matrixc

Public Functions

int	matrixc_print(double complex * _x, unsigned int _r, unsigned int _c)
int	matrixc_add(double complex * _x, double complex * _y, double complex * _z, unsigned int _r, unsigned int _c)
int	matrixc_sub(double complex * _x, double complex * _y, double complex * _z, unsigned int _r, unsigned int _c)
int	matrixc_pmul(double complex * _x, double complex * _y, double complex * _z, unsigned int _r, unsigned int _c)
int	matrixc_pdiv(double complex * _x, double complex * _y, double complex * _z, unsigned int _r, unsigned int _c)
int	matrixc_mul(double complex * _x, unsigned int _rx, unsigned int _cx, double complex * _y, unsigned int _ry, unsigned int _cy, double complex * _z, unsigned int _rz, unsigned int _cz)
int	matrixc_div(double complex * _x, double complex * _y, double complex * _z, unsigned int _n)
double complex	matrixc_det(double complex * _x, unsigned int _r, unsigned int _c)
int	matrixc_trans(double complex * _x, unsigned int _r, unsigned int _c)
int	matrixc_hermitian(double complex * _x, unsigned int _r, unsigned int _c)
int	matrixc_mul_transpose(double complex * _x, unsigned int _m, unsigned int _n, double complex * _xxT)
int	matrixc_transpose_mul(double complex * _x, unsigned int _m, unsigned int _n, double complex * _xTx)
int	matrixc_mul_hermitian(double complex * _x, unsigned int _m, unsigned int _n, double complex * _xxH)
int	matrixc_hermitian_mul(double complex * _x, unsigned int _m, unsigned int _n, double complex * _xHx)
int	matrixc_aug(double complex * _x, unsigned int _rx, unsigned int _cx, double complex * _y, unsigned int _ry, unsigned int _cy, double complex * _z, unsigned int _rz, unsigned int _cz)
int	matrixc_inv(double complex * _x, unsigned int _r, unsigned int _c)
int	matrixc_eye(double complex * _x, unsigned int _n)
int	matrixc_ones(double complex * _x, unsigned int _r, unsigned int _c)
int	matrixc_zeros(double complex * _x, unsigned int _r, unsigned int _c)
int	matrixc_gjelim(double complex * _x, unsigned int _r, unsigned int _c)
int	matrixc_pivot(double complex * _x, unsigned int _r, unsigned int _c, unsigned int _i, unsigned int _j)
int	matrixc_swaprows(double complex * _x, unsigned int _r, unsigned int _c, unsigned int _r1, unsigned int _r2)
int	matrixc_linsolve(double complex * _A, unsigned int _n, double complex * _b, double complex * _x, void * _opts)
int	matrixc_cgsolve(double complex * _A, unsigned int _n, double complex * _b, double complex * _x, void * _opts)
int	matrixc_ludecomp_crout(double complex * _x, unsigned int _rx, unsigned int _cx, double complex * _l, double complex * _u, double complex * _p)
int	matrixc_ludecomp_doolittle(double complex * _x, unsigned int _rx, unsigned int _cx, double complex * _l, double complex * _u, double complex * _p)
int	matrixc_gramschmidt(double complex * _A, unsigned int _r, unsigned int _c, double complex * _v)
int	matrixc_qrdecomp_gramschmidt(double complex * _a, unsigned int _m, unsigned int _n, double complex * _q, double complex * _r)
int	matrixc_chol(double complex * _a, unsigned int _n, double complex * _l)

Interfaces

int matrixc_print(double complex * _x, unsigned int _r, unsigned int _c)∞

Print array as matrix to stdout

• _x : input matrix, shape: (_r, _c)
• _r : rows in matrix
• _c : columns in matrix

int matrixc_add(double complex * _x, double complex * _y, double complex * _z, unsigned int _r, unsigned int _c)∞

Perform point-wise addition between two matrices $\vec{X}$ and $\vec{Y}$, saving the result in the output matrix $\vec{Z}$. That is, $\vec{Z}_{i,j}=\vec{X}_{i,j}+\vec{Y}_{i,j}$, $\forall_{i \in r}$ and $\forall_{j \in c}$

• _x : input matrix, shape: (_r, _c)
• _y : input matrix, shape: (_r, _c)
• _z : output matrix, shape: (_r, _c)
• _r : number of rows in each matrix
• _c : number of columns in each matrix

int matrixc_sub(double complex * _x, double complex * _y, double complex * _z, unsigned int _r, unsigned int _c)∞

Perform point-wise subtraction between two matrices $\vec{X}$ and $\vec{Y}$, saving the result in the output matrix $\vec{Z}$ That is, $\vec{Z}_{i,j}=\vec{X}_{i,j}-\vec{Y}_{i,j}$, $\forall_{i \in r}$ and $\forall_{j \in c}$

• _x : input matrix, shape: (_r, _c)
• _y : input matrix, shape: (_r, _c)
• _z : output matrix, shape: (_r, _c)
• _r : number of rows in each matrix
• _c : number of columns in each matrix

int matrixc_pmul(double complex * _x, double complex * _y, double complex * _z, unsigned int _r, unsigned int _c)∞

Perform point-wise multiplication between two matrices $\vec{X}$ and $\vec{Y}$, saving the result in the output matrix $\vec{Z}$ That is, $\vec{Z}_{i,j}=\vec{X}_{i,j} \vec{Y}_{i,j}$, $\forall_{i \in r}$ and $\forall_{j \in c}$

• _x : input matrix, shape: (_r, _c)
• _y : input matrix, shape: (_r, _c)
• _z : output matrix, shape: (_r, _c)
• _r : number of rows in each matrix
• _c : number of columns in each matrix

int matrixc_pdiv(double complex * _x, double complex * _y, double complex * _z, unsigned int _r, unsigned int _c)∞

Perform point-wise division between two matrices $\vec{X}$ and $\vec{Y}$, saving the result in the output matrix $\vec{Z}$ That is, $\vec{Z}_{i,j}=\vec{X}_{i,j}/\vec{Y}_{i,j}$, $\forall_{i \in r}$ and $\forall_{j \in c}$

• _x : input matrix, shape: (_r, _c)
• _y : input matrix, shape: (_r, _c)
• _z : output matrix, shape: (_r, _c)
• _r : number of rows in each matrix
• _c : number of columns in each matrix

int matrixc_mul(double complex * _x, unsigned int _rx, unsigned int _cx, double complex * _y, unsigned int _ry, unsigned int _cy, double complex * _z, unsigned int _rz, unsigned int _cz)∞

Multiply two matrices $\vec{X}$ and $\vec{Y}$, storing the result in $\vec{Z}$. NOTE: _rz = _rx, _cz = _cy, and _cx = _ry

• _x : input matrix, shape: (_rx, _cx)
• _rx : number of rows in _x
• _cx : number of columns in _x
• _y : input matrix, shape: (_ry, _cy)
• _ry : number of rows in _y
• _cy : number of columns in _y
• _z : output matrix, shape: (_rz, _cz)
• _rz : number of rows in _z
• _cz : number of columns in _z

int matrixc_div(double complex * _x, double complex * _y, double complex * _z, unsigned int _n)∞

Solve $\vec{X} = \vec{Y} \vec{Z}$ for $\vec{Z}$ for square matrices of size $n$

• _x : input matrix, shape: (_n, _n)
• _y : input matrix, shape: (_n, _n)
• _z : output matrix, shape: (_n, _n)
• _n : number of rows and columns in each matrix

double complex matrixc_det(double complex * _x, unsigned int _r, unsigned int _c)∞

Compute the determinant of a square matrix $\vec{X}$

• _x : input matrix, shape: (_r, _c)
• _r : rows
• _c : columns

int matrixc_trans(double complex * _x, unsigned int _r, unsigned int _c)∞

Compute the in-place transpose of the matrix $\vec{X}$

• _x : input matrix, shape: (_r, _c)
• _r : rows
• _c : columns

int matrixc_hermitian(double complex * _x, unsigned int _r, unsigned int _c)∞

Compute the in-place Hermitian transpose of the matrix $\vec{X}$

• _x : input matrix, shape: (_r, _c)
• _r : rows
• _c : columns

int matrixc_mul_transpose(double complex * _x, unsigned int _m, unsigned int _n, double complex * _xxT)∞

Compute $\vec{X}\vec{X}^T$ on a $m \times n$ matrix. The result is a $m \times m$ matrix.

• _x : input matrix, shape: (_m, _n)
• _m : input rows
• _n : input columns
• _xxT : output matrix, shape: (_m, _m)

int matrixc_transpose_mul(double complex * _x, unsigned int _m, unsigned int _n, double complex * _xTx)∞

Compute $\vec{X}^T\vec{X}$ on a $m \times n$ matrix. The result is a $n \times n$ matrix.

• _x : input matrix, shape: (_m, _n)
• _m : input rows
• _n : input columns
• _xTx : output matrix, shape: (_n, _n)

int matrixc_mul_hermitian(double complex * _x, unsigned int _m, unsigned int _n, double complex * _xxH)∞

Compute $\vec{X}\vec{X}^H$ on a $m \times n$ matrix. The result is a $m \times m$ matrix.

• _x : input matrix, shape: (_m, _n)
• _m : input rows
• _n : input columns
• _xxH : output matrix, shape: (_m, _m)

int matrixc_hermitian_mul(double complex * _x, unsigned int _m, unsigned int _n, double complex * _xHx)∞

Compute $\vec{X}^H\vec{X}$ on a $m \times n$ matrix. The result is a $n \times n$ matrix.

• _x : input matrix, shape: (_m, _n)
• _m : input rows
• _n : input columns
• _xHx : output matrix, shape: (_n, _n)

int matrixc_aug(double complex * _x, unsigned int _rx, unsigned int _cx, double complex * _y, unsigned int _ry, unsigned int _cy, double complex * _z, unsigned int _rz, unsigned int _cz)∞

Augment two matrices $\vec{X}$ and $\vec{Y}$, storing the result in $\vec{Z}$ NOTE: _rz = _rx = _ry, _rx = _ry, and _cz = _cx + _cy

• _x : input matrix, shape: (_rx, _cx)
• _rx : number of rows in _x
• _cx : number of columns in _x
• _y : input matrix, shape: (_ry, _cy)
• _ry : number of rows in _y
• _cy : number of columns in _y
• _z : output matrix, shape: (_rz, _cz)
• _rz : number of rows in _z
• _cz : number of columns in _z

int matrixc_inv(double complex * _x, unsigned int _r, unsigned int _c)∞

Compute the inverse of a square matrix $\vec{X}$

• _x : input/output matrix, shape: (_r, _c)
• _r : rows
• _c : columns

int matrixc_eye(double complex * _x, unsigned int _n)∞

Generate the identity square matrix of size $n$

• _x : output matrix, shape: (_n, _n)
• _n : dimensions of _x

int matrixc_ones(double complex * _x, unsigned int _r, unsigned int _c)∞

Generate the all-ones matrix of size $n$

• _x : output matrix, shape: (_r, _c)
• _r : rows
• _c : columns

int matrixc_zeros(double complex * _x, unsigned int _r, unsigned int _c)∞

Generate the all-zeros matrix of size $n$

• _x : output matrix, shape: (_r, _c)
• _r : rows
• _c : columns

int matrixc_gjelim(double complex * _x, unsigned int _r, unsigned int _c)∞

Perform Gauss-Jordan elimination on matrix $\vec{X}$

• _x : input/output matrix, shape: (_r, _c)
• _r : rows
• _c : columns

int matrixc_pivot(double complex * _x, unsigned int _r, unsigned int _c, unsigned int _i, unsigned int _j)∞

Pivot on element $\vec{X}_{i,j}$

• _x : output matrix, shape: (_r, _c)
• _r : rows of _x
• _c : columns of _x
• _i : pivot row
• _j : pivot column

int matrixc_swaprows(double complex * _x, unsigned int _r, unsigned int _c, unsigned int _r1, unsigned int _r2)∞

Swap rows _r1 and _r2 of matrix $\vec{X}$

• _x : input/output matrix, shape: (_r, _c)
• _r : rows of _x
• _c : columns of _x
• _r1 : first row to swap
• _r2 : second row to swap

int matrixc_linsolve(double complex * _A, unsigned int _n, double complex * _b, double complex * _x, void * _opts)∞

Solve linear system of $n$ equations: $\vec{A}\vec{x} = \vec{b}$

• _A : system matrix, shape: (_n, _n)
• _n : system size
• _b : equality vector, shape: (_n, 1)
• _x : solution vector, shape: (_n, 1)
• _opts : options (ignored for now)

int matrixc_cgsolve(double complex * _A, unsigned int _n, double complex * _b, double complex * _x, void * _opts)∞

Solve linear system of equations using conjugate gradient method.

• _A : symmetric positive definite square matrix
• _n : system dimension
• _b : equality, shape: (_n, 1)
• _x : solution estimate, shape: (_n, 1)
• _opts : options (ignored for now)

int matrixc_ludecomp_crout(double complex * _x, unsigned int _rx, unsigned int _cx, double complex * _l, double complex * _u, double complex * _p)∞

Perform L/U/P decomposition using Crout's method

• _x : input/output matrix, shape: (_rx, _cx)
• _rx : rows of _x
• _cx : columns of _x
• _l : first row to swap
• _u : first row to swap
• _p : first row to swap

int matrixc_ludecomp_doolittle(double complex * _x, unsigned int _rx, unsigned int _cx, double complex * _l, double complex * _u, double complex * _p)∞

Perform L/U/P decomposition, Doolittle's method

• _x : input/output matrix, shape: (_rx, _cx)
• _rx : rows of _x
• _cx : columns of _x
• _l : first row to swap
• _u : first row to swap
• _p : first row to swap

int matrixc_gramschmidt(double complex * _A, unsigned int _r, unsigned int _c, double complex * _v)∞

Perform orthnormalization using the Gram-Schmidt algorithm

• _A : input matrix, shape: (_r, _c)
• _r : rows
• _c : columns
• _v : output matrix

int matrixc_qrdecomp_gramschmidt(double complex * _a, unsigned int _m, unsigned int _n, double complex * _q, double complex * _r)∞

Perform Q/R decomposition using the Gram-Schmidt algorithm such that $\vec{A} = \vec{Q} \vec{R}$ and $\vec{Q}^T \vec{Q} = \vec{I}_n$ and \(\vec{R\}\) is a diagonal \(m \times m\) matrix NOTE: all matrices are square

• _a : input matrix, shape: (_m, _m)
• _m : rows
• _n : columns (same as cols)
• _q : output matrix, shape: (_m, _m)
• _r : output matrix, shape: (_m, _m)

int matrixc_chol(double complex * _a, unsigned int _n, double complex * _l)∞

Compute Cholesky decomposition of a symmetric/Hermitian positive-definite matrix as $\vec{A} = \vec{L}\vec{L}^T$

• _a : input square matrix, shape: (_n, _n)
• _n : input matrix dimension
• _l : output lower-triangular matrix