DecompositionOperations<TReal, TComplex>.SymmetricInvert Method

Definition

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

Overload List

SymmetricInvert(MatrixTriangle, Int32, Array2D<TReal>, Array1D<Int32>, Int32)

Computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.

SymmetricInvert(MatrixTriangle, Int32, Span2D<TReal>, ReadOnlySpan<Int32>, Int32)

Computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.

SymmetricInvert(MatrixTriangle, Int32, Span<TReal>, Int32, ReadOnlySpan<Int32>, Int32)

Computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.

SymmetricInvert(MatrixTriangle, Int32, Array2D<TReal>, Array1D<Int32>, Int32)

Computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.

C# 
public void SymmetricInvert(
	MatrixTriangle storedTriangle,
	int n,
	Array2D<TReal> a,
	Array1D<int> ipiv,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
            Specifies whether the details of the factorization are stored
            as an upper or lower triangular matrix.
            = 'U':  Upper triangular, form is A = U*D*UT;
            = 'L':  Lower triangular, form is A = L*D*LT.
n  Int32
            The order of the matrix A.  N >= 0.
a  Array2D<TReal>
            A is TReal array, dimension (LDA,N)
            On entry, the block diagonal matrix D and the multipliers
            used to obtain the factor U or L as computed by DSYTRF.
            On exit, if INFO = 0, the (symmetric) inverse of the original
            matrix.  If UPLO = 'U', the upper triangular part of the
            inverse is formed and the part of A below the diagonal is not
            referenced; if UPLO = 'L' the lower triangular part of the
            inverse is formed and the part of A above the diagonal is
            not referenced.
            
            The leading dimension of the array A.  LDA >= max(1,N).
ipiv  Array1D<Int32>
            Dimension (N)
            Details of the interchanges and the block structure of D
            as determined by DSYTRF.
info  Int32
            = 0: successful exit
            < 0: if INFO = -i, the i-th argument had an illegal value
            > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
                 inverse could not be computed.

Remarks

This method corresponds to the LAPACK routine ?SYTRI.

SymmetricInvert(MatrixTriangle, Int32, Span2D<TReal>, ReadOnlySpan<Int32>, Int32)

Computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.

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

Parameters

storedTriangle  MatrixTriangle
            Specifies whether the details of the factorization are stored
            as an upper or lower triangular matrix.
            = 'U':  Upper triangular, form is A = U*D*UT;
            = 'L':  Lower triangular, form is A = L*D*LT.
n  Int32
            The order of the matrix A.  N >= 0.
a  Span2D<TReal>
            A is TReal array, dimension (LDA,N)
            On entry, the block diagonal matrix D and the multipliers
            used to obtain the factor U or L as computed by DSYTRF.
            On exit, if INFO = 0, the (symmetric) inverse of the original
            matrix.  If UPLO = 'U', the upper triangular part of the
            inverse is formed and the part of A below the diagonal is not
            referenced; if UPLO = 'L' the lower triangular part of the
            inverse is formed and the part of A above the diagonal is
            not referenced.
            
            The leading dimension of the array A.  LDA >= max(1,N).
ipiv  ReadOnlySpan<Int32>
            Dimension (N)
            Details of the interchanges and the block structure of D
            as determined by DSYTRF.
info  Int32
            = 0: successful exit
            < 0: if INFO = -i, the i-th argument had an illegal value
            > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
                 inverse could not be computed.

Remarks

This method corresponds to the LAPACK routine ?SYTRI.

SymmetricInvert(MatrixTriangle, Int32, Span<TReal>, Int32, ReadOnlySpan<Int32>, Int32)

Computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.

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

Parameters

storedTriangle  MatrixTriangle
            Specifies whether the details of the factorization are stored
            as an upper or lower triangular matrix.
            = 'U':  Upper triangular, form is A = U*D*UT;
            = 'L':  Lower triangular, form is A = L*D*LT.
n  Int32
            The order of the matrix A.  N >= 0.
a  Span<TReal>
            A is TReal array, dimension (LDA,N)
            On entry, the block diagonal matrix D and the multipliers
            used to obtain the factor U or L as computed by DSYTRF.
            On exit, if INFO = 0, the (symmetric) inverse of the original
            matrix.  If UPLO = 'U', the upper triangular part of the
            inverse is formed and the part of A below the diagonal is not
            referenced; if UPLO = 'L' the lower triangular part of the
            inverse is formed and the part of A above the diagonal is
            not referenced.
lda  Int32
            The leading dimension of the array A.  LDA >= max(1,N).
ipiv  ReadOnlySpan<Int32>
            Dimension (N)
            Details of the interchanges and the block structure of D
            as determined by DSYTRF.
info  Int32
            = 0: successful exit
            < 0: if INFO = -i, the i-th argument had an illegal value
            > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
                 inverse could not be computed.

Remarks

This method corresponds to the LAPACK routine ?SYTRI.

See Also