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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