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gemqr(3) Library Functions Manual gemqr(3)

NAME

gemqr - gemqr: multiply by Q from geqr

SYNOPSIS

Functions


subroutine CGEMQR (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
CGEMQR subroutine DGEMQR (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
DGEMQR subroutine SGEMQR (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
SGEMQR subroutine ZGEMQR (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
ZGEMQR

Detailed Description

Function Documentation

subroutine CGEMQR (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)

CGEMQR

Purpose:

!>
!> CGEMQR overwrites the general real M-by-N matrix C with
!>
!>                      SIDE = 'L'     SIDE = 'R'
!>      TRANS = 'N':      Q * C          C * Q
!>      TRANS = 'T':      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

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,K)
!>          Part of the data structure to represent Q as returned by CGEQR.
!>

LDA

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

T

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

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
!>                           CLATSQR or CGEQRT
!>
!>  Depending on the matrix dimensions M and N, and row and column
!>  block sizes MB and NB returned by ILAENV, CGEQR will use either
!>  CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute
!>  the QR factorization.
!>  This version of CGEMQR will use either CLAMTSQR or CGEMQRT to
!>  multiply matrix Q by another matrix.
!>  Further Details in CLAMTSQR or CGEMQRT.
!>
!>

Definition at line 172 of file cgemqr.f.

subroutine DGEMQR (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)

DGEMQR

Purpose:

!>
!> 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

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,K)
!>          Part of the data structure to represent Q as returned by DGEQR.
!>

LDA

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

T

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

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
!>                           DLATSQR or DGEQRT
!>
!>  Depending on the matrix dimensions M and N, and row and column
!>  block sizes MB and NB returned by ILAENV, DGEQR will use either
!>  DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute
!>  the QR factorization.
!>  This version of DGEMQR will use either DLAMTSQR or DGEMQRT to
!>  multiply matrix Q by another matrix.
!>  Further Details in DLATMSQR or DGEMQRT.
!>
!>

Definition at line 172 of file dgemqr.f.

subroutine SGEMQR (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)

SGEMQR

Purpose:

!>
!> 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

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,K)
!>          Part of the data structure to represent Q as returned by SGEQR.
!>

LDA

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

T

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

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
!>                           SLATSQR or SGEQRT
!>
!>  Depending on the matrix dimensions M and N, and row and column
!>  block sizes MB and NB returned by ILAENV, SGEQR will use either
!>  SLATSQR (if the matrix is tall-and-skinny) or SGEQRT to compute
!>  the QR factorization.
!>  This version of SGEMQR will use either SLAMTSQR or SGEMQRT to
!>  multiply matrix Q by another matrix.
!>  Further Details in SLAMTSQR or SGEMQRT.
!>
!>

Definition at line 172 of file sgemqr.f.

subroutine ZGEMQR (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)

ZGEMQR

Purpose:

!>
!> ZGEMQR overwrites the general real M-by-N matrix C with
!>
!>                      SIDE = 'L'     SIDE = 'R'
!>      TRANS = 'N':      Q * C          C * Q
!>      TRANS = 'T':      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

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,K)
!>          Part of the data structure to represent Q as returned by ZGEQR.
!>

LDA

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

T

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

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
!>                           ZLATSQR or ZGEQRT
!>
!>  Depending on the matrix dimensions M and N, and row and column
!>  block sizes MB and NB returned by ILAENV, ZGEQR will use either
!>  ZLATSQR (if the matrix is tall-and-skinny) or ZGEQRT to compute
!>  the QR factorization.
!>  This version of ZGEMQR will use either ZLAMTSQR or ZGEMQRT to
!>  multiply matrix Q by another matrix.
!>  Further Details in ZLAMTSQR or ZGEMQRT.
!>
!>

Definition at line 172 of file zgemqr.f.

Author

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