SRC/dgeqrfp.f(3)           Library Functions Manual           SRC/dgeqrfp.f(3)

NAME
       SRC/dgeqrfp.f

SYNOPSIS
   Functions/Subroutines
       subroutine dgeqrfp (m, n, a, lda, tau, work, lwork, info)
           DGEQRFP

Function/Subroutine Documentation
   subroutine dgeqrfp (integer m, integer n, double precision, dimension( lda,
       * ) a, integer lda, double precision, dimension( * ) tau, double
       precision, dimension( * ) work, integer lwork, integer info)
       DGEQRFP

       Purpose:


            DGEQR2P computes a QR factorization of a real M-by-N matrix A:

               A = Q * ( R ),
                       ( 0 )

            where:

               Q is a M-by-M orthogonal matrix;
               R is an upper-triangular N-by-N matrix with nonnegative diagonal
               entries;
               0 is a (M-N)-by-N 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 above the diagonal of the array
                     contain the min(M,N)-by-N upper trapezoidal matrix R (R is
                     upper triangular if m >= n). The diagonal entries of R
                     are nonnegative; the elements below the diagonal,
                     with the array TAU, represent the orthogonal matrix Q as a
                     product of min(m,n) 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(1) H(2) . . . H(k), 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:m) is stored on exit in A(i+1:m,i),
             and tau in TAU(i).

            See Lapack Working Note 203 for details

       Definition at line 148 of file dgeqrfp.f.

Author
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LAPACK                          Version 3.12.0                SRC/dgeqrfp.f(3)