SRC/stpmlqt.f(3)           Library Functions Manual           SRC/stpmlqt.f(3)

NAME
       SRC/stpmlqt.f

SYNOPSIS
   Functions/Subroutines
       subroutine stpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a,
           lda, b, ldb, work, info)
           STPMLQT

Function/Subroutine Documentation
   subroutine stpmlqt (character side, character trans, integer m, integer n,
       integer k, integer l, integer mb, real, dimension( ldv, * ) v, integer
       ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( lda, *
       ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real,
       dimension( * ) work, integer info)
       STPMLQT

       Purpose:


           !>
           !> STPMLQT applies a real orthogonal matrix Q obtained from a
           !>  real block reflector H to a general
           !> real matrix C, which consists of two blocks A and B.
           !>

       Parameters
           SIDE

           !>          SIDE is CHARACTER*1
           !>          = 'L': apply Q or Q**T from the Left;
           !>          = 'R': apply Q or Q**T from the Right.
           !>

           TRANS

           !>          TRANS is CHARACTER*1
           !>          = 'N':  No transpose, apply Q;
           !>          = 'T':  Transpose, apply Q**T.
           !>

           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.
           !>

           MB

           !>          MB is INTEGER
           !>          The block size used for the storage of T.  K >= MB >= 1.
           !>          This must be the same value of MB used to generate T
           !>          in STPLQT.
           !>

           V

           !>          V is REAL array, dimension (LDV,K)
           !>          The i-th row must contain the vector which defines the
           !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
           !>          STPLQT in B.  See Further Details.
           !>

           LDV

           !>          LDV is INTEGER
           !>          The leading dimension of the array V. LDV >= K.
           !>

           T

           !>          T is REAL array, dimension (LDT,K)
           !>          The upper triangular factors of the block reflectors
           !>          as returned by STPLQT, stored as a MB-by-K matrix.
           !>

           LDT

           !>          LDT is INTEGER
           !>          The leading dimension of the array T.  LDT >= MB.
           !>

           A

           !>          A is REAL 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.
           !>

           LDA

           !>          LDA is INTEGER
           !>          The leading dimension of the array A.
           !>          If SIDE = 'L', LDA >= max(1,K);
           !>          If SIDE = 'R', LDA >= max(1,M).
           !>

           B

           !>          B is REAL 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.
           !>

           LDB

           !>          LDB is INTEGER
           !>          The leading dimension of the array B.
           !>          LDB >= max(1,M).
           !>

           WORK

           !>          WORK is REAL array. The dimension of WORK is
           !>           N*MB if SIDE = 'L', or  M*MB 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.

       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 lower trapezoidal, consisting of the first L
           !>  rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower 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 K-by-M.
           !>                      [B]
           !>
           !>  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.
           !>
           !>  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 212 of file stpmlqt.f.

Author
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LAPACK                          Version 3.12.0                SRC/stpmlqt.f(3)