Library Functions Manual

NAME¶

gemqrt - gemqrt: multiply by Q from geqrt

SYNOPSIS¶

Functions¶

subroutine CGEMQRT (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
CGEMQRT subroutine DGEMQRT (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
DGEMQRT subroutine SGEMQRT (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
SGEMQRT subroutine ZGEMQRT (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
ZGEMQRT

Detailed Description¶

Function Documentation¶

subroutine CGEMQRT (character side, character trans, integer m, integer n, integer k, integer nb, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)¶

CGEMQRT

Purpose:

!>
!> 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 orthogonal matrix defined as the product of K
!> elementary reflectors:
!>
!>       Q = H(1) H(2) . . . H(K) = 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

SIDE

!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**H from the Left;
!>          = 'R': apply Q or Q**H from the Right.
!>

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate transpose, apply Q**H.
!>

!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0.
!>

!>          NB is INTEGER
!>          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.
!>

!>          V is COMPLEX array, dimension (LDV,K)
!>          The i-th column must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          CGEQRT in the first K columns of its array argument A.
!>

LDV

!>          LDV is INTEGER
!>          The leading dimension of the array V.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N).
!>

!>          T is COMPLEX array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by CGEQRT, stored as a NB-by-N matrix.
!>

LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB.
!>

!>          C is 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.
!>

LDC

!>          LDC is INTEGER
!>          The leading dimension of the array C. LDC >= max(1,M).
!>

WORK

!>          WORK is COMPLEX array. The dimension of WORK is
!>           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 166 of file cgemqrt.f.

subroutine DGEMQRT (character side, character trans, integer m, integer n, integer k, integer nb, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)¶

DGEMQRT

Purpose:

!>
!> 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(1) H(2) . . . H(K) = 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

SIDE

!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**T from the Left;
!>          = 'R': apply Q or Q**T from the Right.
!>

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Transpose, apply Q**T.
!>

!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0.
!>

!>          NB is INTEGER
!>          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.
!>

!>          V is DOUBLE PRECISION array, dimension (LDV,K)
!>          The i-th column must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          DGEQRT in the first K columns of its array argument A.
!>

LDV

!>          LDV is INTEGER
!>          The leading dimension of the array V.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N).
!>

!>          T is DOUBLE PRECISION array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by DGEQRT, stored as a NB-by-N matrix.
!>

LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB.
!>

!>          C is 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.
!>

LDC

!>          LDC is INTEGER
!>          The leading dimension of the array C. LDC >= max(1,M).
!>

WORK

!>          WORK is DOUBLE PRECISION array. The dimension of
!>          WORK is N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 166 of file dgemqrt.f.

subroutine SGEMQRT (character side, character trans, integer m, integer n, integer k, integer nb, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)¶

SGEMQRT

Purpose:

!>
!> 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(1) H(2) . . . H(K) = 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

SIDE

!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**T from the Left;
!>          = 'R': apply Q or Q**T from the Right.
!>

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'T':  Transpose, apply Q**T.
!>

!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0.
!>

!>          NB is INTEGER
!>          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.
!>

!>          V is REAL array, dimension (LDV,K)
!>          The i-th column must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          SGEQRT in the first K columns of its array argument A.
!>

LDV

!>          LDV is INTEGER
!>          The leading dimension of the array V.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N).
!>

!>          T is REAL array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by SGEQRT, stored as a NB-by-N matrix.
!>

LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB.
!>

!>          C is REAL 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.
!>

LDC

!>          LDC is INTEGER
!>          The leading dimension of the array C. LDC >= max(1,M).
!>

WORK

!>          WORK is REAL array. The dimension of WORK is
!>           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 166 of file sgemqrt.f.

subroutine ZGEMQRT (character side, character trans, integer m, integer n, integer k, integer nb, complex16, dimension( ldv, ) v, integer ldv, complex16, dimension( ldt, ) t, integer ldt, complex16, dimension( ldc, ) c, integer ldc, complex16, dimension( ) work, integer info)¶

ZGEMQRT

Purpose:

!>
!> 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 orthogonal matrix defined as the product of K
!> elementary reflectors:
!>
!>       Q = H(1) H(2) . . . H(K) = 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

SIDE

!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**H from the Left;
!>          = 'R': apply Q or Q**H from the Right.
!>

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate transpose, apply Q**H.
!>

!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>

!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>

!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0.
!>

!>          NB is INTEGER
!>          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.
!>

!>          V is COMPLEX*16 array, dimension (LDV,K)
!>          The i-th column must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,...,k, as returned by
!>          ZGEQRT in the first K columns of its array argument A.
!>

LDV

!>          LDV is INTEGER
!>          The leading dimension of the array V.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N).
!>

!>          T is COMPLEX*16 array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by ZGEQRT, stored as a NB-by-N matrix.
!>

LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB.
!>

!>          C is COMPLEX*16 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.
!>

LDC

!>          LDC is INTEGER
!>          The leading dimension of the array C. LDC >= max(1,M).
!>

WORK

!>          WORK is COMPLEX*16 array. The dimension of WORK is
!>           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 166 of file zgemqrt.f.

Author¶

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LAPACK

Source file:	gemqrt.3.en.gz (from lapack-man 3.12.0-3.2)
Source last updated:	2024-11-04T16:48:44Z
Converted to HTML:	2025-01-18T04:10:05Z

NAME¶

SYNOPSIS¶

Functions¶

Detailed Description¶

Function Documentation¶

subroutine CGEMQRT (character side, character trans, integer m, integer n, integer k, integer nb, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)¶

subroutine SGEMQRT (character side, character trans, integer m, integer n, integer k, integer nb, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)¶

subroutine ZGEMQRT (character side, character trans, integer m, integer n, integer k, integer nb, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)¶

Author¶

subroutine ZGEMQRT (character side, character trans, integer m, integer n, integer k, integer nb, complex16, dimension( ldv, ) v, integer ldv, complex16, dimension( ldt, ) t, integer ldt, complex16, dimension( ldc, ) c, integer ldc, complex16, dimension( ) work, integer info)¶