ManagedLinearAlgebraOperations.TriangularSolveInPlace Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.4

Overload List

TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array2D<Complex<T>>, ArraySlice<Complex<T>>) 
TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array2D<Complex<T>>, ArraySlice<Complex<T>>)

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.

TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan2D<Complex<T>>, SpanSlice<Complex<T>>)

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.

TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan<Complex<Double>>, Int32, Span<Complex<Double>>, 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.

TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan<Double>, Int32, Span<Double>, 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.

TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, Array2D<T>, Array2D<T>)

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(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Complex<T>, Array2D<Complex<T>>, Array2D<Complex<T>>)

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.

TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Complex<T>, ReadOnlySpan2D<Complex<T>>, Span2D<Complex<T>>)

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.

TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Complex<Double>, ReadOnlySpan<Complex<Double>>, Int32, Span<Complex<Double>>, 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.

TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Double, ReadOnlySpan<Double>, Int32, Span<Double>, 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.

TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan<Complex<Double>>, Int32, Span<Complex<Double>>, 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.

C#
public override void TriangularSolveInPlace(
	MatrixTriangle storedTriangle,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan<Complex<double>> a,
	int lda,
	Span<Complex<double>> x,
	int incx
)

Parameters

storedTriangle  MatrixTriangle
Specifies whether the matrix is an upper or lower triangular matrix.
trans  TransposeOperation
             On entry, TRANS specifies the equations to be solved as
             follows:
                TRANS = 'N' or 'n'   A*x = b.
                TRANS = 'T' or 't'   AT*x = b.
                TRANS = 'C' or 'c'   AH*x = b.
            
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<Double>>
            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<Double>>
            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<Double>, Int32, Span<Double>, 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.

C#
public override void TriangularSolveInPlace(
	MatrixTriangle storedTriangle,
	TransposeOperation transA,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan<double> a,
	int lda,
	Span<double> 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<Double>
            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<Double>
            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<Double>, ReadOnlySpan<Complex<Double>>, Int32, Span<Complex<Double>>, 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.

C#
public override void TriangularSolveInPlace(
	MatrixOperationSide side,
	MatrixTriangle triangle,
	TransposeOperation transA,
	MatrixDiagonal diag,
	int m,
	int n,
	Complex<double> alpha,
	ReadOnlySpan<Complex<double>> a,
	int lda,
	Span<Complex<double>> 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<Double>
             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<Double>>
            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<Double>>
            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, Double, ReadOnlySpan<Double>, Int32, Span<Double>, 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.

C#
public override void TriangularSolveInPlace(
	MatrixOperationSide side,
	MatrixTriangle storedTriangle,
	TransposeOperation transA,
	MatrixDiagonal diag,
	int m,
	int n,
	double alpha,
	ReadOnlySpan<double> a,
	int lda,
	Span<double> 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  Double
            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<Double>
            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<Double>
            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

See Also