sgeqp3.f man page




subroutine sgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)

Function/Subroutine Documentation

subroutine sgeqp3 (integer M, integer N, real, dimension( lda, * ) A, integer LDA, integer, dimension( * ) JPVT, real, dimension( * ) TAU, real, dimension( * ) WORK, integer LWORK, integer INFO)



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


          M is INTEGER
          The number of rows of the matrix A. M >= 0.


          N is INTEGER
          The number of columns of the matrix A.  N >= 0.


          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


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


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


          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO=0, WORK(1) returns the optimal 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 is INTEGER
          = 0: successful exit.
          < 0: if INFO = -i, the i-th argument had an illegal value.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


December 2016

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).

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

Definition at line 153 of file sgeqp3.f.


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Referenced By

The man page sgeqp3(3) is an alias of sgeqp3.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK