dtpmlqt.f man page

dtpmlqt.f

Synopsis

Functions/Subroutines

subroutine dtpmlqt (SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
DTPMLQT

Function/Subroutine Documentation

subroutine dtpmlqt (character SIDE, character TRANS, integer M, integer N, integer K, integer L, integer MB, 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)

DTPMLQT

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.

MB

MB is INTEGER
The block size used for the storage of T.  K >= MB >= 1.
This must be the same value of MB used to generate T
in DTPLQT.

V

V is DOUBLE PRECISION array, dimension (LDA,K)
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DTPLQT 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 DTPLQT, stored as a MB-by-K matrix.

LDT

LDT is INTEGER
The leading dimension of the array T.  LDT >= MB.

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*MB if SIDE = 'L', or  M*MB 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.

Date:

November 2017

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 lower trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower 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 K-by-M.
[B]

If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.

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 218 of file dtpmlqt.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page dtpmlqt(3) is an alias of dtpmlqt.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK