DecompositionOperations<TReal, TComplex>.LUEstimateCondition Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.2

Overload List

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.

LUEstimateCondition(MatrixNorm, Int32, Array2D<TComplex>, TReal, TReal, 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) 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, 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.

LUEstimateCondition(MatrixNorm, Int32, Span2D<TComplex>, TReal, TReal, 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) 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, 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.

LUEstimateCondition(MatrixNorm, Int32, Span<TComplex>, Int32, TReal, TReal, 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) 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.

C# 
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)

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

Parameters

norm  MatrixNorm
 
n  Int32
 
a  Array2D<TComplex>
 
anorm  TReal
 
rcond  TReal
 
info  Int32
 

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.

C# 
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)

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
C# 
public void LUEstimateCondition(
	MatrixNorm norm,
	int n,
	Span2D<TComplex> a,
	TReal anorm,
	out TReal rcond,
	out int info
)

Parameters

norm  MatrixNorm
 
n  Int32
 
a  Span2D<TComplex>
 
anorm  TReal
 
rcond  TReal
 
info  Int32
 

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.

C# 
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)

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
C# 
public abstract void LUEstimateCondition(
	MatrixNorm norm,
	int n,
	Span<TComplex> a,
	int lda,
	TReal anorm,
	out TReal rcond,
	out int info
)

Parameters

norm  MatrixNorm
 
n  Int32
 
a  Span<TComplex>
 
lda  Int32
 
anorm  TReal
 
rcond  TReal
 
info  Int32
 

See Also