GenericSparseLinearAlgebraOperations<T>.TriangularSolve Method

Definition

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

Overload List

TriangularSolve(TransposeOperation, Int32, T, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<T>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<T>, Int32, Span<T>, Int32)	Solves for a dense vector for a sparse matrix in compressed sparse column format.
TriangularSolve(TransposeOperation, Int32, Complex<T>, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<Complex<T>>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)	Solves for a dense vector for a sparse matrix in compressed sparse column format.
TriangularSolve(TransposeOperation, Int32, Int32, T, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<T>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<T>, Int32, Span<T>, Int32)	Solves for a dense vector for a sparse matrix in compressed sparse column format.
TriangularSolve(TransposeOperation, Int32, Int32, Complex<T>, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<Complex<T>>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)	Solves for a dense matrix for a sparse matrix in compressed sparse column format.

TriangularSolve(TransposeOperation, Int32, T, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<T>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<T>, Int32, Span<T>, Int32)

Solves for a dense vector for a sparse matrix in compressed sparse column format.

public override void TriangularSolve(
	TransposeOperation transA,
	int m,
	T alpha,
	MatrixStructure structure,
	MatrixTriangle storedTriangle,
	MatrixDiagonal matrixDiagonal,
	ReadOnlySpan<T> a,
	ReadOnlySpan<int> aRows,
	ReadOnlySpan<int> aPointerB,
	ReadOnlySpan<int> aPointerE,
	ReadOnlySpan<T> x,
	int incx,
	Span<T> y,
	int incy
)

Visual Basic

Public Overrides Sub TriangularSolve ( 
	transA As TransposeOperation,
	m As Integer,
	alpha As T,
	structure As MatrixStructure,
	storedTriangle As MatrixTriangle,
	matrixDiagonal As MatrixDiagonal,
	a As ReadOnlySpan(Of T),
	aRows As ReadOnlySpan(Of Integer),
	aPointerB As ReadOnlySpan(Of Integer),
	aPointerE As ReadOnlySpan(Of Integer),
	x As ReadOnlySpan(Of T),
	incx As Integer,
	y As Span(Of T),
	incy As Integer
)

C++/CLI

public:
virtual void TriangularSolve(
	TransposeOperation transA, 
	int m, 
	T alpha, 
	MatrixStructure structure, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal matrixDiagonal, 
	ReadOnlySpan<T> a, 
	ReadOnlySpan<int> aRows, 
	ReadOnlySpan<int> aPointerB, 
	ReadOnlySpan<int> aPointerE, 
	ReadOnlySpan<T> x, 
	int incx, 
	Span<T> y, 
	int incy
) override

abstract TriangularSolve : 
        transA : TransposeOperation * 
        m : int * 
        alpha : 'T * 
        structure : MatrixStructure * 
        storedTriangle : MatrixTriangle * 
        matrixDiagonal : MatrixDiagonal * 
        a : ReadOnlySpan<'T> * 
        aRows : ReadOnlySpan<int> * 
        aPointerB : ReadOnlySpan<int> * 
        aPointerE : ReadOnlySpan<int> * 
        x : ReadOnlySpan<'T> * 
        incx : int * 
        y : Span<'T> * 
        incy : int -> unit 
override TriangularSolve : 
        transA : TransposeOperation * 
        m : int * 
        alpha : 'T * 
        structure : MatrixStructure * 
        storedTriangle : MatrixTriangle * 
        matrixDiagonal : MatrixDiagonal * 
        a : ReadOnlySpan<'T> * 
        aRows : ReadOnlySpan<int> * 
        aPointerB : ReadOnlySpan<int> * 
        aPointerE : ReadOnlySpan<int> * 
        x : ReadOnlySpan<'T> * 
        incx : int * 
        y : Span<'T> * 
        incy : int -> unit

Parameters

transA TransposeOperation: Specifies the operation to be performed on the matrix a.
m Int32: The number of rows in the matrix a.
alpha T: The scalar used to multiply the matrix-vector product.
structure MatrixStructure: A MatrixStructure value that specifies the structure of the matrix.
storedTriangle MatrixTriangle: A MatrixTriangle value that specifies whether the matrix is upper or lower triangular.
matrixDiagonal MatrixDiagonal: A MatrixDiagonal value that indicates whether the diagonal elements are all 1 or not.
a ReadOnlySpan<T>: A span that contains the elements of the matrix.
aRows ReadOnlySpan<Int32>: Integer array that contains the 1-based row indices of the corresponding elements of a.
aPointerB ReadOnlySpan<Int32>: Integer array of length m containing the 1-based indices into a of the first component of each column.
aPointerE ReadOnlySpan<Int32>: Integer array of length m containing the 1-based indices into a of the first component of each column.
x ReadOnlySpan<T>: A reference to a one-dimensional array containing the elements of the vector x.
incx Int32
y Span<T>: A reference to a one-dimensional array containing the elements of the vector y. The elements of y are overwritten with the result.
incy Int32

Implements

ISparseLinearAlgebraOperations<T>.TriangularSolve(TransposeOperation, Int32, T, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<T>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<T>, Int32, Span<T>, Int32)

TriangularSolve(TransposeOperation, Int32, Complex<T>, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<Complex<T>>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)

Solves for a dense vector for a sparse matrix in compressed sparse column format.

public override void TriangularSolve(
	TransposeOperation transA,
	int m,
	Complex<T> alpha,
	MatrixStructure structure,
	MatrixTriangle storedTriangle,
	MatrixDiagonal matrixDiagonal,
	ReadOnlySpan<Complex<T>> a,
	ReadOnlySpan<int> aRows,
	ReadOnlySpan<int> aPointerB,
	ReadOnlySpan<int> aPointerE,
	ReadOnlySpan<Complex<T>> x,
	int incx,
	Span<Complex<T>> y,
	int incy
)

Visual Basic

Public Overrides Sub TriangularSolve ( 
	transA As TransposeOperation,
	m As Integer,
	alpha As Complex(Of T),
	structure As MatrixStructure,
	storedTriangle As MatrixTriangle,
	matrixDiagonal As MatrixDiagonal,
	a As ReadOnlySpan(Of Complex(Of T)),
	aRows As ReadOnlySpan(Of Integer),
	aPointerB As ReadOnlySpan(Of Integer),
	aPointerE As ReadOnlySpan(Of Integer),
	x As ReadOnlySpan(Of Complex(Of T)),
	incx As Integer,
	y As Span(Of Complex(Of T)),
	incy As Integer
)

C++/CLI

public:
virtual void TriangularSolve(
	TransposeOperation transA, 
	int m, 
	Complex<T> alpha, 
	MatrixStructure structure, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal matrixDiagonal, 
	ReadOnlySpan<Complex<T>> a, 
	ReadOnlySpan<int> aRows, 
	ReadOnlySpan<int> aPointerB, 
	ReadOnlySpan<int> aPointerE, 
	ReadOnlySpan<Complex<T>> x, 
	int incx, 
	Span<Complex<T>> y, 
	int incy
) override

abstract TriangularSolve : 
        transA : TransposeOperation * 
        m : int * 
        alpha : Complex<'T> * 
        structure : MatrixStructure * 
        storedTriangle : MatrixTriangle * 
        matrixDiagonal : MatrixDiagonal * 
        a : ReadOnlySpan<Complex<'T>> * 
        aRows : ReadOnlySpan<int> * 
        aPointerB : ReadOnlySpan<int> * 
        aPointerE : ReadOnlySpan<int> * 
        x : ReadOnlySpan<Complex<'T>> * 
        incx : int * 
        y : Span<Complex<'T>> * 
        incy : int -> unit 
override TriangularSolve : 
        transA : TransposeOperation * 
        m : int * 
        alpha : Complex<'T> * 
        structure : MatrixStructure * 
        storedTriangle : MatrixTriangle * 
        matrixDiagonal : MatrixDiagonal * 
        a : ReadOnlySpan<Complex<'T>> * 
        aRows : ReadOnlySpan<int> * 
        aPointerB : ReadOnlySpan<int> * 
        aPointerE : ReadOnlySpan<int> * 
        x : ReadOnlySpan<Complex<'T>> * 
        incx : int * 
        y : Span<Complex<'T>> * 
        incy : int -> unit

Parameters

transA TransposeOperation: Specifies the operation to be performed on the matrix a.
m Int32: The number of rows in the matrix a.
alpha Complex<T>: The scalar used to multiply the matrix-vector product.
structure MatrixStructure: A MatrixStructure value that specifies the structure of the matrix.
storedTriangle MatrixTriangle: A MatrixTriangle value that specifies whether the matrix is upper or lower triangular.
matrixDiagonal MatrixDiagonal: A MatrixDiagonal value that indicates whether the diagonal elements are all 1 or not.
a ReadOnlySpan<Complex<T>>: A span that contains the elements of the matrix.
aRows ReadOnlySpan<Int32>: Integer array that contains the 1-based row indices of the corresponding elements of a.
aPointerB ReadOnlySpan<Int32>: Integer array of length m containing the 1-based indices into a of the first component of each column.
aPointerE ReadOnlySpan<Int32>: Integer array of length m containing the 1-based indices into a of the first component of each column.
x ReadOnlySpan<Complex<T>>: A reference to a one-dimensional array containing the elements of the vector x.
incx Int32
y Span<Complex<T>>: A reference to a one-dimensional array containing the elements of the vector y. The elements of y are overwritten with the result.
incy Int32

Implements

TriangularSolve(TransposeOperation, Int32, Int32, T, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<T>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<T>, Int32, Span<T>, Int32)

Solves for a dense vector for a sparse matrix in compressed sparse column format.

public override void TriangularSolve(
	TransposeOperation transA,
	int m,
	int n,
	T alpha,
	MatrixStructure structure,
	MatrixTriangle storedTriangle,
	MatrixDiagonal matrixDiagonal,
	ReadOnlySpan<T> a,
	ReadOnlySpan<int> aRows,
	ReadOnlySpan<int> aPointerB,
	ReadOnlySpan<int> aPointerE,
	ReadOnlySpan<T> b,
	int ldb,
	Span<T> c,
	int ldc
)

Visual Basic

Public Overrides Sub TriangularSolve ( 
	transA As TransposeOperation,
	m As Integer,
	n As Integer,
	alpha As T,
	structure As MatrixStructure,
	storedTriangle As MatrixTriangle,
	matrixDiagonal As MatrixDiagonal,
	a As ReadOnlySpan(Of T),
	aRows As ReadOnlySpan(Of Integer),
	aPointerB As ReadOnlySpan(Of Integer),
	aPointerE As ReadOnlySpan(Of Integer),
	b As ReadOnlySpan(Of T),
	ldb As Integer,
	c As Span(Of T),
	ldc As Integer
)

C++/CLI

public:
virtual void TriangularSolve(
	TransposeOperation transA, 
	int m, 
	int n, 
	T alpha, 
	MatrixStructure structure, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal matrixDiagonal, 
	ReadOnlySpan<T> a, 
	ReadOnlySpan<int> aRows, 
	ReadOnlySpan<int> aPointerB, 
	ReadOnlySpan<int> aPointerE, 
	ReadOnlySpan<T> b, 
	int ldb, 
	Span<T> c, 
	int ldc
) override

abstract TriangularSolve : 
        transA : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : 'T * 
        structure : MatrixStructure * 
        storedTriangle : MatrixTriangle * 
        matrixDiagonal : MatrixDiagonal * 
        a : ReadOnlySpan<'T> * 
        aRows : ReadOnlySpan<int> * 
        aPointerB : ReadOnlySpan<int> * 
        aPointerE : ReadOnlySpan<int> * 
        b : ReadOnlySpan<'T> * 
        ldb : int * 
        c : Span<'T> * 
        ldc : int -> unit 
override TriangularSolve : 
        transA : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : 'T * 
        structure : MatrixStructure * 
        storedTriangle : MatrixTriangle * 
        matrixDiagonal : MatrixDiagonal * 
        a : ReadOnlySpan<'T> * 
        aRows : ReadOnlySpan<int> * 
        aPointerB : ReadOnlySpan<int> * 
        aPointerE : ReadOnlySpan<int> * 
        b : ReadOnlySpan<'T> * 
        ldb : int * 
        c : Span<'T> * 
        ldc : int -> unit

Parameters

transA TransposeOperation: Specifies the operation to be performed on the matrix a.
m Int32: The number of rows in the matrix a.
n Int32: The number of columns in the matrix b.
alpha T: The scalar used to multiply the matrix-vector product.
structure MatrixStructure: A MatrixStructure value that specifies the structure of the matrix.
storedTriangle MatrixTriangle: A MatrixTriangle value that specifies whether the matrix is upper or lower triangular.
matrixDiagonal MatrixDiagonal: A MatrixDiagonal value that indicates whether the diagonal elements are all 1 or not.
a ReadOnlySpan<T>: A span that contains the elements of the matrix.
aRows ReadOnlySpan<Int32>: Integer array that contains the 1-based row indices of the corresponding elements of a.
aPointerB ReadOnlySpan<Int32>: Integer array of length m containing the 1-based indices into a of the first component of each column.
aPointerE ReadOnlySpan<Int32>: Integer array of length m containing the 1-based indices into a of the first component of each column.
b ReadOnlySpan<T>: A two-dimensional array containing the elements of the right-hand side.
ldb Int32: The leading dimension of the matrix b.
c Span<T>: A two-dimensional array containing the elements of the solution.
ldc Int32: The leading dimension of the matrix c.

Implements

ISparseLinearAlgebraOperations<T>.TriangularSolve(TransposeOperation, Int32, Int32, T, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<T>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<T>, Int32, Span<T>, Int32)

TriangularSolve(TransposeOperation, Int32, Int32, Complex<T>, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<Complex<T>>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)

Solves for a dense matrix for a sparse matrix in compressed sparse column format.

public override void TriangularSolve(
	TransposeOperation transA,
	int m,
	int n,
	Complex<T> alpha,
	MatrixStructure structure,
	MatrixTriangle storedTriangle,
	MatrixDiagonal matrixDiagonal,
	ReadOnlySpan<Complex<T>> a,
	ReadOnlySpan<int> aRows,
	ReadOnlySpan<int> aPointerB,
	ReadOnlySpan<int> aPointerE,
	ReadOnlySpan<Complex<T>> b,
	int ldb,
	Span<Complex<T>> c,
	int ldc
)

Visual Basic

Public Overrides Sub TriangularSolve ( 
	transA As TransposeOperation,
	m As Integer,
	n As Integer,
	alpha As Complex(Of T),
	structure As MatrixStructure,
	storedTriangle As MatrixTriangle,
	matrixDiagonal As MatrixDiagonal,
	a As ReadOnlySpan(Of Complex(Of T)),
	aRows As ReadOnlySpan(Of Integer),
	aPointerB As ReadOnlySpan(Of Integer),
	aPointerE As ReadOnlySpan(Of Integer),
	b As ReadOnlySpan(Of Complex(Of T)),
	ldb As Integer,
	c As Span(Of Complex(Of T)),
	ldc As Integer
)

C++/CLI

public:
virtual void TriangularSolve(
	TransposeOperation transA, 
	int m, 
	int n, 
	Complex<T> alpha, 
	MatrixStructure structure, 
	MatrixTriangle storedTriangle, 
	MatrixDiagonal matrixDiagonal, 
	ReadOnlySpan<Complex<T>> a, 
	ReadOnlySpan<int> aRows, 
	ReadOnlySpan<int> aPointerB, 
	ReadOnlySpan<int> aPointerE, 
	ReadOnlySpan<Complex<T>> b, 
	int ldb, 
	Span<Complex<T>> c, 
	int ldc
) override

abstract TriangularSolve : 
        transA : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : Complex<'T> * 
        structure : MatrixStructure * 
        storedTriangle : MatrixTriangle * 
        matrixDiagonal : MatrixDiagonal * 
        a : ReadOnlySpan<Complex<'T>> * 
        aRows : ReadOnlySpan<int> * 
        aPointerB : ReadOnlySpan<int> * 
        aPointerE : ReadOnlySpan<int> * 
        b : ReadOnlySpan<Complex<'T>> * 
        ldb : int * 
        c : Span<Complex<'T>> * 
        ldc : int -> unit 
override TriangularSolve : 
        transA : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : Complex<'T> * 
        structure : MatrixStructure * 
        storedTriangle : MatrixTriangle * 
        matrixDiagonal : MatrixDiagonal * 
        a : ReadOnlySpan<Complex<'T>> * 
        aRows : ReadOnlySpan<int> * 
        aPointerB : ReadOnlySpan<int> * 
        aPointerE : ReadOnlySpan<int> * 
        b : ReadOnlySpan<Complex<'T>> * 
        ldb : int * 
        c : Span<Complex<'T>> * 
        ldc : int -> unit

Parameters

transA TransposeOperation: Specifies the operation to be performed on the matrix a.
m Int32: The number of rows in the matrix a.
n Int32: The number of columns in the matrix b.
alpha Complex<T>: The scalar used to multiply the matrix-vector product.
structure MatrixStructure: A MatrixStructure value that specifies the structure of the matrix.
storedTriangle MatrixTriangle: A MatrixTriangle value that specifies whether the matrix is upper or lower triangular.
matrixDiagonal MatrixDiagonal: A MatrixDiagonal value that indicates whether the diagonal elements are all 1 or not.
a ReadOnlySpan<Complex<T>>: A span that contains the elements of the matrix.
aRows ReadOnlySpan<Int32>: Integer array that contains the 1-based row indices of the corresponding elements of a.
aPointerB ReadOnlySpan<Int32>: Integer array of length m containing the 1-based indices into a of the first component of each column.
aPointerE ReadOnlySpan<Int32>: Integer array of length m containing the 1-based indices into a of the first component of each column.
b ReadOnlySpan<Complex<T>>: A two-dimensional array containing the elements of the right-hand side.
ldb Int32: The leading dimension of the matrix b.
c Span<Complex<T>>: A two-dimensional array containing the elements of the solution.
ldc Int32: The leading dimension of the matrix c.

GenericSparseLinearAlgebraOperations<T>.TriangularSolve Method

Definition

Overload List

TriangularSolve(TransposeOperation, Int32, T, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<T>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<T>, Int32, Span<T>, Int32)

Parameters

Implements

TriangularSolve(TransposeOperation, Int32, Complex<T>, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<Complex<T>>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)

Parameters

Implements

TriangularSolve(TransposeOperation, Int32, Int32, T, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<T>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<T>, Int32, Span<T>, Int32)

Parameters

Implements

TriangularSolve(TransposeOperation, Int32, Int32, Complex<T>, MatrixStructure, MatrixTriangle, MatrixDiagonal, ReadOnlySpan<Complex<T>>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Int32>, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)

Parameters

Implements

See Also

Reference