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

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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 ( 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 )

STPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks.

Download STPRFB + dependencies [TGZ] [ZIP] [TXT]
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:
 [in] SIDE ``` SIDE is CHARACTER*1 = 'L': apply H or H^H from the Left = 'R': apply H or H^H from the Right``` [in] TRANS ``` TRANS is CHARACTER*1 = 'N': apply H (No transpose) = 'C': apply H^H (Conjugate transpose)``` [in] 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)``` [in] STOREV ``` STOREV is CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored: = 'C': Columns = 'R': Rows``` [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 order of the matrix T, i.e. the number of elementary reflectors whose product defines the block reflector. K >= 0.``` [in] L ``` L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details.``` [in] 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.``` [in] 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.``` [in] T ``` T is REAL array, dimension (LDT,K) The triangular K-by-K matrix T in the representation of the block reflector. ``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= K.``` [in,out] 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.``` [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 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.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).``` [out] WORK ``` WORK is REAL array, dimension (LDWORK,N) if SIDE = 'L', (LDWORK,K) if SIDE = 'R'.``` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= K; if SIDE = 'R', LDWORK >= M.```
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.

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