gelqf(3)

NAME
gelqf - 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 >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
    !>          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 143 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 >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
    !>          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 143 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 >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
    !>          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 143 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 >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
    !>          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 143 of file zgelqf.f.

Author

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