NAME

       sgeqpf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgeqpf (M, N, A, LDA, JPVT, TAU, WORK, INFO)
           SGEQPF

Function/Subroutine Documentation

   subroutine sgeqpf (integerM, integerN, real, dimension( lda, * )A, integerLDA, integer,
       dimension( * )JPVT, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)
       SGEQPF

       Purpose:

            This routine is deprecated and has been replaced by routine SGEQP3.

            SGEQPF computes a QR factorization with column pivoting of a
            real M-by-N matrix A: A*P = Q*R.

       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 upper triangle of the array contains the
                     min(M,N)-by-N upper triangular matrix R; the elements
                     below the diagonal, together with the array TAU,
                     represent the orthogonal matrix Q as a product of
                     min(m,n) elementary reflectors.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A. LDA >= max(1,M).

           JPVT

                     JPVT is INTEGER array, dimension (N)
                     On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
                     to the front of A*P (a leading column); if JPVT(i) = 0,
                     the i-th column of A is a free column.
                     On exit, if JPVT(i) = k, then the i-th column of A*P
                     was the k-th column of A.

           TAU

                     TAU is REAL array, dimension (min(M,N))
                     The scalar factors of the elementary reflectors.

           WORK

                     WORK is REAL array, dimension (3*N)

           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.

       Date:
           November 2011

       Further Details:

             The matrix Q is represented as a product of elementary reflectors

                Q = H(1) H(2) . . . H(n)

             Each H(i) has the form

                H = 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).

             The matrix P is represented in jpvt as follows: If
                jpvt(j) = i
             then the jth column of P is the ith canonical unit vector.

             Partial column norm updating strategy modified by
               Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
               University of Zagreb, Croatia.
             -- April 2011                                                      --
             For more details see LAPACK Working Note 176.

       Definition at line 143 of file sgeqpf.f.

Author

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