gemlq - Man Page

gemlq: multiply by Q from gelq

Synopsis

Functions

subroutine cgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
CGEMLQ
subroutine dgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
DGEMLQ
subroutine sgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
SGEMLQ
subroutine zgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
ZGEMLQ

Detailed Description

Function Documentation

subroutine cgemlq (character side, character trans, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) t, integer tsize, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)

CGEMLQ

Purpose:

     CGEMLQ overwrites the general real 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 short wide
      LQ factorization (CGELQ)
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

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

N

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

K

          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.

A

          A is COMPLEX array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          Part of the data structure to represent Q as returned by CGELQ.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,K).

T

          T is COMPLEX array, dimension (MAX(5,TSIZE)).
          Part of the data structure to represent Q as returned by CGELQ.

TSIZE

          TSIZE is INTEGER
          The dimension of the array T. TSIZE >= 5.

C

          C is COMPLEX array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

LDC

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

WORK

         (workspace) COMPLEX array, dimension (MAX(1,LWORK))

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1, then a workspace query is assumed. The routine
          only calculates the size of the WORK array, returns this
          value as WORK(1), and no error message related to WORK
          is issued by XERBLA.

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.

Further Details

 These details are particular for this LAPACK implementation. Users should not
 take them for granted. These details may change in the future, and are not likely
 true for another LAPACK implementation. These details are relevant if one wants
 to try to understand the code. They are not part of the interface.

 In this version,

          T(2): row block size (MB)
          T(3): column block size (NB)
          T(6:TSIZE): data structure needed for Q, computed by
                           CLASWQR or CGELQT

  Depending on the matrix dimensions M and N, and row and column
  block sizes MB and NB returned by ILAENV, CGELQ will use either
  CLASWLQ (if the matrix is wide-and-short) or CGELQT to compute
  the LQ factorization.
  This version of CGEMLQ will use either CLAMSWLQ or CGEMLQT to
  multiply matrix Q by another matrix.
  Further Details in CLAMSWLQ or CGEMLQT.

Definition at line 170 of file cgemlq.f.

subroutine dgemlq (character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) t, integer tsize, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

DGEMLQ

Purpose:

     DGEMLQ 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 short wide LQ
    factorization (DGELQ)
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

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

N

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

K

          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.

A

          A is DOUBLE PRECISION array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          Part of the data structure to represent Q as returned by DGELQ.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,K).

T

          T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).
          Part of the data structure to represent Q as returned by DGELQ.

TSIZE

          TSIZE is INTEGER
          The dimension of the array T. TSIZE >= 5.

C

          C is DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

LDC

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

WORK

         (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1, then a workspace query is assumed. The routine
          only calculates the size of the WORK array, returns this
          value as WORK(1), and no error message related to WORK
          is issued by XERBLA.

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.

Further Details

 These details are particular for this LAPACK implementation. Users should not
 take them for granted. These details may change in the future, and are not likely
 true for another LAPACK implementation. These details are relevant if one wants
 to try to understand the code. They are not part of the interface.

 In this version,

          T(2): row block size (MB)
          T(3): column block size (NB)
          T(6:TSIZE): data structure needed for Q, computed by
                           DLASWLQ or DGELQT

  Depending on the matrix dimensions M and N, and row and column
  block sizes MB and NB returned by ILAENV, DGELQ will use either
  DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute
  the LQ factorization.
  This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to
  multiply matrix Q by another matrix.
  Further Details in DLAMSWLQ or DGEMLQT.

Definition at line 171 of file dgemlq.f.

subroutine sgemlq (character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) t, integer tsize, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)

SGEMLQ

Purpose:

     SGEMLQ 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 short wide LQ
    factorization (SGELQ)
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

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

N

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

K

          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.

A

          A is REAL array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          Part of the data structure to represent Q as returned by DGELQ.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,K).

T

          T is REAL array, dimension (MAX(5,TSIZE)).
          Part of the data structure to represent Q as returned by SGELQ.

TSIZE

          TSIZE is INTEGER
          The dimension of the array T. TSIZE >= 5.

C

          C is REAL array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

LDC

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

WORK

         (workspace) REAL array, dimension (MAX(1,LWORK))

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1, then a workspace query is assumed. The routine
          only calculates the size of the WORK array, returns this
          value as WORK(1), and no error message related to WORK
          is issued by XERBLA.

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.

Further Details

 These details are particular for this LAPACK implementation. Users should not
 take them for granted. These details may change in the future, and are not likely
 true for another LAPACK implementation. These details are relevant if one wants
 to try to understand the code. They are not part of the interface.

 In this version,

          T(2): row block size (MB)
          T(3): column block size (NB)
          T(6:TSIZE): data structure needed for Q, computed by
                           SLASWLQ or SGELQT

  Depending on the matrix dimensions M and N, and row and column
  block sizes MB and NB returned by ILAENV, SGELQ will use either
  SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute
  the LQ factorization.
  This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to
  multiply matrix Q by another matrix.
  Further Details in SLAMSWLQ or SGEMLQT.

Definition at line 170 of file sgemlq.f.

subroutine zgemlq (character side, character trans, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) t, integer tsize, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)

ZGEMLQ

Purpose:

     ZGEMLQ overwrites the general real 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 short wide
      LQ factorization (ZGELQ)
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

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

N

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

K

          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.

A

          A is COMPLEX*16 array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          Part of the data structure to represent Q as returned by ZGELQ.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,K).

T

          T is COMPLEX*16 array, dimension (MAX(5,TSIZE)).
          Part of the data structure to represent Q as returned by ZGELQ.

TSIZE

          TSIZE is INTEGER
          The dimension of the array T. TSIZE >= 5.

C

          C is COMPLEX*16 array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

LDC

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

WORK

         (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If LWORK = -1, then a workspace query is assumed. The routine
          only calculates the size of the WORK array, returns this
          value as WORK(1), and no error message related to WORK
          is issued by XERBLA.

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.

Further Details

 These details are particular for this LAPACK implementation. Users should not
 take them for granted. These details may change in the future, and are not likely
 true for another LAPACK implementation. These details are relevant if one wants
 to try to understand the code. They are not part of the interface.

 In this version,

          T(2): row block size (MB)
          T(3): column block size (NB)
          T(6:TSIZE): data structure needed for Q, computed by
                           ZLASWLQ or ZGELQT

  Depending on the matrix dimensions M and N, and row and column
  block sizes MB and NB returned by ILAENV, ZGELQ will use either
  ZLASWLQ (if the matrix is wide-and-short) or ZGELQT to compute
  the LQ factorization.
  This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to
  multiply matrix Q by another matrix.
  Further Details in ZLAMSWLQ or ZGEMLQT.

Definition at line 169 of file zgemlq.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK