DecompositionOperations<TReal, TComplex>.BandCholeskyEstimateCondition Method

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23

Overload List

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TReal>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF.

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TComplex>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF.

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TReal>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF.

C# 
public abstract void BandCholeskyEstimateCondition(
	MatrixTriangle storedTriangle,
	int n,
	int kd,
	Array2D<TReal> ab,
	TReal aNorm,
	out TReal rcond,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.
n  Int32
            The order of the matrix A.  N >= 0.
kd  Int32
            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
ab  Array2D<TReal>
            AB is TReal array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = UT*U or A = L*LT of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
            
            The leading dimension of the array AB.  LDAB >= KD+1.
aNorm  TReal
            ANORM is TReal
            The 1-norm (or infinity-norm) of the symmetric band matrix A.
rcond  TReal
            RCOND is TReal
            The reciprocal of the condition number of the matrix A,
            computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
            estimate of the 1-norm of inv(A) computed in this routine.
info  Int32
            = 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 / (ANORM * norm(inv(A))).

This method corresponds to the LAPACK routine DPBCON.

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TComplex>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF.

C# 
public abstract void BandCholeskyEstimateCondition(
	MatrixTriangle uplo,
	int n,
	int kd,
	Array2D<TComplex> ab,
	TReal anorm,
	out TReal rcond,
	out int info
)

Parameters

uplo  MatrixTriangle
            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.
n  Int32
            The order of the matrix A.  N >= 0.
kd  Int32
            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
ab  Array2D<TComplex>
            AB is TComplex array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = UH*U or A = L*LH of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
            
            The leading dimension of the array AB.  LDAB >= KD+1.
anorm  TReal
            ANORM is TReal
            The 1-norm (or infinity-norm) of the Hermitian band matrix A.
rcond  TReal
            RCOND is TReal
            The reciprocal of the condition number of the matrix A,
            computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
            estimate of the 1-norm of inv(A) computed in this routine.
info  Int32
            = 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 / (ANORM * norm(inv(A))).

See Also