stdlib_specialmatrices – Fortran-lang/stdlib

Provides derived-types and associated specialized linear algebra drivers for highly-structured matrices commonly encountered in the discretization of partial differential equations, as well as control and signal processing applications. (Specifications)

Uses

Used by

- Descendants:
- tridiagonal_matrices

Interfaces

public interface dense

This interface provides methods to convert a matrix of one of the types defined by stdlib_specialmatrices to a standard rank-2 array. (Specifications)

private pure module function tridiagonal_to_dense_cdp(A) result(B)

Convert a tridiagonal matrix to its dense representation.

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_cdp_type),	intent(in)			::	A	Input Tridiagonal matrix.

Return Value complex(kind=dp), allocatable, (:,:)

Corresponding dense matrix.

private pure module function tridiagonal_to_dense_csp(A) result(B)

Convert a tridiagonal matrix to its dense representation.

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_csp_type),	intent(in)			::	A	Input Tridiagonal matrix.

Return Value complex(kind=sp), allocatable, (:,:)

Corresponding dense matrix.

private pure module function tridiagonal_to_dense_dp(A) result(B)

Convert a tridiagonal matrix to its dense representation.

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_dp_type),	intent(in)			::	A	Input Tridiagonal matrix.

Return Value real(kind=dp), allocatable, (:,:)

Corresponding dense matrix.

private pure module function tridiagonal_to_dense_sp(A) result(B)

Convert a tridiagonal matrix to its dense representation.

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_sp_type),	intent(in)			::	A	Input Tridiagonal matrix.

Return Value real(kind=sp), allocatable, (:,:)

Corresponding dense matrix.

public interface hermitian

This interface provides methods to compute the hermitian operation for the different matrix types defined by stdlib_specialmatrices. For real-valued matrices, this is equivalent to the standard transpose. Specifications

private pure module function hermitian_tridiagonal_cdp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_cdp_type),	intent(in)			::	A	Input matrix.

Return Value type(tridiagonal_cdp_type)

private pure module function hermitian_tridiagonal_csp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_csp_type),	intent(in)			::	A	Input matrix.

Return Value type(tridiagonal_csp_type)

private pure module function hermitian_tridiagonal_dp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_dp_type),	intent(in)			::	A	Input matrix.

Return Value type(tridiagonal_dp_type)

private pure module function hermitian_tridiagonal_sp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_sp_type),	intent(in)			::	A	Input matrix.

Return Value type(tridiagonal_sp_type)

public interface operator(*)

Overload the * for scalar-matrix multiplications for the different matrix types provided by stdlib_specialmatrices. Specifications

private pure module function scalar_multiplication_bis_tridiagonal_cdp(A, alpha) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_cdp_type),	intent(in)			::	A
complex(kind=dp),	intent(in)			::	alpha

Return Value type(tridiagonal_cdp_type)

private pure module function scalar_multiplication_bis_tridiagonal_csp(A, alpha) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_csp_type),	intent(in)			::	A
complex(kind=sp),	intent(in)			::	alpha

Return Value type(tridiagonal_csp_type)

private pure module function scalar_multiplication_bis_tridiagonal_dp(A, alpha) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_dp_type),	intent(in)			::	A
real(kind=dp),	intent(in)			::	alpha

Return Value type(tridiagonal_dp_type)

private pure module function scalar_multiplication_bis_tridiagonal_sp(A, alpha) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_sp_type),	intent(in)			::	A
real(kind=sp),	intent(in)			::	alpha

Return Value type(tridiagonal_sp_type)

private pure module function scalar_multiplication_tridiagonal_cdp(alpha, A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp),	intent(in)			::	alpha
type(tridiagonal_cdp_type),	intent(in)			::	A

Return Value type(tridiagonal_cdp_type)

private pure module function scalar_multiplication_tridiagonal_csp(alpha, A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=sp),	intent(in)			::	alpha
type(tridiagonal_csp_type),	intent(in)			::	A

Return Value type(tridiagonal_csp_type)

private pure module function scalar_multiplication_tridiagonal_dp(alpha, A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	alpha
type(tridiagonal_dp_type),	intent(in)			::	A

Return Value type(tridiagonal_dp_type)

private pure module function scalar_multiplication_tridiagonal_sp(alpha, A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=sp),	intent(in)			::	alpha
type(tridiagonal_sp_type),	intent(in)			::	A

Return Value type(tridiagonal_sp_type)

public interface operator(+)

Overload the + operator for matrix-matrix addition. The two matrices need to be of the same type and kind. Specifications

private pure module function matrix_add_tridiagonal_cdp(A, B) result(C)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_cdp_type),	intent(in)			::	A
type(tridiagonal_cdp_type),	intent(in)			::	B

Return Value type(tridiagonal_cdp_type)

private pure module function matrix_add_tridiagonal_csp(A, B) result(C)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_csp_type),	intent(in)			::	A
type(tridiagonal_csp_type),	intent(in)			::	B

Return Value type(tridiagonal_csp_type)

private pure module function matrix_add_tridiagonal_dp(A, B) result(C)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_dp_type),	intent(in)			::	A
type(tridiagonal_dp_type),	intent(in)			::	B

Return Value type(tridiagonal_dp_type)

private pure module function matrix_add_tridiagonal_sp(A, B) result(C)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_sp_type),	intent(in)			::	A
type(tridiagonal_sp_type),	intent(in)			::	B

Return Value type(tridiagonal_sp_type)

public interface operator(-)

Overload the - operator for matrix-matrix subtraction. The two matrices need to be of the same type and kind. Specifications

private pure module function matrix_sub_tridiagonal_cdp(A, B) result(C)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_cdp_type),	intent(in)			::	A
type(tridiagonal_cdp_type),	intent(in)			::	B

Return Value type(tridiagonal_cdp_type)

private pure module function matrix_sub_tridiagonal_csp(A, B) result(C)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_csp_type),	intent(in)			::	A
type(tridiagonal_csp_type),	intent(in)			::	B

Return Value type(tridiagonal_csp_type)

private pure module function matrix_sub_tridiagonal_dp(A, B) result(C)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_dp_type),	intent(in)			::	A
type(tridiagonal_dp_type),	intent(in)			::	B

Return Value type(tridiagonal_dp_type)

private pure module function matrix_sub_tridiagonal_sp(A, B) result(C)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_sp_type),	intent(in)			::	A
type(tridiagonal_sp_type),	intent(in)			::	B

Return Value type(tridiagonal_sp_type)

public interface spmv

(Specifications) This interface provides methods to compute the matrix-vector product

$y = \alpha \mathrm{op}(A) x + \beta y$

for the different matrix types defined by stdlib_specialmatrices.

private module subroutine spmv_tridiag_1d_cdp(A, x, y, alpha, beta, op)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_cdp_type),	intent(in)			::	A
complex(kind=dp),	intent(in),		contiguous, target	::	x(:)
complex(kind=dp),	intent(inout),		contiguous, target	::	y(:)
real(kind=dp),	intent(in),	optional		::	alpha
real(kind=dp),	intent(in),	optional		::	beta
character(len=1),	intent(in),	optional		::	op

private module subroutine spmv_tridiag_1d_csp(A, x, y, alpha, beta, op)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_csp_type),	intent(in)			::	A
complex(kind=sp),	intent(in),		contiguous, target	::	x(:)
complex(kind=sp),	intent(inout),		contiguous, target	::	y(:)
real(kind=sp),	intent(in),	optional		::	alpha
real(kind=sp),	intent(in),	optional		::	beta
character(len=1),	intent(in),	optional		::	op

private module subroutine spmv_tridiag_1d_dp(A, x, y, alpha, beta, op)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_dp_type),	intent(in)			::	A
real(kind=dp),	intent(in),		contiguous, target	::	x(:)
real(kind=dp),	intent(inout),		contiguous, target	::	y(:)
real(kind=dp),	intent(in),	optional		::	alpha
real(kind=dp),	intent(in),	optional		::	beta
character(len=1),	intent(in),	optional		::	op

private module subroutine spmv_tridiag_1d_sp(A, x, y, alpha, beta, op)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_sp_type),	intent(in)			::	A
real(kind=sp),	intent(in),		contiguous, target	::	x(:)
real(kind=sp),	intent(inout),		contiguous, target	::	y(:)
real(kind=sp),	intent(in),	optional		::	alpha
real(kind=sp),	intent(in),	optional		::	beta
character(len=1),	intent(in),	optional		::	op

private module subroutine spmv_tridiag_2d_cdp(A, x, y, alpha, beta, op)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_cdp_type),	intent(in)			::	A
complex(kind=dp),	intent(in),		contiguous, target	::	x(:,:)
complex(kind=dp),	intent(inout),		contiguous, target	::	y(:,:)
real(kind=dp),	intent(in),	optional		::	alpha
real(kind=dp),	intent(in),	optional		::	beta
character(len=1),	intent(in),	optional		::	op

private module subroutine spmv_tridiag_2d_csp(A, x, y, alpha, beta, op)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_csp_type),	intent(in)			::	A
complex(kind=sp),	intent(in),		contiguous, target	::	x(:,:)
complex(kind=sp),	intent(inout),		contiguous, target	::	y(:,:)
real(kind=sp),	intent(in),	optional		::	alpha
real(kind=sp),	intent(in),	optional		::	beta
character(len=1),	intent(in),	optional		::	op

private module subroutine spmv_tridiag_2d_dp(A, x, y, alpha, beta, op)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_dp_type),	intent(in)			::	A
real(kind=dp),	intent(in),		contiguous, target	::	x(:,:)
real(kind=dp),	intent(inout),		contiguous, target	::	y(:,:)
real(kind=dp),	intent(in),	optional		::	alpha
real(kind=dp),	intent(in),	optional		::	beta
character(len=1),	intent(in),	optional		::	op

private module subroutine spmv_tridiag_2d_sp(A, x, y, alpha, beta, op)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_sp_type),	intent(in)			::	A
real(kind=sp),	intent(in),		contiguous, target	::	x(:,:)
real(kind=sp),	intent(inout),		contiguous, target	::	y(:,:)
real(kind=sp),	intent(in),	optional		::	alpha
real(kind=sp),	intent(in),	optional		::	beta
character(len=1),	intent(in),	optional		::	op

public interface transpose

This interface provides methods to compute the transpose operation for the different matrix types defined by stdlib_specialmatrices. Specifications

private pure module function transpose_tridiagonal_cdp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_cdp_type),	intent(in)			::	A	Input matrix.

Return Value type(tridiagonal_cdp_type)

private pure module function transpose_tridiagonal_csp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_csp_type),	intent(in)			::	A	Input matrix.

Return Value type(tridiagonal_csp_type)

private pure module function transpose_tridiagonal_dp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_dp_type),	intent(in)			::	A	Input matrix.

Return Value type(tridiagonal_dp_type)

private pure module function transpose_tridiagonal_sp(A) result(B)

Arguments

Type	Intent	Optional	Attributes		Name
type(tridiagonal_sp_type),	intent(in)			::	A	Input matrix.

Return Value type(tridiagonal_sp_type)

public interface tridiagonal

(Specifications) This interface provides different methods to construct a tridiagonal matrix. Only the non-zero elements of $A$ are stored, i.e.

$A = \begin{bmatrix} a_1 & b_1 \\ c_1 & a_2 & b_2 \\ & \ddots & \ddots & \ddots \\ & & c_{n-2} & a_{n-1} & b_{n-1} \\ & & & c_{n-1} & a_n \end{bmatrix}.$

Syntax

Construct a real tridiagonal matrix from rank-1 arrays:

   integer, parameter :: n
   real(dp), allocatable :: dl(:), dv(:), du(:)
   type(tridiagonal_rdp_type) :: A
   integer :: i

   dl = [(i, i=1, n-1)]; dv = [(2*i, i=1, n)]; du = [(3*i, i=1, n)]
   A = Tridiagonal(dl, dv, du)

Construct a real tridiagonal matrix with constant diagonals:

   integer, parameter :: n
   real(dp), parameter :: a = 1.0_dp, b = 1.0_dp, c = 2.0_dp
   type(tridiagonal_rdp_type) :: A

   A = Tridiagonal(a, b, c, n)

private module function initialize_constant_tridiagonal_impure_cdp(dl, dv, du, n, err) result(A)

Construct a tridiagonal matrix with constant elements.