DecompositionOperations<TReal, TComplex>.BandLUEstimateCondition Method

public void BandLUEstimateCondition(
	MatrixNorm norm,
	int n,
	int kl,
	int ku,
	Array2D<TReal> ab,
	Array1D<int> ipiv,
	TReal anorm,
	out TReal rcond,
	out int info
)

Public Sub BandLUEstimateCondition ( 
	norm As MatrixNorm,
	n As Integer,
	kl As Integer,
	ku As Integer,
	ab As Array2D(Of TReal),
	ipiv As Array1D(Of Integer),
	anorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
void BandLUEstimateCondition(
	MatrixNorm norm, 
	int n, 
	int kl, 
	int ku, 
	Array2D<TReal> ab, 
	Array1D<int> ipiv, 
	TReal anorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member BandLUEstimateCondition : 
        norm : MatrixNorm * 
        n : int * 
        kl : int * 
        ku : int * 
        ab : Array2D<'TReal> * 
        ipiv : Array1D<int> * 
        anorm : '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.
            

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
            

            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.

public void BandLUEstimateCondition(
	MatrixNorm norm,
	int n,
	int kl,
	int ku,
	Array2D<TComplex> ab,
	Array1D<int> ipiv,
	TReal anorm,
	out TReal rcond,
	out int info
)

Public Sub BandLUEstimateCondition ( 
	norm As MatrixNorm,
	n As Integer,
	kl As Integer,
	ku As Integer,
	ab As Array2D(Of TComplex),
	ipiv As Array1D(Of Integer),
	anorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
void BandLUEstimateCondition(
	MatrixNorm norm, 
	int n, 
	int kl, 
	int ku, 
	Array2D<TComplex> ab, 
	Array1D<int> ipiv, 
	TReal anorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member BandLUEstimateCondition : 
        norm : MatrixNorm * 
        n : int * 
        kl : int * 
        ku : int * 
        ab : Array2D<'TComplex> * 
        ipiv : Array1D<int> * 
        anorm : '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.
            

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
            

            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

public void BandLUEstimateCondition(
	MatrixNorm norm,
	int n,
	int kl,
	int ku,
	ReadOnlySpan2D<TReal> ab,
	Span<int> ipiv,
	TReal anorm,
	out TReal rcond,
	out int info
)

Public Sub BandLUEstimateCondition ( 
	norm As MatrixNorm,
	n As Integer,
	kl As Integer,
	ku As Integer,
	ab As ReadOnlySpan2D(Of TReal),
	ipiv As Span(Of Integer),
	anorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
void BandLUEstimateCondition(
	MatrixNorm norm, 
	int n, 
	int kl, 
	int ku, 
	ReadOnlySpan2D<TReal> ab, 
	Span<int> ipiv, 
	TReal anorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member BandLUEstimateCondition : 
        norm : MatrixNorm * 
        n : int * 
        kl : int * 
        ku : int * 
        ab : ReadOnlySpan2D<'TReal> * 
        ipiv : Span<int> * 
        anorm : '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.
            

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  ReadOnlySpan2D<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  Span<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
            

            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.

public void BandLUEstimateCondition(
	MatrixNorm norm,
	int n,
	int kl,
	int ku,
	ReadOnlySpan2D<TComplex> ab,
	Span<int> ipiv,
	TReal anorm,
	out TReal rcond,
	out int info
)

Public Sub BandLUEstimateCondition ( 
	norm As MatrixNorm,
	n As Integer,
	kl As Integer,
	ku As Integer,
	ab As ReadOnlySpan2D(Of TComplex),
	ipiv As Span(Of Integer),
	anorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
void BandLUEstimateCondition(
	MatrixNorm norm, 
	int n, 
	int kl, 
	int ku, 
	ReadOnlySpan2D<TComplex> ab, 
	Span<int> ipiv, 
	TReal anorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member BandLUEstimateCondition : 
        norm : MatrixNorm * 
        n : int * 
        kl : int * 
        ku : int * 
        ab : ReadOnlySpan2D<'TComplex> * 
        ipiv : Span<int> * 
        anorm : '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.
            

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  ReadOnlySpan2D<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  Span<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
            

            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

public abstract void BandLUEstimateCondition(
	MatrixNorm norm,
	int n,
	int kl,
	int ku,
	ReadOnlySpan<TReal> ab,
	int ldab,
	Span<int> ipiv,
	TReal anorm,
	out TReal rcond,
	out int info
)

Public MustOverride Sub BandLUEstimateCondition ( 
	norm As MatrixNorm,
	n As Integer,
	kl As Integer,
	ku As Integer,
	ab As ReadOnlySpan(Of TReal),
	ldab As Integer,
	ipiv As Span(Of Integer),
	anorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
virtual void BandLUEstimateCondition(
	MatrixNorm norm, 
	int n, 
	int kl, 
	int ku, 
	ReadOnlySpan<TReal> ab, 
	int ldab, 
	Span<int> ipiv, 
	TReal anorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
) abstract

abstract BandLUEstimateCondition : 
        norm : MatrixNorm * 
        n : int * 
        kl : int * 
        ku : int * 
        ab : ReadOnlySpan<'TReal> * 
        ldab : int * 
        ipiv : Span<int> * 
        anorm : '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.
            

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  ReadOnlySpan<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.
            

ldab  Int32

            The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
            

ipiv  Span<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
            

            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.

public abstract void BandLUEstimateCondition(
	MatrixNorm norm,
	int n,
	int kl,
	int ku,
	ReadOnlySpan<TComplex> ab,
	int ldab,
	Span<int> ipiv,
	TReal anorm,
	out TReal rcond,
	out int info
)

Public MustOverride Sub BandLUEstimateCondition ( 
	norm As MatrixNorm,
	n As Integer,
	kl As Integer,
	ku As Integer,
	ab As ReadOnlySpan(Of TComplex),
	ldab As Integer,
	ipiv As Span(Of Integer),
	anorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

public:
virtual void BandLUEstimateCondition(
	MatrixNorm norm, 
	int n, 
	int kl, 
	int ku, 
	ReadOnlySpan<TComplex> ab, 
	int ldab, 
	Span<int> ipiv, 
	TReal anorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
) abstract

abstract BandLUEstimateCondition : 
        norm : MatrixNorm * 
        n : int * 
        kl : int * 
        ku : int * 
        ab : ReadOnlySpan<'TComplex> * 
        ldab : int * 
        ipiv : Span<int> * 
        anorm : '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.
            

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  ReadOnlySpan<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.
            

ldab  Int32

            The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
            

ipiv  Span<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
            

            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

Reference