lamswlq(3)

NAME
lamswlq - lamswlq: multiply by Q from laswlq

SYNOPSIS

  Functions
subroutine clamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
CLAMSWLQ
subroutine dlamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
DLAMSWLQ
subroutine slamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
SLAMSWLQ
subroutine zlamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
ZLAMSWLQ

Detailed Description

Function Documentation

  subroutine clamswlq (character side, character trans, integer m, integer n, integer k, integer mb, integer nb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension(ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)

CLAMSWLQ

Purpose:

        CLAMSWLQ overwrites the general complex 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 short wide LQ
        factorization (CLASWLQ)

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 C.  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.
              M >= K >= 0;

    MB

              MB is INTEGER
              The row block size to be used in the blocked LQ.
              M >= MB >= 1

    NB

              NB is INTEGER
              The column block size to be used in the blocked LQ.
              NB > M.

    A

              A is COMPLEX array, dimension
                                   (LDA,M) if SIDE = 'L',
                                   (LDA,N) if SIDE = 'R'
              The i-th row must contain the vector which defines the blocked
              elementary reflector H(i), for i = 1,2,...,k, as returned by
              CLASWLQ in the first k rows of its array argument A.

    LDA

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

    T

              T is COMPLEX array, dimension
              ( M * Number of blocks(CEIL(N-K/NB-K)),
              The blocked upper triangular block reflectors stored in compact form
              as a sequence of upper triangular blocks.  See below
              for further details.

    LDT

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

    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 SIDE = 'L', LWORK >= max(1,NB) * MB;
              if SIDE = 'R', LWORK >= max(1,M) * MB.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK 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:

     Short-Wide LQ (SWLQ) performs LQ by a sequence of unitary transformations,
     representing Q as a product of other unitary matrices
       Q = Q(1) * Q(2) * . . . * Q(k)
     where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
       Q(1) zeros out the upper diagonal entries of rows 1:NB of A
       Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
       Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
       . . .
     Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
     stored under the diagonal of rows 1:MB of A, and by upper triangular
     block reflectors, stored in array T(1:LDT,1:N).
     For more information see Further Details in GELQT.
     Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
     stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
     block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
     The last Q(k) may use fewer rows.
     For more information see Further Details in TPLQT.
     For more details of the overall algorithm, see the description of
     Sequential TSQR in Section 2.2 of [1].
     [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
         J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
         SIAM J. Sci. Comput, vol. 34, no. 1, 2012

Definition at line 195 of file clamswlq.f.

  subroutine dlamswlq (character side, character trans, integer m, integer n, integer k, integer mb, integer nb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension(ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

DLAMSWLQ

Purpose:

        DLAMSWLQ 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 (DLASWLQ)

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 C.  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.
              M >= K >= 0;

    MB

              MB is INTEGER
              The row block size to be used in the blocked LQ.
              M >= MB >= 1

    NB

              NB is INTEGER
              The column block size to be used in the blocked LQ.
              NB > M.

    A

              A is DOUBLE PRECISION array, dimension
                                   (LDA,M) if SIDE = 'L',
                                   (LDA,N) if SIDE = 'R'
              The i-th row must contain the vector which defines the blocked
              elementary reflector H(i), for i = 1,2,...,k, as returned by
              DLASWLQ in the first k rows of its array argument A.

    LDA

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

    T

              T is DOUBLE PRECISION array, dimension
              ( M * Number of blocks(CEIL(N-K/NB-K)),
              The blocked upper triangular block reflectors stored in compact form
              as a sequence of upper triangular blocks.  See below
              for further details.

    LDT

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

    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 SIDE = 'L', LWORK >= max(1,NB) * MB;
              if SIDE = 'R', LWORK >= max(1,M) * MB.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK 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:

     Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations,
     representing Q as a product of other orthogonal matrices
       Q = Q(1) * Q(2) * . . . * Q(k)
     where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
       Q(1) zeros out the upper diagonal entries of rows 1:NB of A
       Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
       Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
       . . .
     Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
     stored under the diagonal of rows 1:MB of A, and by upper triangular
     block reflectors, stored in array T(1:LDT,1:N).
     For more information see Further Details in GELQT.
     Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
     stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
     block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
     The last Q(k) may use fewer rows.
     For more information see Further Details in TPLQT.
     For more details of the overall algorithm, see the description of
     Sequential TSQR in Section 2.2 of [1].
     [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
         J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
         SIAM J. Sci. Comput, vol. 34, no. 1, 2012

Definition at line 195 of file dlamswlq.f.

  subroutine slamswlq (character side, character trans, integer m, integer n, integer k, integer mb, integer nb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension(ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)

SLAMSWLQ

Purpose:

        SLAMSWLQ 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 (SLASWLQ)

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 C.  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.
              M >= K >= 0;

    MB

              MB is INTEGER
              The row block size to be used in the blocked LQ.
              M >= MB >= 1

    NB

              NB is INTEGER
              The column block size to be used in the blocked LQ.
              NB > M.

    A

              A is REAL array, dimension
                                   (LDA,M) if SIDE = 'L',
                                   (LDA,N) if SIDE = 'R'
              The i-th row must contain the vector which defines the blocked
              elementary reflector H(i), for i = 1,2,...,k, as returned by
              SLASWLQ in the first k rows of its array argument A.

    LDA

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

    T

              T is REAL array, dimension
              ( M * Number of blocks(CEIL(N-K/NB-K)),
              The blocked upper triangular block reflectors stored in compact form
              as a sequence of upper triangular blocks.  See below
              for further details.

    LDT

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

    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 SIDE = 'L', LWORK >= max(1,NB) * MB;
              if SIDE = 'R', LWORK >= max(1,M) * MB.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK 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:

     Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations,
     representing Q as a product of other orthogonal matrices
       Q = Q(1) * Q(2) * . . . * Q(k)
     where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
       Q(1) zeros out the upper diagonal entries of rows 1:NB of A
       Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
       Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
       . . .
     Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
     stored under the diagonal of rows 1:MB of A, and by upper triangular
     block reflectors, stored in array T(1:LDT,1:N).
     For more information see Further Details in GELQT.
     Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
     stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
     block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
     The last Q(k) may use fewer rows.
     For more information see Further Details in TPLQT.
     For more details of the overall algorithm, see the description of
     Sequential TSQR in Section 2.2 of [1].
     [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
         J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
         SIAM J. Sci. Comput, vol. 34, no. 1, 2012

Definition at line 195 of file slamswlq.f.

  subroutine zlamswlq (character side, character trans, integer m, integer n, integer k, integer mb, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension(ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)

ZLAMSWLQ

Purpose:

        ZLAMSWLQ 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 blocked
        elementary reflectors computed by short wide LQ
        factorization (ZLASWLQ)

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 C.  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.
              M >= K >= 0;

    MB

              MB is INTEGER
              The row block size to be used in the blocked LQ.
              M >= MB >= 1

    NB

              NB is INTEGER
              The column block size to be used in the blocked LQ.
              NB > M.

    A

              A is COMPLEX*16 array, dimension
                                   (LDA,M) if SIDE = 'L',
                                   (LDA,N) if SIDE = 'R'
              The i-th row must contain the vector which defines the blocked
              elementary reflector H(i), for i = 1,2,...,k, as returned by
              ZLASWLQ in the first k rows of its array argument A.

    LDA

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

    T

              T is COMPLEX*16 array, dimension
              ( M * Number of blocks(CEIL(N-K/NB-K)),
              The blocked upper triangular block reflectors stored in compact form
              as a sequence of upper triangular blocks.  See below
              for further details.

    LDT

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

    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 SIDE = 'L', LWORK >= max(1,NB) * MB;
              if SIDE = 'R', LWORK >= max(1,M) * MB.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK 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:

     Short-Wide LQ (SWLQ) performs LQ by a sequence of unitary transformations,
     representing Q as a product of other unitary matrices
       Q = Q(1) * Q(2) * . . . * Q(k)
     where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
       Q(1) zeros out the upper diagonal entries of rows 1:NB of A
       Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
       Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
       . . .
     Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
     stored under the diagonal of rows 1:MB of A, and by upper triangular
     block reflectors, stored in array T(1:LDT,1:N).
     For more information see Further Details in GELQT.
     Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
     stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
     block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
     The last Q(k) may use fewer rows.
     For more information see Further Details in TPLQT.
     For more details of the overall algorithm, see the description of
     Sequential TSQR in Section 2.2 of [1].
     [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
         J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
         SIAM J. Sci. Comput, vol. 34, no. 1, 2012

Definition at line 195 of file zlamswlq.f.

Author

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