gemqrt#

Functions

void sgemqrt(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const INT            nb,
    const f32*  restrict V,
    const INT            ldv,
    const f32*  restrict T,
    const INT            ldt,
          f32*  restrict C,
    const INT            ldc,
          f32*  restrict work,
          INT*           info
);
void sgemqrt(const char *side, const char *trans, const INT m, const INT n, const INT k, const INT nb, const f32 *restrict V, const INT ldv, const f32 *restrict T, const INT ldt, f32 *restrict C, const INT ldc, f32 *restrict work, INT *info)#

SGEMQRT 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 K elementary reflectors:

Q = H(0) H(1) … H(K-1) = I - V T V^T

generated using the compact WY representation as returned by SGEQRT.

Q is of order M if SIDE = ‘L’ and of order N if SIDE = ‘R’.

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 C. 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
nb

The block size used for the storage of T. k >= nb >= 1. This must be the same value of nb used to generate T in SGEQRT.

in
V

Double precision array, dimension (ldv, k). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 0,1,…,k-1, as returned by SGEQRT in the first k columns of its array argument A.

in
ldv

The leading dimension of the array V. If SIDE = “L”, ldv >= max(1, m); if SIDE = “R”, ldv >= max(1, n).

in
T

Double precision array, dimension (ldt, k). The upper triangular factors of the block reflectors as returned by SGEQRT, stored as an nb-by-k matrix.

in
ldt

The leading dimension of the array T. ldt >= nb.

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 is n*nb if SIDE = “L”, or m*nb if SIDE = ‘R’.

out
info

  • = 0: successful exit

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

Functions

void dgemqrt(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const INT            nb,
    const f64*  restrict V,
    const INT            ldv,
    const f64*  restrict T,
    const INT            ldt,
          f64*  restrict C,
    const INT            ldc,
          f64*  restrict work,
          INT*           info
);
void dgemqrt(const char *side, const char *trans, const INT m, const INT n, const INT k, const INT nb, const f64 *restrict V, const INT ldv, const f64 *restrict T, const INT ldt, f64 *restrict C, const INT ldc, f64 *restrict work, INT *info)#

DGEMQRT 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 K elementary reflectors:

Q = H(0) H(1) … H(K-1) = I - V T V^T

generated using the compact WY representation as returned by DGEQRT.

Q is of order M if SIDE = ‘L’ and of order N if SIDE = ‘R’.

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 C. 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
nb

The block size used for the storage of T. k >= nb >= 1. This must be the same value of nb used to generate T in DGEQRT.

in
V

Double precision array, dimension (ldv, k). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 0,1,…,k-1, as returned by DGEQRT in the first k columns of its array argument A.

in
ldv

The leading dimension of the array V. If SIDE = “L”, ldv >= max(1, m); if SIDE = “R”, ldv >= max(1, n).

in
T

Double precision array, dimension (ldt, k). The upper triangular factors of the block reflectors as returned by DGEQRT, stored as an nb-by-k matrix.

in
ldt

The leading dimension of the array T. ldt >= nb.

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 is n*nb if SIDE = “L”, or m*nb if SIDE = ‘R’.

out
info

  • = 0: successful exit

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

Functions

void cgemqrt(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const INT            nb,
    const c64*  restrict V,
    const INT            ldv,
    const c64*  restrict T,
    const INT            ldt,
          c64*  restrict C,
    const INT            ldc,
          c64*  restrict work,
          INT*           info
);
void cgemqrt(const char *side, const char *trans, const INT m, const INT n, const INT k, const INT nb, const c64 *restrict V, const INT ldv, const c64 *restrict T, const INT ldt, c64 *restrict C, const INT ldc, c64 *restrict work, INT *info)#

CGEMQRT 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 K elementary reflectors:

Q = H(0) H(1) … H(K-1) = I - V T V^H

generated using the compact WY representation as returned by CGEQRT.

Q is of order M if SIDE = ‘L’ and of order N if SIDE = ‘R’.

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 C. 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
nb

The block size used for the storage of T. k >= nb >= 1. This must be the same value of nb used to generate T in CGEQRT.

in
V

Single complex array, dimension (ldv, k). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 0,1,…,k-1, as returned by CGEQRT in the first k columns of its array argument A.

in
ldv

The leading dimension of the array V. If SIDE = “L”, ldv >= max(1, m); if SIDE = “R”, ldv >= max(1, n).

in
T

Single complex array, dimension (ldt, k). The upper triangular factors of the block reflectors as returned by CGEQRT, stored as an nb-by-k matrix.

in
ldt

The leading dimension of the array T. ldt >= nb.

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 is n*nb if SIDE = “L”, or m*nb if SIDE = ‘R’.

out
info

  • = 0: successful exit

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

Functions

void zgemqrt(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const INT            nb,
    const c128* restrict V,
    const INT            ldv,
    const c128* restrict T,
    const INT            ldt,
          c128* restrict C,
    const INT            ldc,
          c128* restrict work,
          INT*           info
);
void zgemqrt(const char *side, const char *trans, const INT m, const INT n, const INT k, const INT nb, const c128 *restrict V, const INT ldv, const c128 *restrict T, const INT ldt, c128 *restrict C, const INT ldc, c128 *restrict work, INT *info)#

ZGEMQRT 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 K elementary reflectors:

Q = H(0) H(1) … H(K-1) = I - V T V^H

generated using the compact WY representation as returned by ZGEQRT.

Q is of order M if SIDE = ‘L’ and of order N if SIDE = ‘R’.

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 C. 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
nb

The block size used for the storage of T. k >= nb >= 1. This must be the same value of nb used to generate T in ZGEQRT.

in
V

Double complex array, dimension (ldv, k). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 0,1,…,k-1, as returned by ZGEQRT in the first k columns of its array argument A.

in
ldv

The leading dimension of the array V. If SIDE = “L”, ldv >= max(1, m); if SIDE = “R”, ldv >= max(1, n).

in
T

Double complex array, dimension (ldt, k). The upper triangular factors of the block reflectors as returned by ZGEQRT, stored as an nb-by-k matrix.

in
ldt

The leading dimension of the array T. ldt >= nb.

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 is n*nb if SIDE = “L”, or m*nb if SIDE = ‘R’.

out
info

  • = 0: successful exit

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