SGEQP3(3)      LAPACK routine of NEC Numeric Library Collection      SGEQP3(3)



NAME
       SGEQP3

SYNOPSIS
       SUBROUTINE SGEQP3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)



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




ARGUMENTS
           M         (input)
                     M is INTEGER
                     The number of rows of the matrix A. M >= 0.

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

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

           JPVT      (input/output)
                     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       (output)
                     TAU is REAL array, dimension (min(M,N))
                     The scalar factors of the elementary reflectors.

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

           LWORK     (input)
                     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      (output)
                     INFO is INTEGER
                     = 0: successful exit.
                     < 0: if INFO = -i, the i-th argument had an illegal value.






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).



LAPACK routine                  31 October 2017                      SGEQP3(3)