geqrfp#

Functions

void sgeqrfp(
    const INT           m,
    const INT           n,
          f32* restrict A,
    const INT           lda,
          f32* restrict tau,
          f32* restrict work,
    const INT           lwork,
          INT*          info
);
void sgeqrfp(const INT m, const INT n, f32 *restrict A, const INT lda, f32 *restrict tau, f32 *restrict work, const INT lwork, INT *info)#

SGEQRFP computes a QR factorization of a real M-by-N matrix A:

A = Q * ( R ), ( 0 )

where Q is a M-by-M orthogonal matrix, R is an upper-triangular N-by-N matrix with nonnegative diagonal entries, and 0 is a (M-N)-by-N zero matrix if M > N.

This is the blocked Level 3 BLAS version of the algorithm.

Parameters

in
m

The number of rows of A. m >= 0.

in
n

The number of columns of A. n >= 0.

inout
A

On entry, the m-by-n matrix A. On exit, the elements on and above the diagonal contain the min(m,n)-by-n upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are nonnegative. The elements below the diagonal, with TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors.

in
lda

The leading dimension of A. lda >= max(1, m).

out
tau

Array of dimension min(m, n). The scalar factors of the elementary reflectors.

out
work

Workspace, dimension (max(1, lwork)). On exit, work[0] contains the optimal lwork.

in
lwork

Dimension of work. lwork >= 1 if min(m,n) = 0, lwork >= n otherwise. For optimal performance, lwork >= n*nb. If lwork == -1, workspace query only.

out
info

  • = 0: success; < 0: -i means i-th argument was illegal.

Functions

void dgeqrfp(
    const INT           m,
    const INT           n,
          f64* restrict A,
    const INT           lda,
          f64* restrict tau,
          f64* restrict work,
    const INT           lwork,
          INT*          info
);
void dgeqrfp(const INT m, const INT n, f64 *restrict A, const INT lda, f64 *restrict tau, f64 *restrict work, const INT lwork, INT *info)#

DGEQRFP computes a QR factorization of a real M-by-N matrix A:

A = Q * ( R ), ( 0 )

where Q is a M-by-M orthogonal matrix, R is an upper-triangular N-by-N matrix with nonnegative diagonal entries, and 0 is a (M-N)-by-N zero matrix if M > N.

This is the blocked Level 3 BLAS version of the algorithm.

Parameters

in
m

The number of rows of A. m >= 0.

in
n

The number of columns of A. n >= 0.

inout
A

On entry, the m-by-n matrix A. On exit, the elements on and above the diagonal contain the min(m,n)-by-n upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are nonnegative. The elements below the diagonal, with TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors.

in
lda

The leading dimension of A. lda >= max(1, m).

out
tau

Array of dimension min(m, n). The scalar factors of the elementary reflectors.

out
work

Workspace, dimension (max(1, lwork)). On exit, work[0] contains the optimal lwork.

in
lwork

Dimension of work. lwork >= 1 if min(m,n) = 0, lwork >= n otherwise. For optimal performance, lwork >= n*nb. If lwork == -1, workspace query only.

out
info

  • = 0: success; < 0: -i means i-th argument was illegal.

Functions

void cgeqrfp(
    const INT           m,
    const INT           n,
          c64* restrict A,
    const INT           lda,
          c64* restrict tau,
          c64* restrict work,
    const INT           lwork,
          INT*          info
);
void cgeqrfp(const INT m, const INT n, c64 *restrict A, const INT lda, c64 *restrict tau, c64 *restrict work, const INT lwork, INT *info)#

CGEQRFP computes a QR factorization of a complex M-by-N matrix A:

A = Q * ( R ), ( 0 )

where Q is a M-by-M unitary matrix, R is an upper-triangular N-by-N matrix with nonnegative diagonal entries, and 0 is a (M-N)-by-N zero matrix if M > N.

This is the blocked Level 3 BLAS version of the algorithm.

Parameters

in
m

The number of rows of A. m >= 0.

in
n

The number of columns of A. n >= 0.

inout
A

On entry, the m-by-n matrix A. On exit, the elements on and above the diagonal contain the min(m,n)-by-n upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are real and nonnegative. The elements below the diagonal, with TAU, represent the unitary matrix Q as a product of min(m,n) elementary reflectors.

in
lda

The leading dimension of A. lda >= max(1, m).

out
tau

Array of dimension min(m, n). The scalar factors of the elementary reflectors.

out
work

Workspace, dimension (max(1, lwork)). On exit, work[0] contains the optimal lwork.

in
lwork

Dimension of work. lwork >= 1 if min(m,n) = 0, lwork >= n otherwise. For optimal performance, lwork >= n*nb. If lwork == -1, workspace query only.

out
info

  • = 0: success; < 0: -i means i-th argument was illegal.

Functions

void zgeqrfp(
    const INT            m,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          c128* restrict tau,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zgeqrfp(const INT m, const INT n, c128 *restrict A, const INT lda, c128 *restrict tau, c128 *restrict work, const INT lwork, INT *info)#

ZGEQRFP computes a QR factorization of a complex M-by-N matrix A:

A = Q * ( R ), ( 0 )

where Q is a M-by-M unitary matrix, R is an upper-triangular N-by-N matrix with nonnegative diagonal entries, and 0 is a (M-N)-by-N zero matrix if M > N.

This is the blocked Level 3 BLAS version of the algorithm.

Parameters

in
m

The number of rows of A. m >= 0.

in
n

The number of columns of A. n >= 0.

inout
A

On entry, the m-by-n matrix A. On exit, the elements on and above the diagonal contain the min(m,n)-by-n upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are real and nonnegative. The elements below the diagonal, with TAU, represent the unitary matrix Q as a product of min(m,n) elementary reflectors.

in
lda

The leading dimension of A. lda >= max(1, m).

out
tau

Array of dimension min(m, n). The scalar factors of the elementary reflectors.

out
work

Workspace, dimension (max(1, lwork)). On exit, work[0] contains the optimal lwork.

in
lwork

Dimension of work. lwork >= 1 if min(m,n) = 0, lwork >= n otherwise. For optimal performance, lwork >= n*nb. If lwork == -1, workspace query only.

out
info

  • = 0: success; < 0: -i means i-th argument was illegal.