!>
!> DGEQP3 computes a QR factorization with column pivoting of a
!> matrix A:  A*P = Q*R  using Level 3 BLAS.
!> 

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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors.
!> 

WORK

!>          WORK is DOUBLE PRECISION 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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>  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