linalg::solve_lu Interface Reference

Solves a system of LU-factored equations. More...

Public Member Functions
	solve_lu_mtx
	solve_lu_mtx_cmplx
	solve_lu_vec
	solve_lu_vec_cmplx
	csr_lu_solve

Detailed Description

Solves a system of LU-factored equations.

Syntax

subroutine solve_lu(real(real64) a(:,:), integer(int32) ipvt(:), real(real64) b(:,:), optional class(errors) err)
subroutine solve_lu(complex(real64) a(:,:), integer(int32) ipvt(:), complex(real64) b(:,:), optional class(errors) err)
subroutine solve_lu(real(real64) a(:,:), integer(int32) ipvt(:), real(real64) b(:), optional class(errors) err)
subroutine solve_lu(complex(real64) a(:,:), integer(int32) ipvt(:), complex(real64) b(:), optional class(errors) err)

Parameters

[in]	a	The N-by-N LU factored matrix as output by lu_factor.
[in]	ipvt	The N-element pivot array as output by lu_factor.
[in,out]	b	On input, the N-by-NRHS right-hand-side matrix. On output, the N-by-NRHS solution matrix.
[in,out]	err	An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows. LA_ARRAY_SIZE_ERROR: Occurs if any of the input array sizes are incorrect.

Sparse Syntax

subroutine solve_lu(class(msr_matrix) lu, integer(int32) ju(:), real(real64) b(:), real(real64) x(:), optional class(errors) err)

Parameters

[in]	lu	The N-by-N LU-factored matrix from lu_factor.
[in]	ju	The N-element U row tracking array from lu_factor.
[in]	b	The N-element right-hand-side array.
[out]	x	The N-element solution array.
[in,out]	err	An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows. LA_ARRAY_SIZE_ERROR: Occurs if any of the input array sizes are incorrect.

Notes

The dense routine is based upon the LAPACK routine DGETRS (ZGETRS in the complex case).

Usage

To solve a system of 3 equations of 3 unknowns using LU factorization, the following code will suffice.

program example
    use iso_fortran_env
    use linalg
    implicit none
 
    ! Local Variables
    real(real64) :: a(3,3), b(3)
    integer(int32) :: i, pvt(3)
 
    ! Build the 3-by-3 matrix A.
    !     | 1   2   3 |
    ! A = | 4   5   6 |
    !     | 7   8   0 |
    a = reshape( &
        [1.0d0, 4.0d0, 7.0d0, 2.0d0, 5.0d0, 8.0d0, 3.0d0, 6.0d0, 0.0d0], &
        [3, 3])
 
    ! Build the right-hand-side vector B.
    !     | -1 |
    ! b = | -2 |
    !     | -3 |
    b = [-1.0d0, -2.0d0, -3.0d0]
 
    ! The solution is:
    !     |  1/3 |
    ! x = | -2/3 |
    !     |   0  |
 
    ! Compute the LU factorization
    call lu_factor(a, pvt)
 
    ! Compute the solution.  The results overwrite b.
    call solve_lu(a, pvt, b)
 
    ! Display the results.
    print '(A)', "LU Solution: X = "
    print '(F8.4)', (b(i), i = 1, size(b))
end program

The program generates the following output.

LU Solution: X =
 0.3333
-0.6667
 0.0000

See Also

• Wikipedia
• Wolfram MathWorld

Definition at line 2421 of file linalg.f90.

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The documentation for this interface was generated from the following file:

• D:/Code/linalg/src/linalg.f90