows is equal to the number of columns in mat, and otherwise returns zero.

d_mat_transpose B A

Sets \(B\) to \(A^T\), the transpose of \(A\). Dimensions must be compatible. \(A\) and \(B\) are allowed to be the same object if \(A\) is a square matrix.

d_mat_mul_classical C A B

Sets C to the matrix product \(C = A B\). The matrices must have compatible dimensions for matrix multiplication (an exception is raised otherwise). Aliasing is allowed.

d_mat_gso B A

Takes a subset of \(R^m\) \(S = {a_1, a_2, \ldots, a_n}\) (as the columns of a \(m x n\) matrix A) and generates an orthonormal set \(S' = {b_1, b_2, \ldots, b_n}\) (as the columns of the \(m x n\) matrix B) that spans the same subspace of \(R^m\) as \(S\).

This uses an algorithm of Schwarz-Rutishauser. See pp. 9 of https://people.inf.ethz.ch/gander/papers/qrneu.pdf

d_mat_qr Q R A

Computes the \(QR\) decomposition of a matrix A using the Gram-Schmidt process. (Sets Q and R such that \(A = QR\) where R is an upper triangular matrix and Q is an orthogonal matrix.)

This uses an algorithm of Schwarz-Rutishauser. See pp. 9 of https://people.inf.ethz.ch/gander/papers/qrneu.pdf