Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - computes a QR factorization with column pivoting of a matrix A

**SYNOPSIS**

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 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 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 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) 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 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**T 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 LAPACK routine (version 3.3.1) April 2011 SGEQP3(3lapack)