gelqt3(3)

NAME
gelqt3 - gelqt3: LQ factor, with T, recursive

SYNOPSIS

  Functions

recursive subroutine cgelqt3 (m, n, a, lda, t, ldt, info)
CGELQT3
recursive subroutine dgelqt3 (m, n, a, lda, t, ldt, info)
DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine sgelqt3 (m, n, a, lda, t, ldt, info)
SGELQT3
recursive subroutine zgelqt3 (m, n, a, lda, t, ldt, info)
ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

Detailed Description

Function Documentation

  recursive subroutine cgelqt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

CGELQT3

Purpose:

    !>
    !> CGELQT3 recursively computes a LQ factorization of a complex M-by-N
    !> matrix A, using the compact WY representation of Q.
    !>
    !> Based on the algorithm of Elmroth and Gustavson,
    !> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M =< N.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the complex M-by-N matrix A.  On exit, the elements on and
    !>          below the diagonal contain the N-by-N lower triangular matrix L; the
    !>          elements above the diagonal are the rows of V.  See below for
    !>          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)
    !>          The N-by-N upper triangular factor of the block reflector.
    !>          The elements on and above the diagonal contain the block
    !>          reflector T; the elements below the diagonal are not used.
    !>          See below for further details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= max(1,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 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.  The
    !>  block reflector H is then given by
    !>
    !>               H = I - V * T * V**T
    !>
    !>  where V**T is the transpose of V.
    !>
    !>  For details of the algorithm, see Elmroth and Gustavson (cited above).
    !>

  recursive subroutine dgelqt3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

    !>
    !> DGELQT3 recursively computes a LQ factorization of a real M-by-N
    !> matrix A, using the compact WY representation of Q.
    !>
    !> Based on the algorithm of Elmroth and Gustavson,
    !> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M =< N.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the real M-by-N matrix A.  On exit, the elements on and
    !>          below the diagonal contain the N-by-N lower triangular matrix L; the
    !>          elements above the diagonal are the rows of V.  See below for
    !>          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)
    !>          The N-by-N upper triangular factor of the block reflector.
    !>          The elements on and above the diagonal contain the block
    !>          reflector T; the elements below the diagonal are not used.
    !>          See below for further details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= max(1,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 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.  The
    !>  block reflector H is then given by
    !>
    !>               H = I - V * T * V**T
    !>
    !>  where V**T is the transpose of V.
    !>
    !>  For details of the algorithm, see Elmroth and Gustavson (cited above).
    !>

  recursive subroutine sgelqt3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

SGELQT3

Purpose:

    !>
    !> SGELQT3 recursively computes a LQ factorization of a real M-by-N
    !> matrix A, using the compact WY representation of Q.
    !>
    !> Based on the algorithm of Elmroth and Gustavson,
    !> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M =< N.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the real M-by-N matrix A.  On exit, the elements on and
    !>          below the diagonal contain the N-by-N lower triangular matrix L; the
    !>          elements above the diagonal are the rows of V.  See below for
    !>          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)
    !>          The N-by-N upper triangular factor of the block reflector.
    !>          The elements on and above the diagonal contain the block
    !>          reflector T; the elements below the diagonal are not used.
    !>          See below for further details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= max(1,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 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.  The
    !>  block reflector H is then given by
    !>
    !>               H = I - V * T * V**T
    !>
    !>  where V**T is the transpose of V.
    !>
    !>  For details of the algorithm, see Elmroth and Gustavson (cited above).
    !>

  recursive subroutine zgelqt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

    !>
    !> ZGELQT3 recursively computes a LQ factorization of a complex M-by-N
    !> matrix A, using the compact WY representation of Q.
    !>
    !> Based on the algorithm of Elmroth and Gustavson,
    !> IBM J. Res. Develop. Vol 44 No. 4 July 2000.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M =< N.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the complex M-by-N matrix A.  On exit, the elements on and
    !>          below the diagonal contain the N-by-N lower triangular matrix L; the
    !>          elements above the diagonal are the rows of V.  See below for
    !>          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)
    !>          The N-by-N upper triangular factor of the block reflector.
    !>          The elements on and above the diagonal contain the block
    !>          reflector T; the elements below the diagonal are not used.
    !>          See below for further details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= max(1,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 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.  The
    !>  block reflector H is then given by
    !>
    !>               H = I - V * T * V**T
    !>
    !>  where V**T is the transpose of V.
    !>
    !>  For details of the algorithm, see Elmroth and Gustavson (cited above).
    !>

Author

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