ComplexLU Class |
Namespace: Imsl.Math
The ComplexLU type exposes the following members.
Name | Description | |
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Condition |
Return an estimate of the reciprocal of the condition number.
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Determinant |
Return the determinant of the matrix used to construct this instance.
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Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetL |
Returns the lower triangular portion of the LU
factorization of A.
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GetPermutationMatrix |
Returns the permutation matrix which results from the
LU factorization of A.
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GetType | Gets the Type of the current instance. (Inherited from Object.) | |
GetU |
Returns the unit upper triangular portion of the LU
factorization of A.
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Inverse |
Returns the inverse of the matrix used to construct this instance.
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MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
Solve(Complex) |
Return the solution x of the linear system Ax = bi> using
the LU factorization of A, where A is the input matrix
a.
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Solve(Complex, Complex) |
Return the solution x of the linear system Ax = b using
the LU factorization of A.
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SolveTranspose |
Return the solution x of the linear system .
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ToString | Returns a string that represents the current object. (Inherited from Object.) |
Name | Description | |
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NumberOfProcessors |
Perform the parallel calculations with the maximum possible number of
processors set to NumberOfProcessors.
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ComplexLU performs an LU factorization of a complex general coefficient matrix. ComplexLU's method Condition estimates the condition number of the matrix. The LU factorization is done using scaled partial pivoting. Scaled partial pivoting differs from partial pivoting in that the pivoting strategy is the same as if each row were scaled to have the same infinity norm.
The condition number of the matrix A is defined to be . Since it is expensive to compute , the condition number is only estimated. The estimation algorithm is the same as used by LINPACK and is described by Cline et al. (1979).
Note that A is not retained for use by other methods of this class, only the factorization of A is retained. Thus, A is a required parameter to the condition method.
An estimated condition number greater than (where is machine precision) indicates that very small changes in A can cause very large changes in the solution x. Iterative refinement can sometimes find the solution to such a system.
ComplexLU fails if U, the upper triangular part of the factorization, has a zero diagonal element. This can occur only if A either is singular or is very close to a singular matrix.
The Solve method can be used to solve systems of equations. The method Determinant can be called to compute the determinant of the coefficient matrix.
ComplexLU is based on the LINPACK routine CGECO; see Dongarra et al. (1979). CGECO uses unscaled partial pivoting.