Previous: zgeqlf Up: ../lapack-z.html Next: zgeqr2

NAME ZGEQPF - compute a QR factorization with column pivoting of a complex M-by-N matrix A SYNOPSIS SUBROUTINE ZGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO ) INTEGER INFO, LDA, M, N INTEGER JPVT( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) PURPOSE ZGEQPF computes a QR factorization with column pivoting of a complex M-by-N matrix A: A*P = Q*R. ARGUMENTS M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0 A (input/output) COMPLEX*16 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 triangular matrix R; the elements below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elemen- tary reflectors. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT (input/output) INTEGER array, dimension (N) On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th column of A is a free column. On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A. TAU (output) COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors. WORK (workspace) COMPLEX*16 array, dimension (N) RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) INFO (output) 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(n) Each H(i) has the form H = I - tau * v * v' where tau is a complex scalar, and v is a 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). The matrix P is represented in jpvt as follows: If jpvt(j) = i then the jth column of P is the ith canonical unit vector.