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Contents - Matrix and vector operations - Operations on complex matrices - Complex matrix inverse
LU decomposition has many applications, including the inversion of complex matrices. If we know the LU decomposition of a square complex matrix, we can use algorithm of triangular complex matrix inversion to invert matrix U and get a system of linear equations in A -1 which can easily be solved from the system matrix properties. One of the advantages of this algorithm over the Gauss method is that if we have performed the LU decomposition of matrix A (for example, to calculate the determinant or to solve a system of linear equations), we can use the results to invert the matrix. The algorithm includes two subroutines. The first, CMatrixLUInverse, calculates the inverse matrix by using the result of subroutine CMatrixLU. The second, CMatrixInverse, performs the LU decomposition by itself. Both subroutines return False if the matrix is singular (in this case at least one of the diagonal elements of matrix U equals 0), in that case, the matrix inversion cannot be performed. If the matrix is not singular and the inversion could be performed, the subroutines return True. In that case, the matrix could be ill-conditioned, but the subroutines don't estimate the matrix condition number. This algorithm is transferred from the LAPACK library.
C#
C# 1.0 source. C++
C++ source. C++, multiple precision arithmetic
C++ source. MPFR/GMP is used. Delphi
Delphi source. Visual Basic 6
Visual Basic 6 source. Zonnon beta
Zonnon source. |
cinverse.csharp.zip|
Sergey Bochkanov, Vladimir Bystritsky Copyright © 1999-2008 |