gelqf - Man Page

gelqf: LQ factor

Synopsis

Functions

subroutine cgelqf (m, n, a, lda, tau, work, lwork, info)
CGELQF
subroutine dgelqf (m, n, a, lda, tau, work, lwork, info)
DGELQF
subroutine sgelqf (m, n, a, lda, tau, work, lwork, info)
SGELQF
subroutine zgelqf (m, n, a, lda, tau, work, lwork, info)
ZGELQF

Detailed Description

Function Documentation

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

CGELQF  

Purpose:

 CGELQF 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 (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,M).
          For optimum performance LWORK >= M*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 . . . 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 142 of file cgelqf.f.

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

DGELQF  

Purpose:

 DGELQF 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 (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,M).
          For optimum performance LWORK >= M*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(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 142 of file dgelqf.f.

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

SGELQF  

Purpose:

 SGELQF 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 (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,M).
          For optimum performance LWORK >= M*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(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 142 of file sgelqf.f.

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

ZGELQF  

Purpose:

 ZGELQF 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 (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,M).
          For optimum performance LWORK >= M*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 . . . 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 142 of file zgelqf.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK