Decomposition Operations<TReal, TComplex>.LUEstimate Condition Method
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
LUEstimate | 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. |
LUEstimate | 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) DOUBLE 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) DOUBLE 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) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) DOUBLE 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 |
LUEstimate | 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. |
LUEstimate | 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) DOUBLE 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) DOUBLE 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) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) DOUBLE 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 |
LUEstimate | 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. |
LUEstimate | 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) DOUBLE 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) DOUBLE 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) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) DOUBLE 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<TReal>, TReal, TReal, 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.
public void LUEstimateCondition(
MatrixNorm norm,
int n,
Array2D<TReal> a,
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.
- a Array2D<TReal>
A is TReal array, 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 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 ?GECON.
LUEstimateCondition(MatrixNorm, Int32, Array2D<TComplex>, TReal, TReal, Int32)
public void LUEstimateCondition(
MatrixNorm norm,
int n,
Array2D<TComplex> a,
TReal anorm,
out TReal rcond,
out int info
)
Parameters
LUEstimateCondition(MatrixNorm, Int32, Span2D<TReal>, TReal, TReal, 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.
public void LUEstimateCondition(
MatrixNorm norm,
int n,
Span2D<TReal> a,
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.
- a Span2D<TReal>
A is TReal array, 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 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 ?GECON.
LUEstimateCondition(MatrixNorm, Int32, Span2D<TComplex>, TReal, TReal, Int32)
public void LUEstimateCondition(
MatrixNorm norm,
int n,
Span2D<TComplex> a,
TReal anorm,
out TReal rcond,
out int info
)
Parameters
LUEstimateCondition(MatrixNorm, Int32, Span<TReal>, Int32, TReal, TReal, 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.
public abstract void LUEstimateCondition(
MatrixNorm norm,
int n,
Span<TReal> a,
int lda,
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.
- a Span<TReal>
A is TReal array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by DGETRF.
- lda Int32
The leading dimension of the array A. LDA >= max(1,N).
- 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 ?GECON.
LUEstimateCondition(MatrixNorm, Int32, Span<TComplex>, Int32, TReal, TReal, Int32)
public abstract void LUEstimateCondition(
MatrixNorm norm,
int n,
Span<TComplex> a,
int lda,
TReal anorm,
out TReal rcond,
out int info
)