
NAMEzgeqrt3.f SYNOPSISFunctions/Subroutinesrecursive subroutine zgeqrt3 (M, N, A, LDA, T, LDT, INFO) Function/Subroutine Documentationrecursive subroutine zgeqrt3 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldt, * )T, integerLDT, integerINFO)ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Purpose:ZGEQRT3 recursively computes a QR factorization of a complex MbyN matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000. M
Author:
M is INTEGER The number of rows of the matrix A. M >= N.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 complex MbyN matrix A. On exit, the elements on and above the diagonal contain the NbyN upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details.LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).T T is COMPLEX*16 array, dimension (LDT,N) The NbyN upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details.LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,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:
September 2012
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. The block reflector H is then given by H = I  V * T * V**H where V**H is the conjugate transpose of V. For details of the algorithm, see Elmroth and Gustavson (cited above). AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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