GenericDecompositionOperations<T>.BandCholeskyEstimateCondition Method

public override void BandCholeskyEstimateCondition(
	MatrixTriangle storedTriangle,
	int n,
	int kd,
	ReadOnlySpan<Complex<T>> ab,
	int ldab,
	T anorm,
	out T rcond,
	out int info
)

Public Overrides Sub BandCholeskyEstimateCondition ( 
	storedTriangle As MatrixTriangle,
	n As Integer,
	kd As Integer,
	ab As ReadOnlySpan(Of Complex(Of T)),
	ldab As Integer,
	anorm As T,
	<OutAttribute> ByRef rcond As T,
	<OutAttribute> ByRef info As Integer
)

public:
virtual void BandCholeskyEstimateCondition(
	MatrixTriangle storedTriangle, 
	int n, 
	int kd, 
	ReadOnlySpan<Complex<T>> ab, 
	int ldab, 
	T anorm, 
	[OutAttribute] T% rcond, 
	[OutAttribute] int% info
) override

abstract BandCholeskyEstimateCondition : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        kd : int * 
        ab : ReadOnlySpan<Complex<'T>> * 
        ldab : int * 
        anorm : 'T * 
        rcond : 'T byref * 
        info : int byref -> unit 
override BandCholeskyEstimateCondition : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        kd : int * 
        ab : ReadOnlySpan<Complex<'T>> * 
        ldab : int * 
        anorm : 'T * 
        rcond : 'T byref * 
        info : int byref -> unit 

Parameters

storedTriangle  MatrixTriangle

 

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<Complex<T>>

            AB is TComplex array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = UH*U or A = L*LH 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  T

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

rcond  T

            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
            

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

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

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

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

abstract BandCholeskyEstimateCondition : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        kd : int * 
        ab : Span<'T> * 
        ldab : int * 
        aNorm : 'T * 
        rcond : 'T byref * 
        info : int byref -> unit 
override BandCholeskyEstimateCondition : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        kd : int * 
        ab : Span<'T> * 
        ldab : int * 
        aNorm : 'T * 
        rcond : 'T 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<T>

            AB is TReal array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = UT*U or A = L*LT 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  T

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

rcond  T

            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
            

            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.

Reference