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template<typename T>
void tprfb(char *side, char *trans, char *direct, char *storev, integer *m, integer *n, integer *k, integer *l, T *v, integer *ldv, T *t, integer *ldt, T *a, integer *lda, T *b, integer *ldb, T *work, integer *ldwork)# TPRFB applies a real or complex “triangular-pentagonal” blocked
reflector to a real or complex matrix, which is composed of two blocks.
Purpose:
TPRFB 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 – [in]
SIDE is CHARACTER*1
= ‘L’: apply H or H^H from the Left
= ‘R’: apply H or H^H from the RightTRANS – [in]
TRANS is CHARACTER*1
= ‘N’: apply H (No transpose)
= ‘C’: apply H^H (Conjugate transpose)DIRECT – [in]
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 – [in]
STOREV is CHARACTER*1
Indicates how the vectors which define the elementary reflectors are stored:
= ‘C’: Columns
= ‘R’: Rows
M – [in]
M is INTEGER
The number of rows of the matrix B. M >= 0.
N – [in]
N is INTEGER
The number of columns of the matrix B. N >= 0.
K – [in]
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 – [in]
L is INTEGER
The order of the trapezoidal part of V. K >= L >= 0. See Further Details.
V – [in]
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 – [in]
LDV is INTEGER
The leading dimension of the array V.
If STOREV = ‘C’ and SIDE = ‘L’, LDV >= fla_max(1,M);
if STOREV = ‘C’ and SIDE = ‘R’, LDV >= fla_max(1,N);
if STOREV = ‘R’, LDV >= K.T – [in]
T is REAL array, dimension (LDT,K)
The triangular K-by-K matrix T in the representation of the block reflector.
LDT – [in]
LDT is INTEGER
The leading dimension of the array T. LDT >= K.
A – [inout]
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 Further Details.LDA – [in]
LDA is INTEGER
The leading dimension of the array A.
If SIDE = ‘L’, LDA >= fla_max(1,K);
If SIDE = ‘R’, LDA >= fla_max(1,M).
B – [inout]
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 – [in]
LDB is INTEGER
The leading dimension of the array B. LDB >= fla_max(1,M).
WORK – [out]
WORK is REAL array, dimension
(LDWORK,N) if SIDE = ‘L’,
(LDWORK,K) if SIDE = ‘R’.LDWORK – [in]
LDWORK is INTEGER
The leading dimension of the array WORK.
If SIDE = ‘L’, LDWORK >= K;
if SIDE = ‘R’, LDWORK >= M.