.TH "SRC/stpmqrt.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/stpmqrt.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBstpmqrt\fP (side, trans, m, n, k, l, nb, v, ldv, t, ldt, a, lda, b, ldb, work, info)"
.br
.RI "\fBSTPMQRT\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine stpmqrt (character side, character trans, integer m, integer n, integer k, integer l, integer nb, 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)"

.PP
\fBSTPMQRT\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 STPMQRT 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
          SIDE is CHARACTER*1
          = 'L': apply Q or Q^T from the Left;
          = 'R': apply Q or Q^T from the Right\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q^T\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix B\&. M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix B\&. N >= 0\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q\&.
.fi
.PP
.br
\fIL\fP 
.PP
.nf
          L is INTEGER
          The order of the trapezoidal part of V\&.
          K >= L >= 0\&.  See Further Details\&.
.fi
.PP
.br
\fINB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is REAL array, dimension (LDV,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\&.
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
          LDV is INTEGER
          The leading dimension of the array V\&.
          If SIDE = 'L', LDV >= max(1,M);
          if SIDE = 'R', LDV >= max(1,N)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is REAL array, dimension (LDT,K)
          The upper triangular factors of the block reflectors
          as returned by CTPQRT, stored as a NB-by-K matrix\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= NB\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.
          If SIDE = 'L', LDC >= max(1,K);
          If SIDE = 'R', LDC >= max(1,M)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B\&.
          LDB >= max(1,M)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array\&. The dimension of WORK is
           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB214\fP of file \fBstpmqrt\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.