sgeqp3 (l)  Linux Manuals
sgeqp3: computes a QR factorization with column pivoting of a matrix A
NAME
SGEQP3  computes a QR factorization with column pivoting of a matrix ASYNOPSIS
 SUBROUTINE SGEQP3(
 M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
 INTEGER INFO, LDA, LWORK, M, N
 INTEGER JPVT( * )
 REAL A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
SGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.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) REAL array, dimension (LDA,N)
 On entry, the MbyN matrix A. On exit, the upper triangle of the array contains the min(M,N)byN 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) INTEGER
 The leading dimension of the array A. LDA >= max(1,M).
 JPVT (input/output) INTEGER array, dimension (N)
 On entry, if JPVT(J).ne.0, the Jth column of A is permuted to the front of A*P (a leading column); if JPVT(J)=0, the Jth column of A is a free column. On exit, if JPVT(J)=K, then the Jth column of A*P was the the Kth column of A.
 TAU (output) REAL array, dimension (min(M,N))
 The scalar factors of the elementary reflectors.
 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
 On exit, if INFO=0, WORK(1) returns the optimal LWORK.
 LWORK (input) 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) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectorsQ
Each H(i) has the form
H(i)
where tau is a real/complex scalar, and v is a real/complex vector with v(1:i1) = 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