Decomposition Operations<TReal, TComplex>.Triangular Solve Method
Definition
Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2D<TReal>, Array2D<TReal>, Int32)
Solves a triangular system of the form A * X = B or AT * X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix.
public void TriangularSolve(
MatrixTriangle storedTriangle,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
int nrhs,
Array2D<TReal> a,
Array2D<TReal> b,
out int info
)
Parameters
- storedTriangle MatrixTriangle
= 'U': A is upper triangular; = 'L': A is lower triangular.
- trans TransposeOperation
Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': AT * X = B (Transpose) = 'C': AH * X = B (Conjugate transpose = Transpose)
- diag MatrixDiagonal
= 'N': A is non-unit triangular; = 'U': A is unit triangular.
- 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 matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
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, if INFO = 0, 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 > 0: if INFO = i, the i-th diagonal element of A is zero, indicating that the matrix is singular and the solutions X have not been computed.
Remarks
A check is made to verify that A is nonsingular.
This method corresponds to the LAPACK routine ?TRTRS.
TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2D<TComplex>, Array2D<TComplex>, Int32)
Solves a complex triangular system of equations.
public void TriangularSolve(
MatrixTriangle storedTriangle,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
int nrhs,
Array2D<TComplex> a,
Array2D<TComplex> b,
out int info
)
Parameters
- storedTriangle MatrixTriangle
- A MatrixTriangle value that indicates whether the matrix is upper or lower triangular.
- trans TransposeOperation
- A TransposeOperation value that indicates if the matrix should be transposed or not.
- diag MatrixDiagonal
- A MatrixDiagonal value that indicates whether the matrix is unit diagonal.
- 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.
TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan2D<TReal>, Span2D<TReal>, Int32)
Solves a triangular system of the form A * X = B or AT * X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix.
public void TriangularSolve(
MatrixTriangle storedTriangle,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
int nrhs,
ReadOnlySpan2D<TReal> a,
Span2D<TReal> b,
out int info
)
Parameters
- storedTriangle MatrixTriangle
= 'U': A is upper triangular; = 'L': A is lower triangular.
- trans TransposeOperation
Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': AT * X = B (Transpose) = 'C': AH * X = B (Conjugate transpose = Transpose)
- diag MatrixDiagonal
= 'N': A is non-unit triangular; = 'U': A is unit triangular.
- 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 matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
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, if INFO = 0, 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 > 0: if INFO = i, the i-th diagonal element of A is zero, indicating that the matrix is singular and the solutions X have not been computed.
Remarks
A check is made to verify that A is nonsingular.
This method corresponds to the LAPACK routine ?TRTRS.
TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan2D<TComplex>, Span2D<TComplex>, Int32)
Solves a complex triangular system of equations.
public void TriangularSolve(
MatrixTriangle storedTriangle,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
int nrhs,
ReadOnlySpan2D<TComplex> a,
Span2D<TComplex> b,
out int info
)
Parameters
- storedTriangle MatrixTriangle
- A MatrixTriangle value that indicates whether the matrix is upper or lower triangular.
- trans TransposeOperation
- A TransposeOperation value that indicates if the matrix should be transposed or not.
- diag MatrixDiagonal
- A MatrixDiagonal value that indicates whether the matrix is unit diagonal.
- 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.
TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<TReal>, Int32, Span<TReal>, Int32, Int32)
Solves a triangular system of the form A * X = B or AT * X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix.
public abstract void TriangularSolve(
MatrixTriangle storedTriangle,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
int nrhs,
ReadOnlySpan<TReal> a,
int lda,
Span<TReal> b,
int ldb,
out int info
)
Parameters
- storedTriangle MatrixTriangle
= 'U': A is upper triangular; = 'L': A is lower triangular.
- trans TransposeOperation
Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': AT * X = B (Transpose) = 'C': AH * X = B (Conjugate transpose = Transpose)
- diag MatrixDiagonal
= 'N': A is non-unit triangular; = 'U': A is unit triangular.
- 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 matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
- 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, if INFO = 0, 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 > 0: if INFO = i, the i-th diagonal element of A is zero, indicating that the matrix is singular and the solutions X have not been computed.
Remarks
A check is made to verify that A is nonsingular.
This method corresponds to the LAPACK routine ?TRTRS.
TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32)
Solves a complex triangular system of equations.
public abstract void TriangularSolve(
MatrixTriangle storedTriangle,
TransposeOperation trans,
MatrixDiagonal diag,
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 is upper or lower triangular.
- trans TransposeOperation
- A TransposeOperation value that indicates if the matrix should be transposed or not.
- diag MatrixDiagonal
- A MatrixDiagonal value that indicates whether the matrix is unit diagonal.
- 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.