table of contents
| tpmqrt(3) | LAPACK | tpmqrt(3) |
NAME¶
tpmqrt - tpmqrt: applies Q
SYNOPSIS¶
Functions¶
subroutine ctpmqrt (side, trans, m, n, k, l, nb, v, ldv, t,
ldt, a, lda, b, ldb, work, info)
CTPMQRT subroutine dtpmqrt (side, trans, m, n, k, l, nb, v, ldv,
t, ldt, a, lda, b, ldb, work, info)
DTPMQRT subroutine stpmqrt (side, trans, m, n, k, l, nb, v, ldv,
t, ldt, a, lda, b, ldb, work, info)
STPMQRT subroutine ztpmqrt (side, trans, m, n, k, l, nb, v, ldv,
t, ldt, a, lda, b, ldb, work, info)
ZTPMQRT
Detailed Description¶
Function Documentation¶
subroutine ctpmqrt (character side, character trans, integer m, integer n, integer k, integer l, integer nb, 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( * ) work, integer info)¶
CTPMQRT
Purpose:
CTPMQRT applies a complex orthogonal matrix Q obtained from a
'triangular-pentagonal' complex block reflector H to a general
complex matrix C, which consists of two blocks A and B.
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'C': Conjugate transpose, apply Q**H.
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 number of elementary reflectors whose product defines
the matrix Q.
L
L is INTEGER
The order of the trapezoidal part of V.
K >= L >= 0. See Further Details.
NB
NB is INTEGER
The block size used for the storage of T. K >= NB >= 1.
This must be the same value of NB used to generate T
in CTPQRT.
V
V is COMPLEX array, dimension (LDV,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CTPQRT in B. See Further Details.
LDV
LDV is INTEGER
The leading dimension of the array V.
If SIDE = 'L', LDV >= max(1,M);
if SIDE = 'R', LDV >= max(1,N).
T
T is COMPLEX array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by CTPQRT, stored as a NB-by-K matrix.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= NB.
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
Q*C or Q**H*C or C*Q or C*Q**H. See Further 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 COMPLEX array, dimension (LDB,N)
On entry, the M-by-N matrix B.
On exit, B is overwritten by the corresponding block of
Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.
LDB
LDB is INTEGER
The leading dimension of the array B.
LDB >= max(1,M).
WORK
WORK is COMPLEX array. The dimension of WORK is
N*NB if SIDE = 'L', or M*NB if SIDE = 'R'.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
The columns of the pentagonal matrix V contain the elementary reflectors
H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
trapezoidal block V2:
V = [V1]
[V2].
The size of the trapezoidal block V2 is determined by the parameter L,
where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix. If L=K, V2 is upper triangular;
if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is M-by-K.
[B]
If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is N-by-K.
The complex orthogonal matrix Q is formed from V and T.
If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.
If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
subroutine dtpmqrt (character side, character trans, integer m, integer n, integer k, integer l, integer nb, 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( * ) work, integer info)¶
DTPMQRT
Purpose:
DTPMQRT applies a real orthogonal matrix Q obtained from a
'triangular-pentagonal' real block reflector H to a general
real matrix C, which consists of two blocks A and B.
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
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 number of elementary reflectors whose product defines
the matrix Q.
L
L is INTEGER
The order of the trapezoidal part of V.
K >= L >= 0. See Further Details.
NB
NB is INTEGER
The block size used for the storage of T. K >= NB >= 1.
This must be the same value of NB used to generate T
in CTPQRT.
V
V is DOUBLE PRECISION array, dimension (LDV,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CTPQRT in B. See Further Details.
LDV
LDV is INTEGER
The leading dimension of the array V.
If SIDE = 'L', LDV >= max(1,M);
if SIDE = 'R', LDV >= max(1,N).
T
T is DOUBLE PRECISION array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by CTPQRT, stored as a NB-by-K matrix.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= NB.
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
Q*C or Q**T*C or C*Q or C*Q**T. See Further 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 DOUBLE PRECISION array, dimension (LDB,N)
On entry, the M-by-N matrix B.
On exit, B is overwritten by the corresponding block of
Q*C or Q**T*C or C*Q or C*Q**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. The dimension of WORK is
N*NB if SIDE = 'L', or M*NB if SIDE = 'R'.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
The columns of the pentagonal matrix V contain the elementary reflectors
H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
trapezoidal block V2:
V = [V1]
[V2].
The size of the trapezoidal block V2 is determined by the parameter L,
where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix. If L=K, V2 is upper triangular;
if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is M-by-K.
[B]
If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is N-by-K.
The real orthogonal matrix Q is formed from V and T.
If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.
If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.
subroutine stpmqrt (character side, character trans, integer m, integer n, integer k, integer l, integer nb, 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( * ) work, integer info)¶
STPMQRT
Purpose:
STPMQRT applies a real orthogonal matrix Q obtained from a
'triangular-pentagonal' real block reflector H to a general
real matrix C, which consists of two blocks A and B.
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply Q or Q^T from the Left;
= 'R': apply Q or Q^T from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q^T.
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 number of elementary reflectors whose product defines
the matrix Q.
L
L is INTEGER
The order of the trapezoidal part of V.
K >= L >= 0. See Further Details.
NB
NB is INTEGER
The block size used for the storage of T. K >= NB >= 1.
This must be the same value of NB used to generate T
in CTPQRT.
V
V is REAL array, dimension (LDV,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CTPQRT in B. See Further Details.
LDV
LDV is INTEGER
The leading dimension of the array V.
If SIDE = 'L', LDV >= max(1,M);
if SIDE = 'R', LDV >= max(1,N).
T
T is REAL array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by CTPQRT, stored as a NB-by-K matrix.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= NB.
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
Q*C or Q^T*C or C*Q or C*Q^T. See Further 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
Q*C or Q^T*C or C*Q or C*Q^T. See Further Details.
LDB
LDB is INTEGER
The leading dimension of the array B.
LDB >= max(1,M).
WORK
WORK is REAL array. The dimension of WORK is
N*NB if SIDE = 'L', or M*NB if SIDE = 'R'.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
The columns of the pentagonal matrix V contain the elementary reflectors
H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
trapezoidal block V2:
V = [V1]
[V2].
The size of the trapezoidal block V2 is determined by the parameter L,
where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix. If L=K, V2 is upper triangular;
if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is M-by-K.
[B]
If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is N-by-K.
The real orthogonal matrix Q is formed from V and T.
If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
If TRANS='T' and SIDE='L', C is on exit replaced with Q^T * C.
If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
If TRANS='T' and SIDE='R', C is on exit replaced with C * Q^T.
subroutine ztpmqrt (character side, character trans, integer m, integer n, integer k, integer l, integer nb, 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( * ) work, integer info)¶
ZTPMQRT
Purpose:
ZTPMQRT applies a complex orthogonal matrix Q obtained from a
'triangular-pentagonal' complex block reflector H to a general
complex matrix C, which consists of two blocks A and B.
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'C': Conjugate transpose, apply Q**H.
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 number of elementary reflectors whose product defines
the matrix Q.
L
L is INTEGER
The order of the trapezoidal part of V.
K >= L >= 0. See Further Details.
NB
NB is INTEGER
The block size used for the storage of T. K >= NB >= 1.
This must be the same value of NB used to generate T
in CTPQRT.
V
V is COMPLEX*16 array, dimension (LDV,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CTPQRT in B. See Further Details.
LDV
LDV is INTEGER
The leading dimension of the array V.
If SIDE = 'L', LDV >= max(1,M);
if SIDE = 'R', LDV >= max(1,N).
T
T is COMPLEX*16 array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by CTPQRT, stored as a NB-by-K matrix.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= NB.
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
Q*C or Q**H*C or C*Q or C*Q**H. See Further 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 COMPLEX*16 array, dimension (LDB,N)
On entry, the M-by-N matrix B.
On exit, B is overwritten by the corresponding block of
Q*C or Q**H*C or C*Q or C*Q**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. The dimension of WORK is
N*NB if SIDE = 'L', or M*NB if SIDE = 'R'.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
The columns of the pentagonal matrix V contain the elementary reflectors
H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
trapezoidal block V2:
V = [V1]
[V2].
The size of the trapezoidal block V2 is determined by the parameter L,
where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix. If L=K, V2 is upper triangular;
if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is M-by-K.
[B]
If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is N-by-K.
The complex orthogonal matrix Q is formed from V and T.
If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.
If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
Author¶
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