Decomposition Operations<TReal, TComplex>.Band LUEstimate Condition Method
Definition
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
Overload List
Band | 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. |
Band | 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<TReal>, Array1D<Int32>, TReal, TReal, 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.
public abstract void BandLUEstimateCondition(
MatrixNorm norm,
int n,
int kl,
int ku,
Array2D<TReal> ab,
Array1D<int> ipiv,
TReal anorm,
out TReal 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<TReal>
AB is TReal array, 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 TReal
ANORM is TReal 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 TReal
RCOND is TReal The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
- 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 / ( norm(A) * norm(inv(A)) ).
This method corresponds to the LAPACK routine ?GBCON.
BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, Array2D<TComplex>, Array1D<Int32>, TReal, TReal, 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.
public abstract void BandLUEstimateCondition(
MatrixNorm norm,
int n,
int kl,
int ku,
Array2D<TComplex> ab,
Array1D<int> ipiv,
TReal anorm,
out TReal 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<TComplex>
AB is TComplex 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 TReal
ANORM is TReal 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 TReal
RCOND is TReal The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
- 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 / ( norm(A) * norm(inv(A)) ).
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011