subroutine zgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, INFO)
subroutine zgeqp3 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)ZGEQP3 Purpose:
ZGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.
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 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 trapezoidal 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
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 COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors.WORK
WORK is COMPLEX*16 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 >= N+1. For optimal performance LWORK >= ( 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.RWORK
RWORK is DOUBLE PRECISION array, dimension (2*N)INFO
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 NAG Ltd.Date:
September 2012Further 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**H where tau is a 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).
G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USADefinition at line 159 of file zgeqp3.f.