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dgeqp3.f(3) LAPACK dgeqp3.f(3)dgeqp3.fNAME-Functions/Subroutines subroutine dgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO) DGEQP3SYNOPSISFunction/Subroutine Documentation subroutine dgeqp3 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerLWORK, integerINFO) DGEQP3 Purpose: DGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS. Parameters: M M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. A A is DOUBLE PRECISION 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 LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT JPVT is 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 TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors. WORK WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO=0, WORK(1) returns the optimal LWORK. LWORK LWORK is 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 =, 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 INFO is INTEGER = 0: successful exit. < 0: if INFO =-1, the i-th argument had an illegal value. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 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 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). Contributors: G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA Definition at line 152 of file dgeqp3.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dgeqp3.f(3)

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