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).

Definition at line 128 of file cgelq2.f.

  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).

Definition at line 128 of file dgelq2.f.

  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).

Definition at line 128 of file sgelq2.f.

  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).

Definition at line 128 of file zgelq2.f.

Author

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