Managed Linear Algebra Operations Of Single.Triangular Solve In Place Method
            
            Definition
Assembly: Numerics.NET.SinglePrecision (in Numerics.NET.SinglePrecision.dll) Version: 9.1.5
Overload List
| Triangular | |
| Triangular | Solves one of the systems of equations A*x = b, or AT*x = b, or AH*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.  | 
| Triangular | Solves one of the systems of equations A*x = b, or AT*x = b, or AH*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.  | 
| Triangular | Solves one of the systems of equations A*x = b, or AT*x = b, or AH*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.  | 
| Triangular | Solves one of the systems of equations A*x = b, or AT*x = b, or AH*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.  | 
| Triangular | Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT.  | 
| Triangular | Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT or op( A ) = AH.  | 
| Triangular | Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT or op( A ) = AH.  | 
| Triangular | Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT or op( A ) = AH.  | 
| Triangular | Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT.  | 
TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan<Complex<Single>>, Int32, Span<Complex<Single>>, Int32)
Solves one of the systems of equations A*x = b, or AT*x = b, or AH*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.
public override void TriangularSolveInPlace(
	MatrixTriangle storedTriangle,
	TransposeOperation transA,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan<Complex<float>> a,
	int lda,
	Span<Complex<float>> x,
	int incx
)Parameters
- storedTriangle MatrixTriangle
 - Specifies whether the matrix is an upper or lower triangular matrix.
 - transA TransposeOperation
 - diag MatrixDiagonal
 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.- n Int32
 On entry, N specifies the order of the matrix A. N must be at least zero.- a ReadOnlySpan<Complex<Single>>
 A is complex array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.- lda Int32
 On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).- x Span<Complex<Single>>
 X is complex array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x.- incx Int32
 On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
Implements
ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)Remarks
            No test for singularity or near-singularity is included in this
            routine. Such tests must be performed before calling this routine.
            Further Details:
            Level 2 LinearAlgebra routine.
            -- Written on 22-October-1986.
               Jack Dongarra, Argonne National Lab.
               Jeremy Du Croz, Nag Central Office.
               Sven Hammarling, Nag Central Office.
               Richard Hanson, Sandia National Labs.
            Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan<Single>, Int32, Span<Single>, Int32)
Solves one of the systems of equations A*x = b, or AT*x = b, or AH*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.
public override void TriangularSolveInPlace(
	MatrixTriangle storedTriangle,
	TransposeOperation transA,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan<float> a,
	int lda,
	Span<float> x,
	int incx
)Parameters
- storedTriangle MatrixTriangle
 - Specifies whether the matrix is an upper or lower triangular matrix.
 - transA TransposeOperation
 - diag MatrixDiagonal
 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.- n Int32
 On entry, N specifies the order of the matrix A. N must be at least zero.- a ReadOnlySpan<Single>
 A is complex array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.- lda Int32
 On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).- x Span<Single>
 X is complex array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x.- incx Int32
 On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
Implements
ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)Remarks
            No test for singularity or near-singularity is included in this
            routine. Such tests must be performed before calling this routine.
            Further Details:
            Level 2 LinearAlgebra routine.
            -- Written on 22-October-1986.
               Jack Dongarra, Argonne National Lab.
               Jeremy Du Croz, Nag Central Office.
               Sven Hammarling, Nag Central Office.
               Richard Hanson, Sandia National Labs.
            Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Complex<Single>, ReadOnlySpan<Complex<Single>>, Int32, Span<Complex<Single>>, Int32)
Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT or op( A ) = AH.
public override void TriangularSolveInPlace(
	MatrixOperationSide side,
	MatrixTriangle triangle,
	TransposeOperation transA,
	MatrixDiagonal diag,
	int m,
	int n,
	Complex<float> alpha,
	ReadOnlySpan<Complex<float>> a,
	int lda,
	Span<Complex<float>> b,
	int ldb
)Parameters
- side MatrixOperationSide
 On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = 'L' or 'l' op( A )*X = alpha*B. SIDE = 'R' or 'r' X*op( A ) = alpha*B.- triangle MatrixTriangle
 - transA TransposeOperation
 - Specifies the operation to be performed on the matrix a.
 - diag MatrixDiagonal
 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.- m Int32
 On entry, M specifies the number of rows of B. M must be at least zero.- n Int32
 On entry, N specifies the number of columns of B. N must be at least zero.- alpha Complex<Single>
 On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.- a ReadOnlySpan<Complex<Single>>
 A is complex array of DIMENSION ( LDA, k ), where k is m when SIDE = 'L' or 'l' and k is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.- lda Int32
 On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).- b Span<Complex<Single>>
 B is complex array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.- ldb Int32
 On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).
Implements
ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, ReadOnlySpan<T>, Int32, Span<T>, Int32)Remarks
            The matrix X is overwritten on B.
            Further Details:
            Level 3 LinearAlgebra routine.
            -- Written on 8-February-1989.
               Jack Dongarra, Argonne National Laboratory.
               Iain Duff, AERE Harwell.
               Jeremy Du Croz, Numerical Algorithms Group Ltd.
               Sven Hammarling, Numerical Algorithms Group Ltd.
            Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Single, ReadOnlySpan<Single>, Int32, Span<Single>, Int32)
Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT.
public override void TriangularSolveInPlace(
	MatrixOperationSide side,
	MatrixTriangle storedTriangle,
	TransposeOperation transA,
	MatrixDiagonal diag,
	int m,
	int n,
	float alpha,
	ReadOnlySpan<float> a,
	int lda,
	Span<float> b,
	int ldb
)Parameters
- side MatrixOperationSide
 On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = 'L' or 'l' op( A )*X = alpha*B. SIDE = 'R' or 'r' X*op( A ) = alpha*B.- storedTriangle MatrixTriangle
 - Specifies whether the elements of the matrix a are stored in the upper or lower triangular part.
 - transA TransposeOperation
 - Specifies the operation to be performed on the matrix a.
 - diag MatrixDiagonal
 On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.- m Int32
 On entry, M specifies the number of rows of B. M must be at least zero.- n Int32
 On entry, N specifies the number of columns of B. N must be at least zero.- alpha Single
 ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.- a ReadOnlySpan<Single>
 A is DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m when SIDE = 'L' or 'l' and k is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.- lda Int32
 On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).- b Span<Single>
 B is DOUBLE PRECISION array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.- ldb Int32
 On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).
Implements
ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, ReadOnlySpan<T>, Int32, Span<T>, Int32)Remarks
            The matrix X is overwritten on B.
            Further Details:
            Level 3 LinearAlgebra routine.
            -- Written on 8-February-1989.
               Jack Dongarra, Argonne National Laboratory.
               Iain Duff, AERE Harwell.
               Jeremy Du Croz, Numerical Algorithms Group Ltd.
               Sven Hammarling, Numerical Algorithms Group Ltd.
            Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011