zgeqpf (l) - Linux Man Pages
zgeqpf: routine i deprecated and has been replaced by routine ZGEQP3
NAMEZGEQPF - routine i deprecated and has been replaced by routine ZGEQP3
- 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( * )
PURPOSEThis routine is deprecated and has been replaced by routine ZGEQP3. ZGEQPF computes a QR factorization with column pivoting of a complex M-by-N matrix A: A*P = Q*R.
- 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 unitary matrix Q as a product of min(m,n) elementary 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 DETAILSThe matrix Q is represented as a product of elementary reflectors
Each H(i) has the form
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
then the jth column of P is the ith canonical unit vector. Partial column norm updating strategy modified by
For more details see LAPACK Working Note 176.