gelq2(3)

NAME
gelq2 - gelq2: LQ factor, level 2

SYNOPSIS

  Functions

subroutine cgelq2 (m, n, a, lda, tau, work, info)
CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
subroutine dgelq2 (m, n, a, lda, tau, work, info)
DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
subroutine sgelq2 (m, n, a, lda, tau, work, info)
SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
subroutine zgelq2 (m, n, a, lda, tau, work, info)
ZGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Detailed Description

Function Documentation

  subroutine cgelq2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

    !>
    !> CGELQ2 computes an LQ factorization of a complex m-by-n matrix A:
    !>
    !>    A = ( L 0 ) *  Q
    !>
    !> where:
    !>
    !>    Q is a n-by-n orthogonal matrix;
    !>    L is a lower-triangular m-by-m matrix;
    !>    0 is a m-by-(n-m) zero matrix, if m < n.
    !>
    !>

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.
    !>

    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,
    !>          with the array TAU, represent the unitary matrix Q as a
    !>          product of elementary reflectors (see Further Details).
    !>

    LDA

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

    TAU

    !>          TAU is COMPLEX array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors (see Further
    !>          Details).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (M)
    !>

    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 Q is represented as a product of elementary reflectors
    !>
    !>     Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - tau * v * v**H
    !>
    !>  where tau is a complex scalar, and v is a complex vector with
    !>  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
    !>  A(i,i+1:n), and tau in TAU(i).
    !>

  subroutine dgelq2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

    !>
    !> DGELQ2 computes an LQ factorization of a real m-by-n matrix A:
    !>
    !>    A = ( L 0 ) *  Q
    !>
    !> where:
    !>
    !>    Q is a n-by-n orthogonal matrix;
    !>    L is a lower-triangular m-by-m matrix;
    !>    0 is a m-by-(n-m) zero matrix, if m < n.
    !>
    !>

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.
    !>

    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,
    !>          with the array TAU, represent the orthogonal matrix Q as a
    !>          product of elementary reflectors (see Further Details).
    !>

    LDA

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

    TAU

    !>          TAU is DOUBLE PRECISION array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors (see Further
    !>          Details).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (M)
    !>

    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 Q is represented as a product of elementary reflectors
    !>
    !>     Q = H(k) . . . H(2) H(1), where k = min(m,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - tau * v * v**T
    !>
    !>  where tau is a real scalar, and v is a real vector with
    !>  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
    !>  and tau in TAU(i).
    !>

  subroutine sgelq2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

    !>
    !> SGELQ2 computes an LQ factorization of a real m-by-n matrix A:
    !>
    !>    A = ( L 0 ) *  Q
    !>
    !> where:
    !>
    !>    Q is a n-by-n orthogonal matrix;
    !>    L is a lower-triangular m-by-m matrix;
    !>    0 is a m-by-(n-m) zero matrix, if m < n.
    !>
    !>

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.
    !>

    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,
    !>          with the array TAU, represent the orthogonal matrix Q as a
    !>          product of elementary reflectors (see Further Details).
    !>

    LDA

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

    TAU

    !>          TAU is REAL array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors (see Further
    !>          Details).
    !>

    WORK

    !>          WORK is REAL array, dimension (M)
    !>

    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 Q is represented as a product of elementary reflectors
    !>
    !>     Q = H(k) . . . H(2) H(1), where k = min(m,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - tau * v * v**T
    !>
    !>  where tau is a real scalar, and v is a real vector with
    !>  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
    !>  and tau in TAU(i).
    !>

  subroutine zgelq2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

    !>
    !> ZGELQ2 computes an LQ factorization of a complex m-by-n matrix A:
    !>
    !>    A = ( L 0 ) *  Q
    !>
    !> where:
    !>
    !>    Q is a n-by-n orthogonal matrix;
    !>    L is a lower-triangular m-by-m matrix;
    !>    0 is a m-by-(n-m) zero matrix, if m < n.
    !>
    !>

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.
    !>

    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,
    !>          with the array TAU, represent the unitary matrix Q as a
    !>          product of elementary reflectors (see Further Details).
    !>

    LDA

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

    TAU

    !>          TAU is COMPLEX*16 array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors (see Further
    !>          Details).
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (M)
    !>

    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 Q is represented as a product of elementary reflectors
    !>
    !>     Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
    !>
    !>  Each H(i) has the form
    !>
    !>     H(i) = I - tau * v * v**H
    !>
    !>  where tau is a complex scalar, and v is a complex vector with
    !>  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
    !>  A(i,i+1:n), and tau in TAU(i).
    !>

Author

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