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## sgeqp3()

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

Download SGEQP3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

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

Parameters

  [in]

  M

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

  [in]

  N

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

  [in,out]

  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.
      !>

  [in]

  LDA

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

  [in,out]

  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.
      !>

  [out]

  TAU

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

  [out]

  WORK

      !>          WORK is REAL array, dimension (MAX(1,LWORK))
      !>          On exit, if INFO=0, WORK(1) returns the optimal LWORK.
      !>

  [in]

  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.
      !>

  [out]

  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