
NAMEzgeqrt.f SYNOPSISFunctions/Subroutinessubroutine zgeqrt (M, N, NB, A, LDA, T, LDT, WORK, INFO) Function/Subroutine Documentationsubroutine zgeqrt (integerM, integerN, integerNB, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldt, * )T, integerLDT, complex*16, dimension( * )WORK, integerINFO)ZGEQRT Purpose:ZGEQRT computes a blocked QR factorization of a complex MbyN matrix A using the compact WY representation of Q. M
Author:
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.NB NB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.A A is COMPLEX*16 array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)byN upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).T T is COMPLEX*16 array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB.WORK WORK is COMPLEX*16 array, dimension (NB*N)INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
Further Details:
The matrix V stores the elementary reflectors H(i) in the ith column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K  (B1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NBbyNB (and IBbyIB for the last block) T's are stored in the NBbyN matrix T as T = (T1 T2 ... TB). AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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