
NAMEztpmqrt.f SYNOPSISFunctions/Subroutinessubroutine ztpmqrt (SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO) Function/Subroutine Documentationsubroutine ztpmqrt (characterSIDE, characterTRANS, integerM, integerN, integerK, integerL, integerNB, complex*16, dimension( ldv, * )V, integerLDV, complex*16, dimension( ldt, * )T, integerLDT, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )WORK, integerINFO)ZTPMQRT Purpose:ZTPMQRT applies a complex orthogonal matrix Q obtained from a "triangularpentagonal" complex block reflector H to a general complex matrix C, which consists of two blocks A and B. SIDE
Author:
SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right.TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Transpose, apply Q**H.M M is INTEGER The number of rows of the matrix B. M >= 0.N N is INTEGER The number of columns of the matrix B. N >= 0.K K is INTEGER The number of elementary reflectors whose product defines the matrix Q.L L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details.NB NB is INTEGER The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in CTPQRT.V V is COMPLEX*16 array, dimension (LDA,K) The ith column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CTPQRT in B. See Further Details.LDV LDV is INTEGER The leading dimension of the array V. If SIDE = 'L', LDV >= max(1,M); if SIDE = 'R', LDV >= max(1,N).T T is COMPLEX*16 array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by CTPQRT, stored as a NBbyK matrix.LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB.A A is COMPLEX*16 array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R' On entry, the KbyN or MbyK matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.LDA LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDC >= max(1,K); If SIDE = 'R', LDC >= max(1,M).B B is COMPLEX*16 array, dimension (LDB,N) On entry, the MbyN matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).WORK WORK is COMPLEX*16 array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'.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 columns of the pentagonal matrix V contain the elementary reflectors H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a trapezoidal block V2: V = [V1] [V2]. The size of the trapezoidal block V2 is determined by the parameter L, where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L rows of a KbyK upper triangular matrix. If L=K, V2 is upper triangular; if L=0, there is no trapezoidal block, hence V = V1 is rectangular. If SIDE = 'L': C = [A] where A is KbyN, B is MbyN and V is MbyK. [B] If SIDE = 'R': C = [A B] where A is MbyK, B is MbyN and V is NbyK. The complex orthogonal matrix Q is formed from V and T. If TRANS='N' and SIDE='L', C is on exit replaced with Q * C. If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C. If TRANS='N' and SIDE='R', C is on exit replaced with C * Q. If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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