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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| 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
Download DTPMQRT + dependencies [TGZ] [ZIP] [TXT]
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.
| [in] | SIDE | SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right. |
| [in] | TRANS | TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T. |
| [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 number of elementary reflectors whose product defines
the matrix Q. |
| [in] | L | L is INTEGER
The order of the trapezoidal part of V.
K >= L >= 0. See Further Details. |
| [in] | 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. |
| [in] | 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. |
| [in] | 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). |
| [in] | 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. |
| [in] | LDT | LDT is INTEGER
The leading dimension of the array T. LDT >= NB. |
| [in,out] | 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. |
| [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 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. |
| [in] | LDB | LDB is INTEGER
The leading dimension of the array B.
LDB >= max(1,M). |
| [out] | WORK | WORK is DOUBLE PRECISION array. The dimension of WORK is
N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. |
| [out] | INFO | INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value |
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. Definition at line 214 of file dtpmqrt.f.
1.9.7