Computes the LU factorization of an M-by-N matrix. More...

Detailed Description

Computes the LU factorization of an M-by-N matrix.

Syntax: subroutine lu_factor(real(real64) a(:,:), integer(int32) ipvt(:), optional class(errors))

subroutine lu_factor(complex(real64) a(:,:), integer(int32) ipvt(:), optional class(errors))

Parameters

[in,out]	a	On input, the M-by-N matrix on which to operate. On output, the LU factored matrix in the form [L\U] where the unit diagonal elements of L are not stored.
[out]	ipvt	An MIN(M, N)-element array used to track row-pivot operations. The array stored pivot information such that row I is interchanged with row IPVT(I).
[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 `ipvt` is not sized appropriately. LA_SINGULAR_MATRIX_ERROR: Occurs as a warning if `a` is found to be singular.

Syntax (Sparse Matrices): subroutine lu_factor(class(csr_matrix) a, type(msr_matrix) lu, integer(int32) ju(:), optional real(real64) droptol, optional class(errors) err)

Parameters

[in]	a	The M-by-N sparse matrix to factor.
[out]	lu	The factored matrix, stored in MSR format. The diagonal is stored inverted.
[out]	ju	An M-element array used to track the starting row index of the U matrix.
[in]	droptol	An optional threshold value used to determine when to drop small terms as part of the factorization of matrix A. The default value is set to the square root of machine precision (~1e-8).
[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 `ju` is not sized correctly. LA_OUT_OF_MEMORY_ERROR: Occurs if there is an issue with internal memory allocations. LA_MATRIX_FORMAT_ERROR: Occurs if `a` is improperly formatted. LA_SINGULAR_MATRIX_ERROR: Occurs if `a` is singular.

See Also

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

linalg::lu_factor
Computes the LU factorization of an M-by-N matrix.
Definition linalg.f90:844

linalg::solve_lu
Solves a system of LU-factored equations.
Definition linalg.f90:2421

linalg
Provides a set of common linear algebra routines.
Definition linalg.f90:145

The program generates the following output.
LU Solution: X =

0.3333

-0.6667

0.0000

Definition at line 844 of file linalg.f90.

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

Public Member Functions