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

.in +1c
.ti -1c
.RI "subroutine \fBstprfb\fP (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)"
.br
.RI "\fBSTPRFB\fP applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of two blocks\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine stprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, 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( ldwork, * ) work, integer ldwork)"

.PP
\fBSTPRFB\fP applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of two blocks\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> STPRFB applies a real  block reflector H or its
!> transpose H**T to a real matrix C, which is composed of two
!> blocks A and B, either from the left or right\&.
!>
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'L': apply H or H**T from the Left
!>          = 'R': apply H or H**T from the Right
!> 
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N': apply H (No transpose)
!>          = 'T': apply H**T (Transpose)
!> 
.fi
.PP
.br
\fIDIRECT\fP 
.PP
.nf
!>          DIRECT is CHARACTER*1
!>          Indicates how H is formed from a product of elementary
!>          reflectors
!>          = 'F': H = H(1) H(2) \&. \&. \&. H(k) (Forward)
!>          = 'B': H = H(k) \&. \&. \&. H(2) H(1) (Backward)
!> 
.fi
.PP
.br
\fISTOREV\fP 
.PP
.nf
!>          STOREV is CHARACTER*1
!>          Indicates how the vectors which define the elementary
!>          reflectors are stored:
!>          = 'C': Columns
!>          = 'R': Rows
!> 
.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 order of the matrix T, i\&.e\&. the number of elementary
!>          reflectors whose product defines the block reflector\&.
!>          K >= 0\&.
!> 
.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
\fIV\fP 
.PP
.nf
!>          V is REAL array, dimension
!>                                (LDV,K) if STOREV = 'C'
!>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
!>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
!>          The pentagonal matrix V, which contains the elementary reflectors
!>          H(1), H(2), \&.\&.\&., H(K)\&.  See Further Details\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V\&.
!>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
!>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
!>          if STOREV = 'R', LDV >= K\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is REAL array, dimension (LDT,K)
!>          The triangular K-by-K matrix T in the representation of the
!>          block reflector\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&.
!>          LDT >= K\&.
!> 
.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
!>          H*C or H**T*C or C*H or C*H**T\&.  See Further Details\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.
!>          If SIDE = 'L', LDA >= max(1,K);
!>          If SIDE = 'R', LDA >= 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
!>          H*C or H**T*C or C*H or C*H**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, dimension
!>          (LDWORK,N) if SIDE = 'L',
!>          (LDWORK,K) if SIDE = 'R'\&.
!> 
.fi
.PP
.br
\fILDWORK\fP 
.PP
.nf
!>          LDWORK is INTEGER
!>          The leading dimension of the array WORK\&.
!>          If SIDE = 'L', LDWORK >= K;
!>          if SIDE = 'R', LDWORK >= M\&.
!> 
.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 matrix C is a composite matrix formed from blocks A and B\&.
!>  The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K,
!>  and if SIDE = 'L', A is of size K-by-N\&.
!>
!>  If SIDE = 'R' and DIRECT = 'F', C = [A B]\&.
!>
!>  If SIDE = 'L' and DIRECT = 'F', C = [A]
!>                                      [B]\&.
!>
!>  If SIDE = 'R' and DIRECT = 'B', C = [B A]\&.
!>
!>  If SIDE = 'L' and DIRECT = 'B', C = [B]
!>                                      [A]\&.
!>
!>  The pentagonal matrix V is composed of a rectangular block V1 and a
!>  trapezoidal block V2\&.  The size of the trapezoidal block is determined by
!>  the parameter L, where 0<=L<=K\&.  If L=K, the V2 block of V is triangular;
!>  if L=0, there is no trapezoidal block, thus V = V1 is rectangular\&.
!>
!>  If DIRECT = 'F' and STOREV = 'C':  V = [V1]
!>                                         [V2]
!>     - V2 is upper trapezoidal (first L rows of K-by-K upper triangular)
!>
!>  If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]
!>
!>     - V2 is lower trapezoidal (first L columns of K-by-K lower triangular)
!>
!>  If DIRECT = 'B' and STOREV = 'C':  V = [V2]
!>                                         [V1]
!>     - V2 is lower trapezoidal (last L rows of K-by-K lower triangular)
!>
!>  If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]
!>
!>     - V2 is upper trapezoidal (last L columns of K-by-K upper triangular)
!>
!>  If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K\&.
!>
!>  If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K\&.
!>
!>  If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L\&.
!>
!>  If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB249\fP of file \fBstprfb\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.