SGEQPF (3) - Linux Man Pages
subroutine sgeqpf (integerM, integerN, real, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)
This routine is deprecated and has been replaced by routine SGEQP3. SGEQPF computes a QR factorization with column pivoting of a real M-by-N matrix A: A*P = Q*R.
M is INTEGER The number of rows of the matrix A. M >= 0.
N is INTEGER The number of columns of the matrix A. N >= 0
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 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) elementary reflectors.
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
JPVT is 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 is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
WORK is REAL array, dimension (3*N)
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
- November 2011
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**T where tau is a real scalar, and v is a real 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. Partial column norm updating strategy modified by Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia. -- April 2011 -- For more details see LAPACK Working Note 176.
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