Computes the conjugate transpose of a matrix.
Matrix containing the conjugate transpose of A. (Output)
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, ?_hbc_sparse. (Input)
.h. A
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.
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.
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