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stprfb.f(3)				      LAPACK				      stprfb.f(3)

NAME
       stprfb.f -

SYNOPSIS
   Functions/Subroutines
       subroutine stprfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B,
	   LDB, WORK, LDWORK)
	   STPRFB applies a real or complex 'triangular-pentagonal' blocked reflector to a real
	   or complex matrix, which is composed of two blocks.

Function/Subroutine Documentation
   subroutine stprfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM,
       integerN, integerK, integerL, real, dimension( ldv, * )V, integerLDV, real, dimension(
       ldt, * )T, integerLDT, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B,
       integerLDB, real, dimension( ldwork, * )WORK, integerLDWORK)
       STPRFB applies a real or complex 'triangular-pentagonal' blocked reflector to a real or
       complex matrix, which is composed of two blocks.

       Purpose:

	    STPRFB applies a real "triangular-pentagonal" block reflector H or its
	    conjugate transpose H^H to a real matrix C, which is composed of two
	    blocks A and B, either from the left or right.

       Parameters:
	   SIDE

		     SIDE is CHARACTER*1
		     = 'L': apply H or H^H from the Left
		     = 'R': apply H or H^H from the Right

	   TRANS

		     TRANS is CHARACTER*1
		     = 'N': apply H (No transpose)
		     = 'C': apply H^H (Conjugate transpose)

	   DIRECT

		     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)

	   STOREV

		     STOREV is CHARACTER*1
		     Indicates how the vectors which define the elementary
		     reflectors are stored:
		     = 'C': Columns
		     = 'R': Rows

	   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 order of the matrix T, i.e. the number of elementary
		     reflectors whose product defines the block reflector.
		     K >= 0.

	   L

		     L is INTEGER
		     The order of the trapezoidal part of V.
		     K >= L >= 0.  See Further Details.

	   V

		     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.

	   LDV

		     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.

	   T

		     T is REAL array, dimension (LDT,K)
		     The triangular K-by-K matrix T in the representation of the
		     block reflector.

	   LDT

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

	   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
		     H*C or H^H*C or C*H or C*H^H.  See Futher 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 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^H*C or C*H or C*H^H.  See Further Details.

	   LDB

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

	   WORK

		     WORK is REAL array, dimension
		     (LDWORK,N) if SIDE = 'L',
		     (LDWORK,K) if SIDE = 'R'.

	   LDWORK

		     LDWORK is INTEGER
		     The leading dimension of the array WORK.
		     If SIDE = 'L', LDWORK >= K;
		     if SIDE = 'R', LDWORK >= M.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Further Details:

	     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.

       Definition at line 251 of file stprfb.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      stprfb.f(3)
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