geqlf(3)

NAME
geqlf - geqlf: QL factor

SYNOPSIS

  Functions
subroutine cgeqlf (m, n, a, lda, tau, work, lwork, info)
CGEQLF
subroutine dgeqlf (m, n, a, lda, tau, work, lwork, info)
DGEQLF
subroutine sgeqlf (m, n, a, lda, tau, work, lwork, info)
SGEQLF
subroutine zgeqlf (m, n, a, lda, tau, work, lwork, info)
ZGEQLF

Detailed Description

Function Documentation

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

CGEQLF

Purpose:

     CGEQLF 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 (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.  LWORK >= max(1,N).
              For optimum performance LWORK >= N*NB, where NB is
              the optimal blocksize.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 137 of file cgeqlf.f.

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

DGEQLF

Purpose:

     DGEQLF 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 (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.  LWORK >= max(1,N).
              For optimum performance LWORK >= N*NB, where NB is the
              optimal blocksize.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 137 of file dgeqlf.f.

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

SGEQLF

Purpose:

     SGEQLF 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 (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.  LWORK >= max(1,N).
              For optimum performance LWORK >= N*NB, where NB is the
              optimal blocksize.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 137 of file sgeqlf.f.

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

ZGEQLF

Purpose:

     ZGEQLF 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 (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.  LWORK >= max(1,N).
              For optimum performance LWORK >= N*NB, where NB is
              the optimal blocksize.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 137 of file zgeqlf.f.

Author

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