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).
    !>

  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).
    !>

  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:

    !>
    !> SGELQT 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).
    !>

  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).
    !>

Author

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