matrix_m Module

  1. matrix.f
  2. matrix_m

This file defines functions that perform some common matrix operations.


Uses


Contents

Functions


Functions

public pure function identity(n) result(R)

Constructs an n×n identity matrix.

Arguments

Type IntentOptional AttributesName
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 allows the procedure to be used for real matrices.

Arguments

Type IntentOptional AttributesName
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)

Invert a square n×n matrix using Gauss-Jordan elimination with partial pivoting. In the special case n=2, the inverse is evaluated using a cofactoring algorithm. [This 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 IntentOptional AttributesName
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)

Calculate the trace of a general complex matrix.

Arguments

Type IntentOptional AttributesName
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)

Calculate the commutator between two complex square matrices.

Arguments

Type IntentOptional AttributesName
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)

Calculate the anticommutator between two complex square matrices.

Arguments

Type IntentOptional AttributesName
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)

Extract the diagonal of a general complex matrix.

Arguments

Type IntentOptional AttributesName
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)

Construct a block-diagonal matrix R from two general matrices A and B.

Arguments

Type IntentOptional AttributesName
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)