Processing math: 100%

linalg_tri Module


Uses


Interfaces

public interface solve_triangular_system

  • private module subroutine solve_tri_mtx(lside, upper, trans, nounit, alpha, a, b, err)

    Solves a triangular system of equations of the form op(A)X=αB or Xop(A)=αB where A is a triangular matrix (either upper or lower) for the unknown X.

    Arguments

    Type IntentOptional Attributes Name
    logical, intent(in) :: lside

    Set to true to solve op(A)X=αB; else, set to false to solve Xop(A)=αB.
    logical, intent(in) :: upper

    Set to true if A is upper triangular; else, set to false if A is lower triangular.
    logical, intent(in) :: trans

    Set to true if op(A)=AT; else, set to false if op(A)=A.
    logical, intent(in) :: nounit

    Set to true if A is unit-triangular (ones on the diagonal); else, false if A is not unit-triangular.
    real(kind=real64), intent(in) :: alpha

    The scalar multiplier α.
    real(kind=real64), intent(in), dimension(:,:) :: a

    If lside is true, the M-by-M triangular matrix A; else, A is N-by-N if lside is false.
    real(kind=real64), intent(inout), dimension(:,:) :: b

    On input, the M-by-N matrix B. On output, the M-by-N solution matrix X.
    class(errors), intent(inout), optional, target :: err

    The error object to be updated.

  • private subroutine solve_tri_mtx_cmplx(lside, upper, trans, nounit, alpha, a, b, err)

    Solves a triangular system of equations of the form op(A)X=αB or Xop(A)=αB where A is a triangular matrix (either upper or lower) for the unknown X.

    Arguments

    Type IntentOptional Attributes Name
    logical, intent(in) :: lside

    Set to true to solve op(A)X=αB; else, set to false to solve Xop(A)=αB.
    logical, intent(in) :: upper

    Set to true if A is upper triangular; else, set to false if A is lower triangular.
    logical, intent(in) :: trans

    Set to true if op(A)=AH; else, set to false if op(A)=A.
    logical, intent(in) :: nounit

    Set to true if A is unit-triangular (ones on the diagonal); else, false if A is not unit-triangular.
    complex(kind=real64), intent(in) :: alpha

    The scalar multiplier α.
    complex(kind=real64), intent(in), dimension(:,:) :: a

    If lside is true, the M-by-M triangular matrix A; else, A is N-by-N if lside is false.
    complex(kind=real64), intent(inout), dimension(:,:) :: b

    On input, the M-by-N matrix B. On output, the M-by-N solution matrix X.
    class(errors), intent(inout), optional, target :: err

    The error object to be updated.

  • private subroutine solve_tri_vec(upper, trans, nounit, a, x, err)

    Solves the triangular system op(A)→x=→b where A is a triangular matrix.

    Arguments

    Type IntentOptional Attributes Name
    logical, intent(in) :: upper

    Set to true if A is upper triangular; else, set to false if A is lower triangular.
    logical, intent(in) :: trans

    Set to true if op(A)=AT; else, set to false if op(A)=A.
    logical, intent(in) :: nounit

    Set to true if A is unit-triangular (ones on the diagonal); else, false if A is not unit-triangular.
    real(kind=real64), intent(in), dimension(:,:) :: a

    The N-by-N triangular matrix A.
    real(kind=real64), intent(inout), dimension(:) :: x

    On input, the N-element vector →b. On output, the N-element solution vector →x.
    class(errors), intent(inout), optional, target :: err

    The error object to be updated.

  • private subroutine solve_tri_vec_cmplx(upper, trans, nounit, a, x, err)

    Solves the triangular system op(A)→x=→b where A is a triangular matrix.

    Arguments

    Type IntentOptional Attributes Name
    logical, intent(in) :: upper

    Set to true if A is upper triangular; else, set to false if A is lower triangular.
    logical, intent(in) :: trans

    Set to true if op(A)=AT; else, set to false if op(A)=A.
    logical, intent(in) :: nounit

    Set to true if A is unit-triangular (ones on the diagonal); else, false if A is not unit-triangular.
    complex(kind=real64), intent(in), dimension(:,:) :: a

    The N-by-N triangular matrix A.
    complex(kind=real64), intent(inout), dimension(:) :: x

    On input, the N-element vector →b. On output, the N-element solution vector →x.
    class(errors), intent(inout), optional, target :: err

    The error object to be updated.