sgeqp3.f(3)

NAME
sgeqp3.f -

SYNOPSIS

  Functions/Subroutines
subroutine sgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
SGEQP3

Function/Subroutine Documentation

  subroutine sgeqp3 (integerM, integerN, real, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, real, dimension( * )TAU, real, dimension( * )WORK, integerLWORK, integerINFO)

SGEQP3

Purpose:

     SGEQP3 computes a QR factorization with column pivoting of a
     matrix A:  A*P = Q*R  using Level 3 BLAS.

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 trapezoidal 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(J).ne.0, the J-th column of A is permuted
              to the front of A*P (a leading column); if JPVT(J)=0,
              the J-th column of A is a free column.
              On exit, if JPVT(J)=K, then the J-th column of A*P was the
              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 (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 >= 3*N+1.
              For optimal performance LWORK >= 2*N+( N+1 )*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.

Date:
    September 2012

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/complex 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).

Contributors:
    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA

Definition at line 152 of file sgeqp3.f.

Author

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