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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