geqrt3(3)

NAME
geqrt3 - geqrt3: QR factor, with T, recursive panel

SYNOPSIS

  Functions

recursive subroutine cgeqrt3 (m, n, a, lda, t, ldt, info)
CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine dgeqrt3 (m, n, a, lda, t, ldt, info)
DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine sgeqrt3 (m, n, a, lda, t, ldt, info)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine zgeqrt3 (m, n, a, lda, t, ldt, info)
ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Detailed Description

Function Documentation

  recursive subroutine cgeqrt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

    !>
    !> CGEQRT3 recursively computes a QR 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
    !>          above the diagonal contain the N-by-N upper triangular matrix R; the
    !>          elements below the diagonal are the columns 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 column
    !>  below the diagonal. For example, if M=5 and N=3, the matrix V is
    !>
    !>               V = (  1       )
    !>                   ( v1  1    )
    !>                   ( v1 v2  1 )
    !>                   ( v1 v2 v3 )
    !>                   ( v1 v2 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**H
    !>
    !>  where V**H is the conjugate transpose of V.
    !>
    !>  For details of the algorithm, see Elmroth and Gustavson (cited above).
    !>

  recursive subroutine dgeqrt3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

    !>
    !> DGEQRT3 recursively computes a QR 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
    !>          above the diagonal contain the N-by-N upper triangular matrix R; the
    !>          elements below the diagonal are the columns 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 column
    !>  below the diagonal. For example, if M=5 and N=3, the matrix V is
    !>
    !>               V = (  1       )
    !>                   ( v1  1    )
    !>                   ( v1 v2  1 )
    !>                   ( v1 v2 v3 )
    !>                   ( v1 v2 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 sgeqrt3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

    !>
    !> SGEQRT3 recursively computes a QR 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
    !>          above the diagonal contain the N-by-N upper triangular matrix R; the
    !>          elements below the diagonal are the columns 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 column
    !>  below the diagonal. For example, if M=5 and N=3, the matrix V is
    !>
    !>               V = (  1       )
    !>                   ( v1  1    )
    !>                   ( v1 v2  1 )
    !>                   ( v1 v2 v3 )
    !>                   ( v1 v2 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 zgeqrt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

    !>
    !> ZGEQRT3 recursively computes a QR 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 above the diagonal contain the N-by-N upper triangular matrix R;
    !>          the elements below the diagonal are the columns 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 column
    !>  below the diagonal. For example, if M=5 and N=3, the matrix V is
    !>
    !>               V = (  1       )
    !>                   ( v1  1    )
    !>                   ( v1 v2  1 )
    !>                   ( v1 v2 v3 )
    !>                   ( v1 v2 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**H
    !>
    !>  where V**H is the conjugate transpose of V.
    !>
    !>  For details of the algorithm, see Elmroth and Gustavson (cited above).
    !>

Author

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