tridiagonal Interface

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)

Functions

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

Construct a tridiagonal matrix with constant elements.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp),	intent(in)			::	dl	Tridiagonal matrix elements.
complex(kind=dp),	intent(in)			::	dv	Tridiagonal matrix elements.
complex(kind=dp),	intent(in)			::	du	Tridiagonal matrix elements.
integer(kind=ilp),	intent(in)			::	n	Matrix dimension.
type(linalg_state_type),	intent(out)			::	err	Error handling.

Return Value type(tridiagonal_cdp_type)

Corresponding Tridiagonal matrix.

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

Construct a tridiagonal matrix with constant elements.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=sp),	intent(in)			::	dl	Tridiagonal matrix elements.
complex(kind=sp),	intent(in)			::	dv	Tridiagonal matrix elements.
complex(kind=sp),	intent(in)			::	du	Tridiagonal matrix elements.
integer(kind=ilp),	intent(in)			::	n	Matrix dimension.
type(linalg_state_type),	intent(out)			::	err	Error handling.

Return Value type(tridiagonal_csp_type)

Corresponding Tridiagonal matrix.

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

Construct a tridiagonal matrix with constant elements.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	dl	Tridiagonal matrix elements.
real(kind=dp),	intent(in)			::	dv	Tridiagonal matrix elements.
real(kind=dp),	intent(in)			::	du	Tridiagonal matrix elements.
integer(kind=ilp),	intent(in)			::	n	Matrix dimension.
type(linalg_state_type),	intent(out)			::	err	Error handling.

Return Value type(tridiagonal_dp_type)

Corresponding Tridiagonal matrix.

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

Construct a tridiagonal matrix with constant elements.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=sp),	intent(in)			::	dl	Tridiagonal matrix elements.
real(kind=sp),	intent(in)			::	dv	Tridiagonal matrix elements.
real(kind=sp),	intent(in)			::	du	Tridiagonal matrix elements.
integer(kind=ilp),	intent(in)			::	n	Matrix dimension.
type(linalg_state_type),	intent(out)			::	err	Error handling.

Return Value type(tridiagonal_sp_type)

Corresponding Tridiagonal matrix.

private pure module function initialize_constant_tridiagonal_pure_cdp(dl, dv, du, n) result(A)

Construct a tridiagonal matrix with constant elements.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp),	intent(in)			::	dl	Tridiagonal matrix elements.
complex(kind=dp),	intent(in)			::	dv	Tridiagonal matrix elements.
complex(kind=dp),	intent(in)			::	du	Tridiagonal matrix elements.
integer(kind=ilp),	intent(in)			::	n	Matrix dimension.

Return Value type(tridiagonal_cdp_type)

Corresponding Tridiagonal matrix.

private pure module function initialize_constant_tridiagonal_pure_csp(dl, dv, du, n) result(A)

Construct a tridiagonal matrix with constant elements.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=sp),	intent(in)			::	dl	Tridiagonal matrix elements.
complex(kind=sp),	intent(in)			::	dv	Tridiagonal matrix elements.
complex(kind=sp),	intent(in)			::	du	Tridiagonal matrix elements.
integer(kind=ilp),	intent(in)			::	n	Matrix dimension.

Return Value type(tridiagonal_csp_type)

Corresponding Tridiagonal matrix.

private pure module function initialize_constant_tridiagonal_pure_dp(dl, dv, du, n) result(A)

Construct a tridiagonal matrix with constant elements.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	dl	Tridiagonal matrix elements.
real(kind=dp),	intent(in)			::	dv	Tridiagonal matrix elements.
real(kind=dp),	intent(in)			::	du	Tridiagonal matrix elements.
integer(kind=ilp),	intent(in)			::	n	Matrix dimension.

Return Value type(tridiagonal_dp_type)

Corresponding Tridiagonal matrix.

private pure module function initialize_constant_tridiagonal_pure_sp(dl, dv, du, n) result(A)

Construct a tridiagonal matrix with constant elements.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=sp),	intent(in)			::	dl	Tridiagonal matrix elements.
real(kind=sp),	intent(in)			::	dv	Tridiagonal matrix elements.
real(kind=sp),	intent(in)			::	du	Tridiagonal matrix elements.
integer(kind=ilp),	intent(in)			::	n	Matrix dimension.

Return Value type(tridiagonal_sp_type)

Corresponding Tridiagonal matrix.

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

Construct a tridiagonal matrix from the rank-1 arrays dl, dv and du.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp),	intent(in)			::	dl(:)	Tridiagonal matrix elements.
complex(kind=dp),	intent(in)			::	dv(:)	Tridiagonal matrix elements.
complex(kind=dp),	intent(in)			::	du(:)	Tridiagonal matrix elements.
type(linalg_state_type),	intent(out)			::	err	Error handling.

Return Value type(tridiagonal_cdp_type)

Corresponding Tridiagonal matrix.

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

Construct a tridiagonal matrix from the rank-1 arrays dl, dv and du.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=sp),	intent(in)			::	dl(:)	Tridiagonal matrix elements.
complex(kind=sp),	intent(in)			::	dv(:)	Tridiagonal matrix elements.
complex(kind=sp),	intent(in)			::	du(:)	Tridiagonal matrix elements.
type(linalg_state_type),	intent(out)			::	err	Error handling.

Return Value type(tridiagonal_csp_type)

Corresponding Tridiagonal matrix.

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

Construct a tridiagonal matrix from the rank-1 arrays dl, dv and du.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	dl(:)	Tridiagonal matrix elements.
real(kind=dp),	intent(in)			::	dv(:)	Tridiagonal matrix elements.
real(kind=dp),	intent(in)			::	du(:)	Tridiagonal matrix elements.
type(linalg_state_type),	intent(out)			::	err	Error handling.

Return Value type(tridiagonal_dp_type)

Corresponding Tridiagonal matrix.

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

Construct a tridiagonal matrix from the rank-1 arrays dl, dv and du.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=sp),	intent(in)			::	dl(:)	Tridiagonal matrix elements.
real(kind=sp),	intent(in)			::	dv(:)	Tridiagonal matrix elements.
real(kind=sp),	intent(in)			::	du(:)	Tridiagonal matrix elements.
type(linalg_state_type),	intent(out)			::	err	Error handling.

Return Value type(tridiagonal_sp_type)

Corresponding Tridiagonal matrix.

private pure module function initialize_tridiagonal_pure_cdp(dl, dv, du) result(A)

Construct a tridiagonal matrix from the rank-1 arrays dl, dv and du.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp),	intent(in)			::	dl(:)	Tridiagonal matrix elements.
complex(kind=dp),	intent(in)			::	dv(:)	Tridiagonal matrix elements.
complex(kind=dp),	intent(in)			::	du(:)	Tridiagonal matrix elements.

Return Value type(tridiagonal_cdp_type)

Corresponding Tridiagonal matrix.

private pure module function initialize_tridiagonal_pure_csp(dl, dv, du) result(A)

Construct a tridiagonal matrix from the rank-1 arrays dl, dv and du.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=sp),	intent(in)			::	dl(:)	Tridiagonal matrix elements.
complex(kind=sp),	intent(in)			::	dv(:)	Tridiagonal matrix elements.
complex(kind=sp),	intent(in)			::	du(:)	Tridiagonal matrix elements.

Return Value type(tridiagonal_csp_type)

Corresponding Tridiagonal matrix.

private pure module function initialize_tridiagonal_pure_dp(dl, dv, du) result(A)

Construct a tridiagonal matrix from the rank-1 arrays dl, dv and du.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	dl(:)	Tridiagonal matrix elements.
real(kind=dp),	intent(in)			::	dv(:)	Tridiagonal matrix elements.
real(kind=dp),	intent(in)			::	du(:)	Tridiagonal matrix elements.

Return Value type(tridiagonal_dp_type)

Corresponding Tridiagonal matrix.

private pure module function initialize_tridiagonal_pure_sp(dl, dv, du) result(A)

Construct a tridiagonal matrix from the rank-1 arrays dl, dv and du.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=sp),	intent(in)			::	dl(:)	Tridiagonal matrix elements.
real(kind=sp),	intent(in)			::	dv(:)	Tridiagonal matrix elements.
real(kind=sp),	intent(in)			::	du(:)	Tridiagonal matrix elements.

Return Value type(tridiagonal_sp_type)

Corresponding Tridiagonal matrix.