gelqt(3)

NAME
gelqt - gelqt: LQ factor, with T

SYNOPSIS

  Functions
subroutine cgelqt (m, n, mb, a, lda, t, ldt, work, info)
CGELQT
subroutine dgelqt (m, n, mb, a, lda, t, ldt, work, info)
DGELQT
subroutine sgelqt (m, n, mb, a, lda, t, ldt, work, info)
SGELQT
subroutine zgelqt (m, n, mb, a, lda, t, ldt, work, info)
ZGELQT

Detailed Description

Function Documentation

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

CGELQT

Purpose:

     CGELQT computes a blocked LQ factorization of a complex M-by-N matrix A
     using the compact WY representation of Q.

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 >= 0.

    MB

              MB is INTEGER
              The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.

    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 M-by-MIN(M,N) lower trapezoidal matrix L (L is
              lower triangular if M <= N); the elements above the diagonal
              are the rows of V.

    LDA

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

    T

              T is COMPLEX array, dimension (LDT,MIN(M,N))
              The 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.

    WORK

              WORK is COMPLEX array, dimension (MB*N)

    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:

      The matrix V stores the elementary reflectors H(i) in the i-th row
      above the diagonal. For example, if M=5 and N=3, the matrix V is
                   V = (  1  v1 v1 v1 v1 )
                       (     1  v2 v2 v2 )
                       (         1 v3 v3 )
      where the vi's represent the vectors which define H(i), which are returned
      in the matrix A.  The 1's along the diagonal of V are not stored in A.
      Let K=MIN(M,N).  The number of blocks is B = ceiling(K/MB), where each
      block is of order MB except for the last block, which is of order
      IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
      reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
      for the last block) T's are stored in the MB-by-K matrix T as
                   T = (T1 T2 ... TB).

Definition at line 123 of file cgelqt.f.

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

DGELQT

Purpose:

     DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
     using the compact WY representation of Q.

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 >= 0.

    MB

              MB is INTEGER
              The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.

    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 M-by-MIN(M,N) lower trapezoidal matrix L (L is
              lower triangular if M <= N); the elements above the diagonal
              are the rows of V.

    LDA

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

    T

              T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N))
              The 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.

    WORK

              WORK is DOUBLE PRECISION array, dimension (MB*N)

    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:

      The matrix V stores the elementary reflectors H(i) in the i-th row
      above the diagonal. For example, if M=5 and N=3, the matrix V is
                   V = (  1  v1 v1 v1 v1 )
                       (     1  v2 v2 v2 )
                       (         1 v3 v3 )
      where the vi's represent the vectors which define H(i), which are returned
      in the matrix A.  The 1's along the diagonal of V are not stored in A.
      Let K=MIN(M,N).  The number of blocks is B = ceiling(K/MB), where each
      block is of order MB except for the last block, which is of order
      IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
      reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
      for the last block) T's are stored in the MB-by-K matrix T as
                   T = (T1 T2 ... TB).

Definition at line 138 of file dgelqt.f.

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

SGELQT

Purpose:

     DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
     using the compact WY representation of Q.

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 >= 0.

    MB

              MB is INTEGER
              The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.

    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 M-by-MIN(M,N) lower trapezoidal matrix L (L is
              lower triangular if M <= N); the elements above the diagonal
              are the rows of V.

    LDA

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

    T

              T is REAL array, dimension (LDT,MIN(M,N))
              The 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.

    WORK

              WORK is REAL array, dimension (MB*N)

    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:

      The matrix V stores the elementary reflectors H(i) in the i-th row
      above the diagonal. For example, if M=5 and N=3, the matrix V is
                   V = (  1  v1 v1 v1 v1 )
                       (     1  v2 v2 v2 )
                       (         1 v3 v3 )
      where the vi's represent the vectors which define H(i), which are returned
      in the matrix A.  The 1's along the diagonal of V are not stored in A.
      Let K=MIN(M,N).  The number of blocks is B = ceiling(K/MB), where each
      block is of order MB except for the last block, which is of order
      IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
      reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
      for the last block) T's are stored in the MB-by-K matrix T as
                   T = (T1 T2 ... TB).

Definition at line 123 of file sgelqt.f.

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

ZGELQT

Purpose:

     ZGELQT computes a blocked LQ factorization of a complex M-by-N matrix A
     using the compact WY representation of Q.

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 >= 0.

    MB

              MB is INTEGER
              The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.

    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 M-by-MIN(M,N) lower trapezoidal matrix L (L is
              lower triangular if M <= N); the elements above the diagonal
              are the rows of V.

    LDA

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

    T

              T is COMPLEX*16 array, dimension (LDT,MIN(M,N))
              The 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.

    WORK

              WORK is COMPLEX*16 array, dimension (MB*N)

    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:

      The matrix V stores the elementary reflectors H(i) in the i-th row
      above the diagonal. For example, if M=5 and N=3, the matrix V is
                   V = (  1  v1 v1 v1 v1 )
                       (     1  v2 v2 v2 )
                       (         1 v3 v3 )
      where the vi's represent the vectors which define H(i), which are returned
      in the matrix A.  The 1's along the diagonal of V are not stored in A.
      Let K=MIN(M,N).  The number of blocks is B = ceiling(K/MB), where each
      block is of order MB except for the last block, which is of order
      IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
      reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
      for the last block) T's are stored in the MB-by-K matrix T as
                   T = (T1 T2 ... TB).

Definition at line 138 of file zgelqt.f.

Author

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