Computes transpose matrix-matrix or transpose matrix-vector product.
Matrix containing the product of AT and B. (Output)
A — Left operand
matrix. This is an array of rank 2, or 3. It may be real, double, complex, double complex, or one of
the computational sparse matrix derived types, ?_hbc_sparse. (Input)
Note
that A and B cannot both be ?_hbc_sparse.
B — Right operand
matrix or vector. This is an array of rank 1, 2, or 3. It may be real, double,
complex, double complex, or one of the computational sparse matrix derived
types, ?_hbc_sparse. (Input)
Note
that A and B cannot both be ?_hbc_sparse.
If
A has rank three, B must have rank three.
If B has rank three, A must have
rank three.
A .tx. B
Computes the product of the transpose of matrix A and matrix or vector B. The results are in a precision and data type that ascends to the most accurate or complex operand.
Rank three operation is defined as follows:
do i = 1, min(size(A,3),
size(B,3))
X(:,:,i) =
A(:,:,i) .tx. B(:,:,i)
end do
.tx. can be used with either dense or sparse matrices. It is MPI capable for dense matrices only.
Dense Matrix Example (operator_ex05.f90)
use linear_operators
implicit none
! This is the equivalent of Example 1 for LIN_SOL_SELF using
operators
! and functions.
integer, parameter :: m=64, n=32
real(kind(1e0)) :: one=1.0e0, err
real(kind(1e0)) A(n,n), b(n,n), C(m,n), d(m,n), x(n,n)
! Generate two rectangular random matrices.
C = rand(C); d=rand(d)
! Form the normal equations for the rectangular system.
A = C .tx. C; b = C .tx. d
! Compute the solution for Ax = b, A is symmetric.
x = A .ix. b
! Check the results.
err = norm(b - (A .x. x))/(norm(A)+norm(b))
if (err <= sqrt(epsilon(one))) then
write (*,*) 'Example 1 for LIN_SOL_SELF (operators) is correct.'
end if
end
Sparse Matrix Example
use wrrrn_int
use linear_operators
type (s_sparse) S
type (s_hbc_sparse) H
integer, parameter :: N=3
real (kind(1.e0)) x(N,N), y(N,N), B(N,N)
real (kind(1.e0)) err
S = s_entry (1, 1, 2.0)
S = s_entry (1, 3, 1.0)
S = s_entry (2, 2, 4.0)
S = s_entry (3, 3, 6.0)
H = S ! sparse
X = H ! dense equivalent of H
B = rand(B)
Y = H .tx. B
call wrrrn ( 'H', X)
call wrrrn ( 'B', b)
call wrrrn ( 'H .tx. B ', y)
! Check the results.
err = norm(y - (X .tx. B))
if (err <= sqrt(epsilon(one))) then
write (*,*) 'Sparse example for .tx. operator is correct.'
end if
end
Output
H
1 2 3
1 2.000 0.000 1.000
2 0.000 4.000 0.000
3 0.000 0.000 6.000
B
1 2 3
1 0.8711 0.4467 0.4743
2 0.8315 0.7257 0.4518
3 0.6839 0.0561 0.6972
H .tx. B
1 2 3
1 1.742 0.893 0.949
2 3.326 2.903 1.807
3 4.975 0.784 4.657
Sparse example for .tx. operator is correct.
use linear_operators
use mpi_setup_int
implicit none
! This is the equivalent of Parallel Example 5 using box data
types,
! operators and functions.
integer, parameter :: m=64, n=32, nr=4
real(kind(1e0)) :: one=1e0, err(nr)
real(kind(1e0)), dimension(n,n,nr) :: A, b, x
real(kind(1e0)), dimension(m,n,nr) :: C, d
! Setup for MPI.
mp_nprocs = mp_setup()
! Generate two rectangular random matrices, only
! at the root node.
if (mp_rank == 0) then
C = rand(C); d=rand(d)
endif
! Form the normal equations for the rectangular system.
A = C .tx. C; b = C .tx. d
! Compute the solution for Ax = b.
x = A .ix. b
! Check the results.
err = norm(b - (A .x. x))/(norm(A)+norm(b))
if (ALL(err <= sqrt(epsilon(one))) .AND. MP_RANK == 0) &
write (*,*) 'Parallel Example 5 is correct.'
! See to any error messages and quit MPI.
mp_nprocs = mp_setup('Final')
end
PHONE: 713.784.3131 FAX:713.781.9260 |