DecompositionOperations<TReal, TComplex>.CholeskySolve Method

Definition

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

Overload List

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

Solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

CholeskySolve(MatrixTriangle, Int32, Int32, Array2D<TComplex>, Array2D<TComplex>, Int32) Solves a hermitian system of equations.
CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TReal>, Span2D<TReal>, Int32)

Solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TComplex>, Span2D<TComplex>, Int32) Solves a hermitian system of equations.
CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<TReal>, Int32, Span<TReal>, Int32, Int32)

Solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32) Solves a hermitian system of equations.

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

Solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

C# 
public void CholeskySolve(
	MatrixTriangle storedTriangle,
	int n,
	int nrhs,
	Array2D<TReal> a,
	Array2D<TReal> b,
	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.
nrhs  Int32
            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
a  Array2D<TReal>
            A is TReal array, dimension (LDA,N)
            The triangular factor U or L from the Cholesky factorization
            A = UT*U or A = L*LT, as computed by DPOTRF.
            
            The leading dimension of the array A.  LDA >= max(1,N).
b  Array2D<TReal>
            B is TReal array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, the solution matrix X.
            
            The leading dimension of the array B.  LDB >= max(1,N).
info  Int32
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value

Remarks

This method corresponds to the LAPACK routine ?POTRS.

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

Solves a hermitian system of equations.
C# 
public void CholeskySolve(
	MatrixTriangle storedTriangle,
	int n,
	int nrhs,
	Array2D<TComplex> a,
	Array2D<TComplex> b,
	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.
nrhs  Int32
The number of right hand sides.
a  Array2D<TComplex>
A complex array that contains the elements of the matrix.
b  Array2D<TComplex>
A complex array that contains the components of the right-hand side(s).
info  Int32
On return, indicates error conditions.

CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TReal>, Span2D<TReal>, Int32)

Solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

C# 
public void CholeskySolve(
	MatrixTriangle storedTriangle,
	int n,
	int nrhs,
	ReadOnlySpan2D<TReal> a,
	Span2D<TReal> b,
	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.
nrhs  Int32
            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
a  ReadOnlySpan2D<TReal>
            A is TReal array, dimension (LDA,N)
            The triangular factor U or L from the Cholesky factorization
            A = UT*U or A = L*LT, as computed by DPOTRF.
            
            The leading dimension of the array A.  LDA >= max(1,N).
b  Span2D<TReal>
            B is TReal array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, the solution matrix X.
            
            The leading dimension of the array B.  LDB >= max(1,N).
info  Int32
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value

Remarks

This method corresponds to the LAPACK routine ?POTRS.

CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TComplex>, Span2D<TComplex>, Int32)

Solves a hermitian system of equations.
C# 
public void CholeskySolve(
	MatrixTriangle storedTriangle,
	int n,
	int nrhs,
	ReadOnlySpan2D<TComplex> a,
	Span2D<TComplex> b,
	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.
nrhs  Int32
The number of right hand sides.
a  ReadOnlySpan2D<TComplex>
A complex array that contains the elements of the matrix.
b  Span2D<TComplex>
A complex array that contains the components of the right-hand side(s).
info  Int32
On return, indicates error conditions.

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

Solves a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPOTRF.

C# 
public abstract void CholeskySolve(
	MatrixTriangle storedTriangle,
	int n,
	int nrhs,
	ReadOnlySpan<TReal> a,
	int lda,
	Span<TReal> b,
	int ldb,
	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.
nrhs  Int32
            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
a  ReadOnlySpan<TReal>
            A is TReal array, dimension (LDA,N)
            The triangular factor U or L from the Cholesky factorization
            A = UT*U or A = L*LT, as computed by DPOTRF.
lda  Int32
            The leading dimension of the array A.  LDA >= max(1,N).
b  Span<TReal>
            B is TReal array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, the solution matrix X.
ldb  Int32
            The leading dimension of the array B.  LDB >= max(1,N).
info  Int32
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value

Remarks

This method corresponds to the LAPACK routine ?POTRS.

CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32)

Solves a hermitian system of equations.
C# 
public abstract void CholeskySolve(
	MatrixTriangle storedTriangle,
	int n,
	int nrhs,
	ReadOnlySpan<TComplex> a,
	int lda,
	Span<TComplex> b,
	int ldb,
	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.
nrhs  Int32
The number of right hand sides.
a  ReadOnlySpan<TComplex>
A complex array that contains the elements of the matrix.
lda  Int32
The leading dimension of the matrix a.
b  Span<TComplex>
A complex array that contains the components of the right-hand side(s).
ldb  Int32
The leading dimension of the matrix b.
info  Int32
On return, indicates error conditions.

See Also