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cgeqp3(3P)		    Sun Performance Library		    cgeqp3(3P)

NAME
       cgeqp3 - compute a QR factorization with column pivoting of a matrix A

SYNOPSIS
       SUBROUTINE CGEQP3(M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, INFO)

       COMPLEX A(LDA,*), TAU(*), WORK(*)
       INTEGER M, N, LDA, LWORK, INFO
       INTEGER JPVT(*)
       REAL RWORK(*)

       SUBROUTINE CGEQP3_64(M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
	     INFO)

       COMPLEX A(LDA,*), TAU(*), WORK(*)
       INTEGER*8 M, N, LDA, LWORK, INFO
       INTEGER*8 JPVT(*)
       REAL RWORK(*)

   F95 INTERFACE
       SUBROUTINE GEQP3([M], [N], A, [LDA], JPVT, TAU, [WORK], [LWORK],
	      [RWORK], [INFO])

       COMPLEX, DIMENSION(:) :: TAU, WORK
       COMPLEX, DIMENSION(:,:) :: A
       INTEGER :: M, N, LDA, LWORK, INFO
       INTEGER, DIMENSION(:) :: JPVT
       REAL, DIMENSION(:) :: RWORK

       SUBROUTINE GEQP3_64([M], [N], A, [LDA], JPVT, TAU, [WORK], [LWORK],
	      [RWORK], [INFO])

       COMPLEX, DIMENSION(:) :: TAU, WORK
       COMPLEX, DIMENSION(:,:) :: A
       INTEGER(8) :: M, N, LDA, LWORK, INFO
       INTEGER(8), DIMENSION(:) :: JPVT
       REAL, DIMENSION(:) :: RWORK

   C INTERFACE
       #include <sunperf.h>

       void cgeqp3(int m, int n, complex *a, int lda, int *jpvt, complex *tau,
		 int *info);

       void cgeqp3_64(long m, long n, complex *a, long lda, long  *jpvt,  com‐
		 plex *tau, long *info);

PURPOSE
       cgeqp3  computes a QR factorization with column pivoting of a matrix A:
       A*P = Q*R  using Level 3 BLAS.

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

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

       A (input/output)
		 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  unitary matrix Q as a product of
		 min(M,N) elementary reflectors.

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

       JPVT (input/output)
		 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)
		 The scalar factors of the elementary reflectors.

       WORK (workspace)
		 On exit, if INFO=0, WORK(1) returns the optimal LWORK.

       LWORK (input)
		 The  dimension	 of the array WORK. LWORK >= N+1.  For optimal
		 performance LWORK >= ( 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.

       RWORK (workspace)
		 dimension(2*N)

       INFO (output)
		 = 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'

       where tau is a real/complex 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).

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

				  6 Mar 2009			    cgeqp3(3P)
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