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.

December 2016

  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