gemqr

sgemqr

Functions

void sgemqr(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const f32*  restrict A,
    const INT            lda,
    const f32*  restrict T,
    const INT            tsize,
          f32*  restrict C,
    const INT            ldc,
          f32*  restrict work,
    const INT            lwork,
          INT*           info
);

void sgemqr(const char *side, const char *trans, const INT m, const INT n, const INT k, const f32 *restrict A, const INT lda, const f32 *restrict T, const INT tsize, f32 *restrict C, const INT ldc, f32 *restrict work, const INT lwork, INT *info)

SGEMQR overwrites the general real M-by-N matrix C with.

         SIDE = 'L'     SIDE = 'R'

TRANS = ‘N’: Q * C C * Q TRANS = ‘T’: Q^T * C C * Q^T

where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by tall skinny QR factorization (SGEQR)

Parameters

in

side

‘L’: apply Q or Q^T from the Left; ‘R’: apply Q or Q^T from the Right.

in

trans

‘N’: No transpose, apply Q; ‘T’: Transpose, apply Q^T.

in

m

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

in

n

The number of columns of the matrix C. n >= 0.

in

k

The number of elementary reflectors whose product defines the matrix Q. If SIDE = ‘L’, m >= k >= 0; if SIDE = ‘R’, n >= k >= 0.

in

A

Double precision array, dimension (lda, k). Part of the data structure to represent Q as returned by SGEQR.

in

lda

The leading dimension of the array A. If SIDE = ‘L’, lda >= max(1, m); if SIDE = ‘R’, lda >= max(1, n).

in

T

Double precision array, dimension (max(5, tsize)). Part of the data structure to represent Q as returned by SGEQR.

in

tsize

The dimension of the array T. tsize >= 5.

inout

C

Double precision array, dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C, Q^T*C, C*Q^T, or C*Q.

in

ldc

The leading dimension of the array C. ldc >= max(1, m).

out

work

Double precision workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the minimal lwork.

in

lwork

The dimension of the array work. lwork >= 1. If lwork = -1, then a workspace query is assumed.

out

info

• = 0: successful exit

• < 0: if info = -i, the i-th argument had an illegal value.

dgemqr

Functions

void dgemqr(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const f64*  restrict A,
    const INT            lda,
    const f64*  restrict T,
    const INT            tsize,
          f64*  restrict C,
    const INT            ldc,
          f64*  restrict work,
    const INT            lwork,
          INT*           info
);

void dgemqr(const char *side, const char *trans, const INT m, const INT n, const INT k, const f64 *restrict A, const INT lda, const f64 *restrict T, const INT tsize, f64 *restrict C, const INT ldc, f64 *restrict work, const INT lwork, INT *info)

DGEMQR overwrites the general real M-by-N matrix C with.

         SIDE = 'L'     SIDE = 'R'

TRANS = ‘N’: Q * C C * Q TRANS = ‘T’: Q^T * C C * Q^T

where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by tall skinny QR factorization (DGEQR)

Parameters

in

side

‘L’: apply Q or Q^T from the Left; ‘R’: apply Q or Q^T from the Right.

in

trans

‘N’: No transpose, apply Q; ‘T’: Transpose, apply Q^T.

in

m

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

in

n

The number of columns of the matrix C. n >= 0.

in

k

The number of elementary reflectors whose product defines the matrix Q. If SIDE = ‘L’, m >= k >= 0; if SIDE = ‘R’, n >= k >= 0.

in

A

Double precision array, dimension (lda, k). Part of the data structure to represent Q as returned by DGEQR.

in

lda

The leading dimension of the array A. If SIDE = ‘L’, lda >= max(1, m); if SIDE = ‘R’, lda >= max(1, n).

in

T

Double precision array, dimension (max(5, tsize)). Part of the data structure to represent Q as returned by DGEQR.

in

tsize

The dimension of the array T. tsize >= 5.

inout

C

Double precision array, dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C, Q^T*C, C*Q^T, or C*Q.

in

ldc

The leading dimension of the array C. ldc >= max(1, m).

out

work

Double precision workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the minimal lwork.

in

lwork

The dimension of the array work. lwork >= 1. If lwork = -1, then a workspace query is assumed.

out

info

• = 0: successful exit

• < 0: if info = -i, the i-th argument had an illegal value.

cgemqr

Functions

void cgemqr(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const c64*  restrict A,
    const INT            lda,
    const c64*  restrict T,
    const INT            tsize,
          c64*  restrict C,
    const INT            ldc,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);

void cgemqr(const char *side, const char *trans, const INT m, const INT n, const INT k, const c64 *restrict A, const INT lda, const c64 *restrict T, const INT tsize, c64 *restrict C, const INT ldc, c64 *restrict work, const INT lwork, INT *info)

CGEMQR overwrites the general complex M-by-N matrix C with.

         SIDE = 'L'     SIDE = 'R'

TRANS = ‘N’: Q * C C * Q TRANS = ‘C’: Q^H * C C * Q^H

where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by tall skinny QR factorization (CGEQR)

Parameters

in

side

‘L’: apply Q or Q^H from the Left; ‘R’: apply Q or Q^H from the Right.

in

trans

‘N’: No transpose, apply Q; ‘C’: Conjugate transpose, apply Q^H.

in

m

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

in

n

The number of columns of the matrix C. n >= 0.

in

k

The number of elementary reflectors whose product defines the matrix Q. If SIDE = ‘L’, m >= k >= 0; if SIDE = ‘R’, n >= k >= 0.

in

A

Single complex array, dimension (lda, k). Part of the data structure to represent Q as returned by CGEQR.

in

lda

The leading dimension of the array A. If SIDE = ‘L’, lda >= max(1, m); if SIDE = ‘R’, lda >= max(1, n).

in

T

Single complex array, dimension (max(5, tsize)). Part of the data structure to represent Q as returned by CGEQR.

in

tsize

The dimension of the array T. tsize >= 5.

inout

C

Single complex array, dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C, Q^H*C, C*Q^H, or C*Q.

in

ldc

The leading dimension of the array C. ldc >= max(1, m).

out

work

Single complex workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the minimal lwork.

in

lwork

The dimension of the array work. lwork >= 1. If lwork = -1, then a workspace query is assumed.

out

info

• = 0: successful exit

• < 0: if info = -i, the i-th argument had an illegal value.

zgemqr

Functions

void zgemqr(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const c128* restrict A,
    const INT            lda,
    const c128* restrict T,
    const INT            tsize,
          c128* restrict C,
    const INT            ldc,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);

void zgemqr(const char *side, const char *trans, const INT m, const INT n, const INT k, const c128 *restrict A, const INT lda, const c128 *restrict T, const INT tsize, c128 *restrict C, const INT ldc, c128 *restrict work, const INT lwork, INT *info)

ZGEMQR overwrites the general complex M-by-N matrix C with.

         SIDE = 'L'     SIDE = 'R'

TRANS = ‘N’: Q * C C * Q TRANS = ‘C’: Q^H * C C * Q^H

where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by tall skinny QR factorization (ZGEQR)

Parameters

in

side

‘L’: apply Q or Q^H from the Left; ‘R’: apply Q or Q^H from the Right.

in

trans

‘N’: No transpose, apply Q; ‘C’: Conjugate transpose, apply Q^H.

in

m

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

in

n

The number of columns of the matrix C. n >= 0.

in

k

The number of elementary reflectors whose product defines the matrix Q. If SIDE = ‘L’, m >= k >= 0; if SIDE = ‘R’, n >= k >= 0.

in

A

Double complex array, dimension (lda, k). Part of the data structure to represent Q as returned by ZGEQR.

in

lda

The leading dimension of the array A. If SIDE = ‘L’, lda >= max(1, m); if SIDE = ‘R’, lda >= max(1, n).

in

T

Double complex array, dimension (max(5, tsize)). Part of the data structure to represent Q as returned by ZGEQR.

in

tsize

The dimension of the array T. tsize >= 5.

inout

C

Double complex array, dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C, Q^H*C, C*Q^H, or C*Q.

in

ldc

The leading dimension of the array C. ldc >= max(1, m).

out

work

Double complex workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the minimal lwork.

in

lwork

The dimension of the array work. lwork >= 1. If lwork = -1, then a workspace query is assumed.

out

info

• = 0: successful exit

• < 0: if info = -i, the i-th argument had an illegal value.