DecompositionOperations<TReal, TComplex>.BandCholeskyEstimateCondition Method

Definition

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

Overload List

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TReal>, TReal, TReal, Int32)	Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U^TU or A = LL^T computed by DPBTRF.
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TComplex>, TReal, TReal, Int32)	Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U^HU or A = LL^H computed by ZPBTRF.
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TComplex>, TReal, TReal, Int32)	Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U^HU or A = LL^H computed by ZPBTRF.
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span2D<TReal>, TReal, TReal, Int32)	Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U^TU or A = LL^T computed by DPBTRF.
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan<TComplex>, Int32, TReal, TReal, Int32)	Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U^HU or A = LL^H computed by ZPBTRF.
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span<TReal>, Int32, TReal, TReal, Int32)	Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U^TU or A = LL^T computed by DPBTRF.

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TReal>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U^T*U or A = L*L^T computed by DPBTRF.

public void BandCholeskyEstimateCondition(
	MatrixTriangle storedTriangle,
	int n,
	int kd,
	Array2D<TReal> ab,
	TReal aNorm,
	out TReal rcond,
	out int info
)

Visual Basic

Public Sub BandCholeskyEstimateCondition ( 
	storedTriangle As MatrixTriangle,
	n As Integer,
	kd As Integer,
	ab As Array2D(Of TReal),
	aNorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
void BandCholeskyEstimateCondition(
	MatrixTriangle storedTriangle, 
	int n, 
	int kd, 
	Array2D<TReal> ab, 
	TReal aNorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member BandCholeskyEstimateCondition : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        kd : int * 
        ab : Array2D<'TReal> * 
        aNorm : 'TReal * 
        rcond : 'TReal byref * 
        info : int byref -> unit

Parameters

storedTriangle MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

ab Array2D<TReal>

            AB is TReal array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = U^T*U or A = L*L^T of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

            The leading dimension of the array AB.  LDAB >= KD+1.

aNorm TReal

            ANORM is TReal
            The 1-norm (or infinity-norm) of the symmetric band matrix A.

rcond TReal

            RCOND is TReal
            The reciprocal of the condition number of the matrix A,
            computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
            estimate of the 1-norm of inv(A) computed in this routine.

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 / (ANORM * norm(inv(A))).

This method corresponds to the LAPACK routine DPBCON.

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TComplex>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U^H*U or A = L*L^H computed by ZPBTRF.

public void BandCholeskyEstimateCondition(
	MatrixTriangle uplo,
	int n,
	int kd,
	Array2D<TComplex> ab,
	TReal anorm,
	out TReal rcond,
	out int info
)

Visual Basic

Public Sub BandCholeskyEstimateCondition ( 
	uplo As MatrixTriangle,
	n As Integer,
	kd As Integer,
	ab As Array2D(Of TComplex),
	anorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
void BandCholeskyEstimateCondition(
	MatrixTriangle uplo, 
	int n, 
	int kd, 
	Array2D<TComplex> ab, 
	TReal anorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member BandCholeskyEstimateCondition : 
        uplo : MatrixTriangle * 
        n : int * 
        kd : int * 
        ab : Array2D<'TComplex> * 
        anorm : 'TReal * 
        rcond : 'TReal byref * 
        info : int byref -> unit

Parameters

uplo MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

ab Array2D<TComplex>

            AB is TComplex array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = U^H*U or A = L*L^H of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

            The leading dimension of the array AB.  LDAB >= KD+1.

anorm TReal

            ANORM is TReal
            The 1-norm (or infinity-norm) of the Hermitian band matrix A.

rcond TReal

            RCOND is TReal
            The reciprocal of the condition number of the matrix A,
            computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
            estimate of the 1-norm of inv(A) computed in this routine.

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 / (ANORM * norm(inv(A))).

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TComplex>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U^H*U or A = L*L^H computed by ZPBTRF.

public void BandCholeskyEstimateCondition(
	MatrixTriangle uplo,
	int n,
	int kd,
	ReadOnlySpan2D<TComplex> ab,
	TReal anorm,
	out TReal rcond,
	out int info
)

Visual Basic

Public Sub BandCholeskyEstimateCondition ( 
	uplo As MatrixTriangle,
	n As Integer,
	kd As Integer,
	ab As ReadOnlySpan2D(Of TComplex),
	anorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
void BandCholeskyEstimateCondition(
	MatrixTriangle uplo, 
	int n, 
	int kd, 
	ReadOnlySpan2D<TComplex> ab, 
	TReal anorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member BandCholeskyEstimateCondition : 
        uplo : MatrixTriangle * 
        n : int * 
        kd : int * 
        ab : ReadOnlySpan2D<'TComplex> * 
        anorm : 'TReal * 
        rcond : 'TReal byref * 
        info : int byref -> unit

Parameters

uplo MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

ab ReadOnlySpan2D<TComplex>

            AB is TComplex array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = U^H*U or A = L*L^H of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

            The leading dimension of the array AB.  LDAB >= KD+1.

anorm TReal

            ANORM is TReal
            The 1-norm (or infinity-norm) of the Hermitian band matrix A.

rcond TReal

            RCOND is TReal
            The reciprocal of the condition number of the matrix A,
            computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
            estimate of the 1-norm of inv(A) computed in this routine.

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 / (ANORM * norm(inv(A))).

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span2D<TReal>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U^T*U or A = L*L^T computed by DPBTRF.

public void BandCholeskyEstimateCondition(
	MatrixTriangle storedTriangle,
	int n,
	int kd,
	Span2D<TReal> ab,
	TReal aNorm,
	out TReal rcond,
	out int info
)

Visual Basic

Public Sub BandCholeskyEstimateCondition ( 
	storedTriangle As MatrixTriangle,
	n As Integer,
	kd As Integer,
	ab As Span2D(Of TReal),
	aNorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
void BandCholeskyEstimateCondition(
	MatrixTriangle storedTriangle, 
	int n, 
	int kd, 
	Span2D<TReal> ab, 
	TReal aNorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
)

member BandCholeskyEstimateCondition : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        kd : int * 
        ab : Span2D<'TReal> * 
        aNorm : 'TReal * 
        rcond : 'TReal byref * 
        info : int byref -> unit

Parameters

storedTriangle MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

ab Span2D<TReal>

            AB is TReal array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = U^T*U or A = L*L^T of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

            The leading dimension of the array AB.  LDAB >= KD+1.

aNorm TReal

            ANORM is TReal
            The 1-norm (or infinity-norm) of the symmetric band matrix A.

rcond TReal

            RCOND is TReal
            The reciprocal of the condition number of the matrix A,
            computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
            estimate of the 1-norm of inv(A) computed in this routine.

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 / (ANORM * norm(inv(A))).

This method corresponds to the LAPACK routine DPBCON.

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan<TComplex>, Int32, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U^H*U or A = L*L^H computed by ZPBTRF.

public abstract void BandCholeskyEstimateCondition(
	MatrixTriangle uplo,
	int n,
	int kd,
	ReadOnlySpan<TComplex> ab,
	int ldab,
	TReal anorm,
	out TReal rcond,
	out int info
)

Visual Basic

Public MustOverride Sub BandCholeskyEstimateCondition ( 
	uplo As MatrixTriangle,
	n As Integer,
	kd As Integer,
	ab As ReadOnlySpan(Of TComplex),
	ldab As Integer,
	anorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
virtual void BandCholeskyEstimateCondition(
	MatrixTriangle uplo, 
	int n, 
	int kd, 
	ReadOnlySpan<TComplex> ab, 
	int ldab, 
	TReal anorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
) abstract

abstract BandCholeskyEstimateCondition : 
        uplo : MatrixTriangle * 
        n : int * 
        kd : int * 
        ab : ReadOnlySpan<'TComplex> * 
        ldab : int * 
        anorm : 'TReal * 
        rcond : 'TReal byref * 
        info : int byref -> unit

Parameters

uplo MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

ab ReadOnlySpan<TComplex>

            AB is TComplex array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = U^H*U or A = L*L^H of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

ldab Int32

            The leading dimension of the array AB.  LDAB >= KD+1.

anorm TReal

            ANORM is TReal
            The 1-norm (or infinity-norm) of the Hermitian band matrix A.

rcond TReal

            RCOND is TReal
            The reciprocal of the condition number of the matrix A,
            computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
            estimate of the 1-norm of inv(A) computed in this routine.

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 / (ANORM * norm(inv(A))).

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span<TReal>, Int32, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U^T*U or A = L*L^T computed by DPBTRF.

public abstract void BandCholeskyEstimateCondition(
	MatrixTriangle storedTriangle,
	int n,
	int kd,
	Span<TReal> ab,
	int ldab,
	TReal aNorm,
	out TReal rcond,
	out int info
)

Visual Basic

Public MustOverride Sub BandCholeskyEstimateCondition ( 
	storedTriangle As MatrixTriangle,
	n As Integer,
	kd As Integer,
	ab As Span(Of TReal),
	ldab As Integer,
	aNorm As TReal,
	<OutAttribute> ByRef rcond As TReal,
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
virtual void BandCholeskyEstimateCondition(
	MatrixTriangle storedTriangle, 
	int n, 
	int kd, 
	Span<TReal> ab, 
	int ldab, 
	TReal aNorm, 
	[OutAttribute] TReal% rcond, 
	[OutAttribute] int% info
) abstract

abstract BandCholeskyEstimateCondition : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        kd : int * 
        ab : Span<'TReal> * 
        ldab : int * 
        aNorm : 'TReal * 
        rcond : 'TReal byref * 
        info : int byref -> unit

Parameters

storedTriangle MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

ab Span<TReal>

            AB is TReal array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = U^T*U or A = L*L^T of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

ldab Int32

            The leading dimension of the array AB.  LDAB >= KD+1.

aNorm TReal

            ANORM is TReal
            The 1-norm (or infinity-norm) of the symmetric band matrix A.

rcond TReal

            RCOND is TReal
            The reciprocal of the condition number of the matrix A,
            computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
            estimate of the 1-norm of inv(A) computed in this routine.

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 / (ANORM * norm(inv(A))).

This method corresponds to the LAPACK routine DPBCON.

DecompositionOperations<TReal, TComplex>.BandCholeskyEstimateCondition Method

Definition

Overload List

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TReal>, TReal, TReal, Int32)

Parameters

Remarks

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TComplex>, TReal, TReal, Int32)

Parameters

Remarks

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TComplex>, TReal, TReal, Int32)

Parameters

Remarks

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span2D<TReal>, TReal, TReal, Int32)

Parameters

Remarks

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan<TComplex>, Int32, TReal, TReal, Int32)

Parameters

Remarks

BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span<TReal>, Int32, TReal, TReal, Int32)

Parameters

Remarks

See Also

Reference