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LAPACK
3.4.2
LAPACK: Linear Algebra PACKage
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Go to the source code of this file.
Functions/Subroutines | |
| subroutine | ztprfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK) |
| ZTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks. | |
| subroutine ztprfb | ( | character | SIDE, |
| character | TRANS, | ||
| character | DIRECT, | ||
| character | STOREV, | ||
| integer | M, | ||
| integer | N, | ||
| integer | K, | ||
| integer | L, | ||
| complex*16, dimension( ldv, * ) | V, | ||
| integer | LDV, | ||
| complex*16, dimension( ldt, * ) | T, | ||
| integer | LDT, | ||
| complex*16, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| complex*16, dimension( ldb, * ) | B, | ||
| integer | LDB, | ||
| complex*16, dimension( ldwork, * ) | WORK, | ||
| integer | LDWORK | ||
| ) |
ZTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks.
Download ZTPRFB + dependencies [TGZ] [ZIP] [TXT]ZTPRFB applies a complex "triangular-pentagonal" block reflector H or its conjugate transpose H**H to a complex matrix C, which is composed of two blocks A and B, either from the left or right.
| [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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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. |
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 ztprfb.f.
1.8.1.1