LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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dtpmqrt.f File Reference

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Functions/Subroutines

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

Function/Subroutine Documentation

subroutine dtpmqrt ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
integer  L,
integer  NB,
double precision, dimension( ldv, * )  V,
integer  LDV,
double precision, dimension( ldt, * )  T,
integer  LDT,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  WORK,
integer  INFO 
)

DTPMQRT

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Purpose: 
 DTPMQRT applies a real orthogonal matrix Q obtained from a 
 "triangular-pentagonal" real block reflector H to a general
 real matrix C, which consists of two blocks A and B.
Parameters:
[in]SIDE
          SIDE is CHARACTER*1
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right.
[in]TRANS
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'C':  Transpose, apply Q**T.
[in]M
          M is INTEGER
          The number of rows of the matrix B. M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix B. N >= 0.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
[in]L
          L is INTEGER
          The order of the trapezoidal part of V.  
          K >= L >= 0.  See Further Details.
[in]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.
[in]V
          V is DOUBLE PRECISION 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.
[in]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).
[in]T
          T is DOUBLE PRECISION array, dimension (LDT,K)
          The upper triangular factors of the block reflectors
          as returned by CTPQRT, stored as a NB-by-K matrix.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.
[in,out]A
          A is DOUBLE PRECISION 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**T*C or C*Q or C*Q**T.  See Further Details.
[in]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).
[in,out]B
          B is DOUBLE PRECISION 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**T*C or C*Q or C*Q**T.  See Further Details.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. 
          LDB >= max(1,M).
[out]WORK
          WORK is DOUBLE PRECISION array. The dimension of WORK is
           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'.
[out]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:
April 2012
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 real 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='T' and SIDE='L', C is on exit replaced with Q**T * C.

  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

  If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.

Definition at line 216 of file dtpmqrt.f.

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