sgeqp3.f - Man Page

subroutine sgeqp3 (m, n, a, lda, jpvt, tau, work, lwork, info)
SGEQP3

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.

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 150 of file sgeqp3.f.