geql2(3)

NAME
geql2 - geql2: QL factor, level 2

SYNOPSIS

  Functions
subroutine cgeql2 (m, n, a, lda, tau, work, info)
CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.
subroutine dgeql2 (m, n, a, lda, tau, work, info)
DGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.
subroutine sgeql2 (m, n, a, lda, tau, work, info)
SGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.
subroutine zgeql2 (m, n, a, lda, tau, work, info)
ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Detailed Description

Function Documentation

  subroutine cgeql2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

     CGEQL2 computes a QL factorization of a complex m by n matrix A:
     A = Q * L.

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, if m >= n, the lower triangle of the subarray
              A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
              if m <= n, the elements on and below the (n-m)-th
              superdiagonal contain the m by n lower trapezoidal matrix L;
              the remaining elements, 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 (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 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**H
      where tau is a complex scalar, and v is a complex vector with
      v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
      A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line 122 of file cgeql2.f.

  subroutine dgeql2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

     DGEQL2 computes a QL factorization of a real m by n matrix A:
     A = Q * L.

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, if m >= n, the lower triangle of the subarray
              A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
              if m <= n, the elements on and below the (n-m)-th
              superdiagonal contain the m by n lower trapezoidal matrix L;
              the remaining elements, 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 (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 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
      A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line 122 of file dgeql2.f.

  subroutine sgeql2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

     SGEQL2 computes a QL factorization of a real m by n matrix A:
     A = Q * L.

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, if m >= n, the lower triangle of the subarray
              A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
              if m <= n, the elements on and below the (n-m)-th
              superdiagonal contain the m by n lower trapezoidal matrix L;
              the remaining elements, 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 (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 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
      A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line 122 of file sgeql2.f.

  subroutine zgeql2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

     ZGEQL2 computes a QL factorization of a complex m by n matrix A:
     A = Q * L.

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, if m >= n, the lower triangle of the subarray
              A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
              if m <= n, the elements on and below the (n-m)-th
              superdiagonal contain the m by n lower trapezoidal matrix L;
              the remaining elements, 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 (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 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**H
      where tau is a complex scalar, and v is a complex vector with
      v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
      A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line 122 of file zgeql2.f.

Author

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