GenericDecompositionOperations<T>.LUEstimateCondition Method

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics.Generic (in Extreme.Numerics.Generic.dll) Version: 8.1.4

Overload List

LUEstimateCondition(MatrixNorm, Int32, Array2D<T>, T, T, Int32)

Estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF.

LUEstimateCondition(MatrixNorm, Int32, Array2D<Complex<T>>, T, T, Int32) ZGECON estimates the reciprocal of the condition number of a general real matrix A, inthis. either the 1-norm or the infinity-norm, using the LU decomposition computed by ZGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Arguments ========= NORM (input) CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N (input) INTEGER The elementOrder of the matrix A. N >= 0. A (input) ZOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). ANORM (input) ZOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND (output) ZOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) ZOUBLE PRECISION array, dimension (4*N) IWORK (workspace) INTEGER array, dimension (N) info (output) INTEGER = 0: successful exit < 0: if info = -i, the i-th argument had an illegal value

LUEstimateCondition(MatrixNorm, Int32, Array2D<T>, T, T, Int32)

Estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF.

C# 
public override void LUEstimateCondition(
	MatrixNorm norm,
	int n,
	Array2D<T> a,
	T anorm,
	out T rcond,
	out int info
)

Parameters

norm  MatrixNorm
            Specifies whether the 1-norm condition number or the
            infinity-norm condition number is required:
            = '1' or 'O':  1-norm;
            = 'I':         Infinity-norm.
n  Int32
            The order of the matrix A.  N >= 0.
a  Array2D<T>
            Dimension (LDA,N)
            The factors L and U from the factorization A = P*L*U
            as computed by DGETRF.
            
            The leading dimension of the array A.  LDA >= max(1,N).
anorm  T
            If NORM = '1' or 'O', the 1-norm of the original matrix A.
            If NORM = 'I', the infinity-norm of the original matrix A.
rcond  T
            The reciprocal of the condition number of the matrix A,
            computed as RCOND = 1/(norm(A) * norm(inv(A))).
info  Int32
info is INTEGER
            = 0:  successful exit
            < 0:  if info = -i, the i-th argument had an illegal value

Remarks

            An estimate is obtained for norm(inv(A)), and the reciprocal of the
            condition number is computed as
               RCOND = 1 / ( norm(A) * norm(inv(A)) ).

This method corresponds to the LAPACK routine DGECON.

LUEstimateCondition(MatrixNorm, Int32, Array2D<Complex<T>>, T, T, Int32)

ZGECON estimates the reciprocal of the condition number of a general real matrix A, inthis. either the 1-norm or the infinity-norm, using the LU decomposition computed by ZGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Arguments ========= NORM (input) CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N (input) INTEGER The elementOrder of the matrix A. N >= 0. A (input) ZOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). ANORM (input) ZOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND (output) ZOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) ZOUBLE PRECISION array, dimension (4*N) IWORK (workspace) INTEGER array, dimension (N) info (output) INTEGER = 0: successful exit < 0: if info = -i, the i-th argument had an illegal value
C# 
public override void LUEstimateCondition(
	MatrixNorm norm,
	int n,
	Array2D<Complex<T>> a,
	T anorm,
	out T rcond,
	out int info
)

Parameters

norm  MatrixNorm
 
n  Int32
 
a  Array2D<Complex<T>>
 
anorm  T
 
rcond  T
 
info  Int32
 

See Also