GenericDecompositionOperations<T>.BandLUEstimateCondition Method

Definition

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

Overload List

BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, Array2D<T>, Array1D<Int32>, T, T, Int32)

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

BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, Array2D<Complex<T>>, Array1D<Int32>, T, T, Int32)

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

BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, Array2D<T>, Array1D<Int32>, T, T, Int32)

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

C# 
public override void BandLUEstimateCondition(
	MatrixNorm norm,
	int n,
	int kl,
	int ku,
	Array2D<T> ab,
	Array1D<int> ipiv,
	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.
kl  Int32
            The number of subdiagonals within the band of A.  KL >= 0.
ku  Int32
            The number of superdiagonals within the band of A.  KU >= 0.
ab  Array2D<T>
            Dimension (LDAB,N)
            Details of the LU factorization of the band matrix A, as
            computed by DGBTRF.  U is stored as an upper triangular band
            matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
            the multipliers used during the factorization are stored in
            rows KL+KU+2 to 2*KL+KU+1.
            
            The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
ipiv  Array1D<Int32>
            Dimension (N)
            The pivot indices; for 1 <= i <= N, row i of the matrix was
            interchanged with row IPIV(i).
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 DGBCON.

BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, Array2D<Complex<T>>, Array1D<Int32>, T, T, Int32)

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

C# 
public override void BandLUEstimateCondition(
	MatrixNorm norm,
	int n,
	int kl,
	int ku,
	Array2D<Complex<T>> ab,
	Array1D<int> ipiv,
	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.
kl  Int32
            The number of subdiagonals within the band of A.  KL >= 0.
ku  Int32
            The number of superdiagonals within the band of A.  KU >= 0.
ab  Array2D<Complex<T>>
            AB is COMPLEX*16 array, dimension (LDAB,N)
            Details of the LU factorization of the band matrix A, as
            computed by ZGBTRF.  U is stored as an upper triangular band
            matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
            the multipliers used during the factorization are stored in
            rows KL+KU+2 to 2*KL+KU+1.
            
            The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
ipiv  Array1D<Int32>
            Dimension (N)
            The pivot indices; for 1 <= i <= N, row i of the matrix was
            interchanged with row IPIV(i).
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)) ).

See Also