laswlq - Man Page

laswlq: short-wide LQ factor

Synopsis

Functions

subroutine claswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
CLASWLQ
subroutine dlaswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
DLASWLQ
subroutine slaswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
SLASWLQ
subroutine zlaswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
ZLASWLQ

Detailed Description

Function Documentation

subroutine claswlq (integer m, integer n, integer mb, integer nb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, *) t, integer ldt, complex, dimension( * ) work, integer lwork, integer info)

CLASWLQ

Purpose:

 CLASWLQ computes a blocked Tall-Skinny LQ factorization of
 a complex M-by-N matrix A for M <= N:

    A = ( L 0 ) *  Q,

 where:

    Q is a n-by-N orthogonal matrix, stored on exit in an implicit
    form in the elements above the diagonal of the array A and in
    the elements of the array T;
    L is a lower-triangular M-by-M matrix stored on exit in
    the elements on and below the diagonal of the array A.
    0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.
Parameters

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 A.  N >= M >= 0.

MB

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

NB

          NB is INTEGER
          The column block size to be used in the blocked QR.
          NB > 0.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and below the diagonal
          of the array contain the N-by-N lower triangular matrix L;
          the elements above the diagonal represent Q by the rows
          of blocked V (see Further Details).

LDA

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

T

          T is COMPLEX array,
          dimension (LDT, N * Number_of_row_blocks)
          where Number_of_row_blocks = CEIL((N-M)/(NB-M))
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.
          See Further Details below.

LDT

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

WORK

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

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= MB*M.
          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 TPQRT.

 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 165 of file claswlq.f.

subroutine dlaswlq (integer m, integer n, integer mb, integer nb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, *) t, integer ldt, double precision, dimension( * ) work, integer lwork, integer info)

DLASWLQ

Purpose:

 DLASWLQ computes a blocked Tall-Skinny LQ factorization of
 a real M-by-N matrix A for M <= N:

    A = ( L 0 ) *  Q,

 where:

    Q is a n-by-N orthogonal matrix, stored on exit in an implicit
    form in the elements above the diagonal of the array A and in
    the elements of the array T;
    L is a lower-triangular M-by-M matrix stored on exit in
    the elements on and below the diagonal of the array A.
    0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.
Parameters

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 A.  N >= M >= 0.

MB

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

NB

          NB is INTEGER
          The column block size to be used in the blocked QR.
          NB > 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and below the diagonal
          of the array contain the N-by-N lower triangular matrix L;
          the elements above the diagonal represent Q by the rows
          of blocked V (see Further Details).

LDA

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

T

          T is DOUBLE PRECISION array,
          dimension (LDT, N * Number_of_row_blocks)
          where Number_of_row_blocks = CEIL((N-M)/(NB-M))
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.
          See Further Details below.

LDT

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

WORK

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

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= MB*M.
          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 TPQRT.

 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 165 of file dlaswlq.f.

subroutine slaswlq (integer m, integer n, integer mb, integer nb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, *) t, integer ldt, real, dimension( * ) work, integer lwork, integer info)

SLASWLQ

Purpose:

 SLASWLQ computes a blocked Tall-Skinny LQ factorization of
 a real M-by-N matrix A for M <= N:

    A = ( L 0 ) *  Q,

 where:

    Q is a n-by-N orthogonal matrix, stored on exit in an implicit
    form in the elements above the diagonal of the array A and in
    the elements of the array T;
    L is a lower-triangular M-by-M matrix stored on exit in
    the elements on and below the diagonal of the array A.
    0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.
Parameters

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 A.  N >= M >= 0.

MB

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

NB

          NB is INTEGER
          The column block size to be used in the blocked QR.
          NB > 0.

A

          A is REAL array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and below the diagonal
          of the array contain the N-by-N lower triangular matrix L;
          the elements above the diagonal represent Q by the rows
          of blocked V (see Further Details).

LDA

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

T

          T is REAL array,
          dimension (LDT, N * Number_of_row_blocks)
          where Number_of_row_blocks = CEIL((N-M)/(NB-M))
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.
          See Further Details below.

LDT

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

WORK

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

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= MB * M.
          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 TPQRT.

 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 165 of file slaswlq.f.

subroutine zlaswlq (integer m, integer n, integer mb, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, *) t, integer ldt, complex*16, dimension( * ) work, integer lwork, integer info)

ZLASWLQ

Purpose:

 ZLASWLQ computes a blocked Tall-Skinny LQ factorization of
 a complexx M-by-N matrix A for M <= N:

    A = ( L 0 ) *  Q,

 where:

    Q is a n-by-N orthogonal matrix, stored on exit in an implicit
    form in the elements above the diagonal of the array A and in
    the elements of the array T;
    L is a lower-triangular M-by-M matrix stored on exit in
    the elements on and below the diagonal of the array A.
    0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.
Parameters

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 A.  N >= M >= 0.

MB

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

NB

          NB is INTEGER
          The column block size to be used in the blocked QR.
          NB > 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and below the diagonal
          of the array contain the N-by-N lower triangular matrix L;
          the elements above the diagonal represent Q by the rows
          of blocked V (see Further Details).

LDA

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

T

          T is COMPLEX*16 array,
          dimension (LDT, N * Number_of_row_blocks)
          where Number_of_row_blocks = CEIL((N-M)/(NB-M))
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.
          See Further Details below.

LDT

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

WORK

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

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= MB*M.
          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 TPQRT.

 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 165 of file zlaswlq.f.

Author

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