(S|D|C|Z)GELS¶

Single, double, single complex, and double complex GELS.

Description¶

Solves an over or underdetermined system of linear equations.

For overdetermined systems, finds the least squares solution:

$\min || B - A \mult X ||$

For underdetermined systems, finds the minimum norm solution:

$A \mult X = B$

For SGELS and DGELS, if TRANS is T then uses the transpose of A. For CGELS and ZGELS, if TRANS is C then uses the Hermitian of A.

The matrix A is assumed to be full rank. Either QR or LQ factorization is used to compute results.

The matrix B encodes multiple right-hand sides and produces multiple solution vectors in the matrix X. Each column of B and column of X can be considered a single solution to

$A \mult x = b$

LAPACK Interface¶

void sgels(const char *TRANS, const qml_long *M, const qml_long *N,
    const qml_long *NRHS, float *A, const qml_long *LDA, float *B,
    const qml_long *LDB, float *WORK, const qml_long *LWORK,
    qml_long *INFO);

void dgels(const char *TRANS, const qml_long *M, const qml_long *N,
    const qml_long *NRHS, double *A, const qml_long *LDA, double *B,
    const qml_long *LDB, double *WORK, const qml_long *LWORK,
    qml_long *INFO);

void cgels(const char *TRANS, const qml_long *M, const qml_long *N,
    const qml_long *NRHS, qml_single_complex *A, const qml_long *LDA,
    qml_single_complex *B, const qml_long *LDB, qml_single_complex *WORK,
    const qml_long *LWORK, qml_long *INFO);

void zgels(const char *TRANS, const qml_long *M, const qml_long *N,
    const qml_long *NRHS, qml_double_complex *A, const qml_long *LDA,
    qml_double_complex *B, const qml_long *LDB, qml_double_complex *WORK,
    const qml_long *LWORK, qml_long *INFO);

Arguments¶

TRANS	One of ‘N’ (no transpose), ‘T’ (transpose), or ‘C’ (Hermitian)
M	Number of rows of A
N	Number of columns of A
NRHS	Number of right hand sides, number of columns of B and X
A	Matrix of size M x N, overwritten by factorization on exit
LDA	Leading dimension of A
B	Matrix of right hand side vectors, overwritten with X on exit
LDB	Leading dimension of B
WORK	Work space of size at least LWORK
LWORK	Size of work space, at least min(M,N)+max(min(M, N), NRHS) (-1 to query)
INFO	0 on success, <0 for illegal arguments, >0 if not full rank