DecompositionOperations<TReal, TComplex>.CholeskyInvert Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3

Overload List

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

Computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

CholeskyInvert(MatrixTriangle, Int32, Array2D<TComplex>, Int32) Computes the inverse of a factored hermitian matrix.
CholeskyInvert(MatrixTriangle, Int32, Span2D<TReal>, Int32)

Computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

CholeskyInvert(MatrixTriangle, Int32, Span2D<TComplex>, Int32) Computes the inverse of a factored hermitian matrix.
CholeskyInvert(MatrixTriangle, Int32, Span<TReal>, Int32, Int32)

Computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

CholeskyInvert(MatrixTriangle, Int32, Span<TComplex>, Int32, Int32) Computes the inverse of a factored hermitian matrix.

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

Computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

C#
public void CholeskyInvert(
	MatrixTriangle storedTriangle,
	int n,
	Array2D<TReal> a,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
            = 'U':  Upper triangle of A is stored;
            = 'L':  Lower triangle of A is stored.
            
n  Int32
            The order of the matrix A.  N >= 0.
            
a  Array2D<TReal>
            A is TReal array, dimension (LDA,N)
            On entry, the triangular factor U or L from the Cholesky
            factorization A = UT*U or A = L*LT, as computed by
            DPOTRF.
            On exit, the upper or lower triangle of the (symmetric)
            inverse of A, overwriting the input factor U or L.
            
            The leading dimension of the array A.  LDA >= max(1,N).
            
info  Int32
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i, the (i,i) element of the factor U or L is
                  zero, and the inverse could not be computed.
            

Remarks

This method corresponds to the LAPACK routine ?POTRI.

CholeskyInvert(MatrixTriangle, Int32, Array2D<TComplex>, Int32)

Computes the inverse of a factored hermitian matrix.
C#
public void CholeskyInvert(
	MatrixTriangle storedTriangle,
	int n,
	Array2D<TComplex> a,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
A MatrixTriangle value that indicates whether the matrix components are stored in the upper or lower triangular part.
n  Int32
The number of rows and columns of the matrix.
a  Array2D<TComplex>
A complex array that contains the elements of the matrix.
info  Int32
On return, indicates error conditions.

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

Computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

C#
public void CholeskyInvert(
	MatrixTriangle storedTriangle,
	int n,
	Span2D<TReal> a,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
            = 'U':  Upper triangle of A is stored;
            = 'L':  Lower triangle of A is stored.
            
n  Int32
            The order of the matrix A.  N >= 0.
            
a  Span2D<TReal>
            A is TReal array, dimension (LDA,N)
            On entry, the triangular factor U or L from the Cholesky
            factorization A = UT*U or A = L*LT, as computed by
            DPOTRF.
            On exit, the upper or lower triangle of the (symmetric)
            inverse of A, overwriting the input factor U or L.
            
            The leading dimension of the array A.  LDA >= max(1,N).
            
info  Int32
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i, the (i,i) element of the factor U or L is
                  zero, and the inverse could not be computed.
            

Remarks

This method corresponds to the LAPACK routine ?POTRI.

CholeskyInvert(MatrixTriangle, Int32, Span2D<TComplex>, Int32)

Computes the inverse of a factored hermitian matrix.
C#
public void CholeskyInvert(
	MatrixTriangle storedTriangle,
	int n,
	Span2D<TComplex> a,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
A MatrixTriangle value that indicates whether the matrix components are stored in the upper or lower triangular part.
n  Int32
The number of rows and columns of the matrix.
a  Span2D<TComplex>
A complex array that contains the elements of the matrix.
info  Int32
On return, indicates error conditions.

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

Computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

C#
public abstract void CholeskyInvert(
	MatrixTriangle storedTriangle,
	int n,
	Span<TReal> a,
	int lda,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
            = 'U':  Upper triangle of A is stored;
            = 'L':  Lower triangle of A is stored.
            
n  Int32
            The order of the matrix A.  N >= 0.
            
a  Span<TReal>
            A is TReal array, dimension (LDA,N)
            On entry, the triangular factor U or L from the Cholesky
            factorization A = UT*U or A = L*LT, as computed by
            DPOTRF.
            On exit, the upper or lower triangle of the (symmetric)
            inverse of A, overwriting the input factor U or L.
            
lda  Int32
            The leading dimension of the array A.  LDA >= max(1,N).
            
info  Int32
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            > 0:  if INFO = i, the (i,i) element of the factor U or L is
                  zero, and the inverse could not be computed.
            

Remarks

This method corresponds to the LAPACK routine ?POTRI.

CholeskyInvert(MatrixTriangle, Int32, Span<TComplex>, Int32, Int32)

Computes the inverse of a factored hermitian matrix.
C#
public abstract void CholeskyInvert(
	MatrixTriangle storedTriangle,
	int n,
	Span<TComplex> a,
	int lda,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
A MatrixTriangle value that indicates whether the matrix components are stored in the upper or lower triangular part.
n  Int32
The number of rows and columns of the matrix.
a  Span<TComplex>
A complex array that contains the elements of the matrix.
lda  Int32
The leading dimension of the matrix a.
info  Int32
On return, indicates error conditions.

See Also