.h.
Computes the conjugate transpose of a matrix.
Operator Return Value
Matrix containing the conjugate transpose of A. (Output)
Required Operand
A — Matrix for which the conjugate transpose is to be computed. 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, c_hbc_sparse or z_hbc_sparse. (Input)
FORTRAN 90 Interface
.h. A
Description
Computes the conjugate transpose of matrix A. The operation may be read adjoint, and the results are the mathematical objects in a precision and data type that matches the operand. Since this is a unary operation, it has higher Fortran 90 precedence than any other intrinsic unary array operation.
.h. can be used with either dense or sparse matrices.
Examples
Dense Matrix Example (operator_ex34.f90)
use linear_operators
implicit none
! This is the equivalent of Example 2 (using operators) for LIN_GEIG_GEN.
integer, parameter :: n=32
real(kind(1d0)), parameter :: one=1d0, zero=0d0
real(kind(1d0)) err, alpha(n)
complex(kind(1d0)), dimension(n,n) :: A, B, C, D, V
! Generate random matrices for both A and B.
C = rand(C); D = rand(D)
A = C + .h.C; B = D .hx. D; B = (B + .h.B)/2
ALPHA = EIG(A, B=B, W=V)
! Check that residuals are small. Use a real array for alpha
! since the eigenvalues are known to be real.
err= norm((A .x. V) - (B .x. V .x. diag(alpha)),1)/&
(norm(A,1)+norm(B,1)*norm(alpha,1))
if (err <= sqrt(epsilon(one))) then
write (*,*) 'Example 2 for LIN_GEIG_GEN (operators) is correct.'
end if
end
Sparse Matrix Example
use wrcrn_int
use linear_operators
type (c_sparse) S
type (c_hbc_sparse) H, HT
integer, parameter :: N=3
complex (kind(1.e0)) X(3,3), XT(3,3)
real (kind(1.e0)) err
S = c_entry (1, 1, (2.0, 1.0) )
S = c_entry (1, 3, (1.0, 3.0))
S = c_entry (2, 2, (4.0, -1.0))
S = c_entry (3, 3, (6.0, 2.0))
H = S ! sparse
X = H ! dense equivalent of H
HT = .h. H
XT = HT ! dense equivalent of HT
call wrcrn ( 'H', X)
call wrcrn ( 'H Conjugate Transpose', XT)
! Check the results.
err = norm(XT - (.h. X))
if (err <= sqrt(epsilon(one))) then
write (*,*) 'Sparse example for .h. operator is correct.'
end if
end
Output
H
1 2 3
1 ( 2.000, 1.000) ( 0.000, 0.000) ( 1.000, 3.000)
2 ( 0.000, 0.000) ( 4.000,-1.000) ( 0.000, 0.000)
3 ( 0.000, 0.000) ( 0.000, 0.000) ( 6.000, 2.000)
H Conjugate Transpose
1 2 3
1 ( 2.000,-1.000) ( 0.000, 0.000) ( 0.000, 0.000)
2 ( 0.000, 0.000) ( 4.000, 1.000) ( 0.000, 0.000)
3 ( 1.000,-3.000) ( 0.000, 0.000) ( 6.000,-2.000)
Sparse example for .h. operator is correct.
