DecompositionOperations<TReal, TComplex>.TriangularEstimateCondition Method

public void TriangularEstimateCondition(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int n,
	Array2D<TReal> a,
	out TReal rcond,
	out int info
)

Public Sub TriangularEstimateCondition ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	n As Integer,
	a As Array2D(Of TReal),
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
void TriangularEstimateCondition(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int n, 
	Array2D<TReal> a, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member TriangularEstimateCondition : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        n : int * 
        a : Array2D<'TReal> * 
        rcond : 'TReal byref * 
        info : int byref -> unit 

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.
            

storedTriangle  MatrixTriangle

            = 'U':  A is upper triangular;
            = 'L':  A is lower triangular.
            

diag  MatrixDiagonal

            = 'N':  A is non-unit triangular;
            = 'U':  A is unit triangular.
            

n  Int32

            The order of the matrix A.  N >= 0.
            

a  Array2D<TReal>

            A is TReal array, dimension (LDA,N)
            The triangular matrix A.  If UPLO = 'U', the leading N-by-N
            upper triangular part of the array A contains the upper
            triangular matrix, and the strictly lower triangular part of
            A is not referenced.  If UPLO = 'L', the leading N-by-N lower
            triangular part of the array A contains the lower triangular
            matrix, and the strictly upper triangular part of A is not
            referenced.  If DIAG = 'U', the diagonal elements of A are
            also not referenced and are assumed to be 1.
            

            The leading dimension of the array A.  LDA >= max(1,N).
            

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
            

            The norm of A is computed and an estimate is obtained for
            norm(inv(A)), then the reciprocal of the condition number is
            computed as
               RCOND = 1 / ( norm(A) * norm(inv(A)) ).
            

This method corresponds to the LAPACK routine ?TRCON.

public void TriangularEstimateCondition(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int n,
	Array2D<TComplex> a,
	out TReal rcond,
	out int info
)

Public Sub TriangularEstimateCondition ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	n As Integer,
	a As Array2D(Of TComplex),
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
void TriangularEstimateCondition(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int n, 
	Array2D<TComplex> a, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member TriangularEstimateCondition : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        n : int * 
        a : Array2D<'TComplex> * 
        rcond : 'TReal byref * 
        info : int byref -> unit 

Parameters

norm  MatrixNorm

A MatrixNorm value that specifies which norm to use in the expression for the condition number.

storedTriangle  MatrixTriangle

A MatrixTriangle value that indicates whether the matrix is upper or lower triangular.

diag  MatrixDiagonal

A MatrixDiagonal value that indicates whether the matrix is unit diagonal.

n  Int32

The number of rows and columns of the matrix.

a  Array2D<TComplex>

A complex array that contains the elements of the matrix.

rcond  TReal

On return, an estimate for the reciprocal of the condition number of the matrix.

info  Int32

On return, indicates error conditions.

public void TriangularEstimateCondition(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan2D<TReal> a,
	out TReal rcond,
	out int info
)

Public Sub TriangularEstimateCondition ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	n As Integer,
	a As ReadOnlySpan2D(Of TReal),
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
void TriangularEstimateCondition(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int n, 
	ReadOnlySpan2D<TReal> a, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member TriangularEstimateCondition : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        n : int * 
        a : ReadOnlySpan2D<'TReal> * 
        rcond : 'TReal byref * 
        info : int byref -> unit 

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.
            

storedTriangle  MatrixTriangle

            = 'U':  A is upper triangular;
            = 'L':  A is lower triangular.
            

diag  MatrixDiagonal

            = 'N':  A is non-unit triangular;
            = 'U':  A is unit triangular.
            

n  Int32

            The order of the matrix A.  N >= 0.
            

a  ReadOnlySpan2D<TReal>

            A is TReal array, dimension (LDA,N)
            The triangular matrix A.  If UPLO = 'U', the leading N-by-N
            upper triangular part of the array A contains the upper
            triangular matrix, and the strictly lower triangular part of
            A is not referenced.  If UPLO = 'L', the leading N-by-N lower
            triangular part of the array A contains the lower triangular
            matrix, and the strictly upper triangular part of A is not
            referenced.  If DIAG = 'U', the diagonal elements of A are
            also not referenced and are assumed to be 1.
            

            The leading dimension of the array A.  LDA >= max(1,N).
            

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
            

            The norm of A is computed and an estimate is obtained for
            norm(inv(A)), then the reciprocal of the condition number is
            computed as
               RCOND = 1 / ( norm(A) * norm(inv(A)) ).
            

This method corresponds to the LAPACK routine ?TRCON.

public void TriangularEstimateCondition(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan2D<TComplex> a,
	out TReal rcond,
	out int info
)

Public Sub TriangularEstimateCondition ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	n As Integer,
	a As ReadOnlySpan2D(Of TComplex),
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
void TriangularEstimateCondition(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int n, 
	ReadOnlySpan2D<TComplex> a, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member TriangularEstimateCondition : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        n : int * 
        a : ReadOnlySpan2D<'TComplex> * 
        rcond : 'TReal byref * 
        info : int byref -> unit 

Parameters

norm  MatrixNorm

A MatrixNorm value that specifies which norm to use in the expression for the condition number.

storedTriangle  MatrixTriangle

A MatrixTriangle value that indicates whether the matrix is upper or lower triangular.

diag  MatrixDiagonal

A MatrixDiagonal value that indicates whether the matrix is unit diagonal.

n  Int32

The number of rows and columns of the matrix.

a  ReadOnlySpan2D<TComplex>

A complex array that contains the elements of the matrix.

rcond  TReal

On return, an estimate for the reciprocal of the condition number of the matrix.

info  Int32

On return, indicates error conditions.

public abstract void TriangularEstimateCondition(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan<TReal> a,
	int lda,
	out TReal rcond,
	out int info
)

Public MustOverride Sub TriangularEstimateCondition ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	n As Integer,
	a As ReadOnlySpan(Of TReal),
	lda As Integer,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
virtual void TriangularEstimateCondition(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int n, 
	ReadOnlySpan<TReal> a, 
	int lda, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
) abstract

abstract TriangularEstimateCondition : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        n : int * 
        a : ReadOnlySpan<'TReal> * 
        lda : int * 
        rcond : 'TReal byref * 
        info : int byref -> unit 

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.
            

storedTriangle  MatrixTriangle

            = 'U':  A is upper triangular;
            = 'L':  A is lower triangular.
            

diag  MatrixDiagonal

            = 'N':  A is non-unit triangular;
            = 'U':  A is unit triangular.
            

n  Int32

            The order of the matrix A.  N >= 0.
            

a  ReadOnlySpan<TReal>

            A is TReal array, dimension (LDA,N)
            The triangular matrix A.  If UPLO = 'U', the leading N-by-N
            upper triangular part of the array A contains the upper
            triangular matrix, and the strictly lower triangular part of
            A is not referenced.  If UPLO = 'L', the leading N-by-N lower
            triangular part of the array A contains the lower triangular
            matrix, and the strictly upper triangular part of A is not
            referenced.  If DIAG = 'U', the diagonal elements of A are
            also not referenced and are assumed to be 1.
            

lda  Int32

            The leading dimension of the array A.  LDA >= max(1,N).
            

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
            

            The norm of A is computed and an estimate is obtained for
            norm(inv(A)), then the reciprocal of the condition number is
            computed as
               RCOND = 1 / ( norm(A) * norm(inv(A)) ).
            

This method corresponds to the LAPACK routine ?TRCON.

public abstract void TriangularEstimateCondition(
	MatrixNorm norm,
	MatrixTriangle storedTriangle,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan<TComplex> a,
	int lda,
	out TReal rcond,
	out int info
)

Public MustOverride Sub TriangularEstimateCondition ( 
	norm As MatrixNorm,
	storedTriangle As MatrixTriangle,
	diag As MatrixDiagonal,
	n As Integer,
	a As ReadOnlySpan(Of TComplex),
	lda As Integer,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
virtual void TriangularEstimateCondition(
	MatrixNorm norm, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal diag, 
	int n, 
	ReadOnlySpan<TComplex> a, 
	int lda, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
) abstract

abstract TriangularEstimateCondition : 
        norm : MatrixNorm * 
        storedTriangle : MatrixTriangle * 
        diag : MatrixDiagonal * 
        n : int * 
        a : ReadOnlySpan<'TComplex> * 
        lda : int * 
        rcond : 'TReal byref * 
        info : int byref -> unit 

Parameters

norm  MatrixNorm

A MatrixNorm value that specifies which norm to use in the expression for the condition number.

storedTriangle  MatrixTriangle

A MatrixTriangle value that indicates whether the matrix is upper or lower triangular.

diag  MatrixDiagonal

A MatrixDiagonal value that indicates whether the matrix is unit diagonal.

n  Int32

The number of rows and columns of the matrix.

a  ReadOnlySpan<TComplex>

A complex array that contains the elements of the matrix.

lda  Int32

The leading dimension of the matrix a.

rcond  TReal

On return, an estimate for the reciprocal of the condition number of the matrix.

info  Int32

On return, indicates error conditions.

Reference