Provided by: liblapack-doc_3.12.0-3build1.1_all bug

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 >= 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).

   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).

   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).

   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).

Author

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