matrix_m Module
- Jabir Ali Ouassou
-
- Foundation
- 86 statements
- Source File
This module implements standard operations from linear algebra, including including matrix construction, inversion, commutation, and taking traces.
Uses
Functions
public pure function identity(n) result(R)
Constructs an n×n identity matrix.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer, | intent(in) | :: | n |
Matrix dimension |
Return Value real(kind=wp), dimension(n, n)
Identity matrix [n×n]
public pure function matrix_inverse_re(A) result(R)
Wrapper for matrix_inverse_cx that operates on real matrices.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:, :) | :: | A |
Matrix A [n×n] |
Return Value real(kind=wp), dimension(size(A, 1), size(A, 1))
Matrix R=A¯¹
public pure function matrix_inverse_cx(A) result(R)
Inverts a square matrix via Gauss-Jordan elimination with partial pivot (general) or a cofactoring algorithm (2x2 matrices). The implementation is based on Algorithm #2 in "Efficient matrix inversion via Gauss-Jordan elimination and its parallelization" by E.S. Quintana et al. (1998).
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=wp), | intent(in), | dimension(:, :) | :: | A |
Matrix A [n×n] |
Return Value complex(kind=wp), dimension(size(A, 1), size(A, 1))
Matrix R=A¯¹
public pure function matrix_trace(A) result(r)
Calculates the trace of a general complex matrix.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=wp), | intent(in), | dimension(:, :) | :: | A |
Matrix [n×m] |
Return Value complex(kind=wp)
r = Tr(A)
public pure function commutator(A, B) result(R)
Calculates the commutator between two complex square matrices.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=wp), | intent(in), | dimension(:, :) | :: | A |
Left matrix [n×n] |
|
| complex(kind=wp), | intent(in), | dimension(size(A, 1), size(A, 1)) | :: | B |
Right matrix [n×n] |
Return Value complex(kind=wp), dimension(size(A, 1), size(A, 1))
Commutator R = [A,B]
public pure function anticommutator(A, B) result(R)
Calculates the anticommutator between two complex square matrices.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=wp), | intent(in), | dimension(:, :) | :: | A |
Left matrix [n×n] |
|
| complex(kind=wp), | intent(in), | dimension(size(A, 1), size(A, 1)) | :: | B |
Right matrix [n×n] |
Return Value complex(kind=wp), dimension(size(A, 1), size(A, 1))
Anticommutator R = {A,B}
public pure function vector_diag(A) result(r)
Extracts the diagonal of a general complex matrix.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=wp), | intent(in), | dimension(:, :) | :: | A |
Matrix [n×m] |
Return Value complex(kind=wp), dimension(min(size(A, 1), size(A, 2)))
r = Diag(A)
public pure function matrix_diag(A, B) result(R)
Constructs a block-diagonal matrix R from two general matrices A and B.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=wp), | intent(in), | dimension(:, :) | :: | A |
Left matrix [n×m] |
|
| complex(kind=wp), | intent(in), | dimension(:, :) | :: | B |
Right matrix [p×q] |
Return Value complex(kind=wp), dimension(size(A, 1) + size(B, 1), size(A, 2) + size(B, 2))
R = Diag(A,B)