table of contents
| tprfb(3) | LAPACK | tprfb(3) |
NAME¶
tprfb - tprfb: applies Q (like larfb)
SYNOPSIS¶
Functions¶
subroutine ctprfb (side, trans, direct, storev, m, n, k, l,
v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)
CTPRFB applies a complex 'triangular-pentagonal' block reflector to a
complex matrix, which is composed of two blocks. subroutine dtprfb
(side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb,
work, ldwork)
DTPRFB applies a real 'triangular-pentagonal' block reflector to a real
matrix, which is composed of two blocks. subroutine stprfb (side,
trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work,
ldwork)
STPRFB applies a real 'triangular-pentagonal' block reflector to a real
matrix, which is composed of two blocks. subroutine ztprfb (side,
trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work,
ldwork)
ZTPRFB applies a complex 'triangular-pentagonal' block reflector to a
complex matrix, which is composed of two blocks.
Detailed Description¶
Function Documentation¶
subroutine ctprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldwork, * ) work, integer ldwork)¶
CTPRFB applies a complex 'triangular-pentagonal' block reflector to a complex matrix, which is composed of two blocks.
Purpose:
CTPRFB 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.
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 COMPLEX 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 COMPLEX 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 COMPLEX 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
LDA is INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,K);
If SIDE = 'R', LDA >= max(1,M).
B
B is COMPLEX 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 COMPLEX 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.
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.
subroutine dtprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldwork, * ) work, integer ldwork)¶
DTPRFB applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.
Purpose:
DTPRFB applies a real 'triangular-pentagonal' 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.
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply H or H**T from the Left
= 'R': apply H or H**T from the Right
TRANS
TRANS is CHARACTER*1
= 'N': apply H (No transpose)
= 'T': apply H**T (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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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.
LDA
LDA is INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,K);
If SIDE = 'R', LDA >= max(1,M).
B
B is DOUBLE PRECISION 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.
LDB
LDB is INTEGER
The leading dimension of the array B.
LDB >= max(1,M).
WORK
WORK is DOUBLE PRECISION 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.
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.
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 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.
Purpose:
STPRFB applies a real 'triangular-pentagonal' 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.
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply H or H**T from the Left
= 'R': apply H or H**T from the Right
TRANS
TRANS is CHARACTER*1
= 'N': apply H (No transpose)
= 'T': apply H**T (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**T*C or C*H or C*H**T. See Further Details.
LDA
LDA is INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,K);
If SIDE = 'R', LDA >= 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**T*C or C*H or C*H**T. 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.
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.
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 complex 'triangular-pentagonal' block reflector to a complex matrix, which is composed of two blocks.
Purpose:
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.
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 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.
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 COMPLEX*16 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 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 Further Details.
LDA
LDA is INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,K);
If SIDE = 'R', LDA >= max(1,M).
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.
LDB
LDB is INTEGER
The leading dimension of the array B.
LDB >= max(1,M).
WORK
WORK is COMPLEX*16 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.
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.
Author¶
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