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ztpmqrt.f(3) LAPACK ztpmqrt.f(3)

ztpmqrt.f -


subroutine ztpmqrt (SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
 
ZTPMQRT

ZTPMQRT
Purpose:
 ZTPMQRT applies a complex orthogonal matrix Q obtained from a 
 "triangular-pentagonal" complex block reflector H to a general
 complex matrix C, which consists of two blocks A and B.
Parameters:
SIDE
          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 i-th 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 NB-by-K 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 K-by-N or M-by-K 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 M-by-N 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 i-th argument had an illegal value
Author:
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 K-by-K 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 K-by-N, B is M-by-N and V is M-by-K. [B] If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is N-by-K.
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.
Definition at line 216 of file ztpmqrt.f.

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