Linear Algebra Operations &lt; T &gt; . Triangular Solve In Place Method

             On entry, UPLO specifies whether the matrix is an upper or
             lower triangular matrix as follows:
                UPLO = 'U' or 'u'   A is an upper triangular matrix.
                UPLO = 'L' or 'l'   A is a lower triangular matrix.

             On entry, TRANS specifies the equations to be solved as
             follows:
                TRANS = 'N' or 'n'   A*x = b.
                TRANS = 'T' or 't'   A^T*x = b.
                TRANS = 'C' or 'c'   A^T*x = b.

             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.

             On entry, N specifies the order of the matrix A.
             N must be at least zero.

a Array2D<T>

            A is DOUBLE PRECISION 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.

             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 ArraySlice<T>

            X is DOUBLE PRECISION 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.

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.
            2 LinearAlgebra routine.
            itten on 22-October-1986.
            ack Dongarra, Argonne National Lab.
            Jeremy Du Croz, Nag Central Office.
            Sven Hammarling, Nag Central Office.
            Richard Hanson, Sandia National Labs.

Remarks

            No test for singularity or near-singularity is included in this
            routine. Such tests must be performed before calling this routine.

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

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

Solves one of the systems of equations A*x = b, or A^T*x = b, or A^H*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 void TriangularSolveInPlace(
	MatrixTriangle uplo,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	Array2D<Complex<T>> a,
	ArraySlice<Complex<T>> x
)

Visual Basic

Public Sub TriangularSolveInPlace ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	a As Array2D(Of Complex(Of T)),
	x As ArraySlice(Of Complex(Of T))
)

C++/CLI

public:
void TriangularSolveInPlace(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	Array2D<Complex<T>> a, 
	ArraySlice<Complex<T>> x
)

member TriangularSolveInPlace : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        a : Array2D<Complex<'T>> * 
        x : ArraySlice<Complex<'T>> -> unit

Parameters

             On entry, UPLO specifies whether the matrix is an upper or
             lower triangular matrix as follows:
                UPLO = 'U' or 'u'   A is an upper triangular matrix.
                UPLO = 'L' or 'l'   A is a lower triangular matrix.

             On entry, TRANS specifies the equations to be solved as
             follows:
                TRANS = 'N' or 'n'   A*x = b.
                TRANS = 'T' or 't'   A^T*x = b.
                TRANS = 'C' or 'c'   A^H*x = b.

             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.

             On entry, N specifies the order of the matrix A.
             N must be at least zero.

a Array2D<Complex<T>>

            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.

             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 ArraySlice<Complex<T>>

            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.

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

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, ReadOnlySpan2D<Complex<T>>, SpanSlice<Complex<T>>)

Solves one of the systems of equations A*x = b, or A^T*x = b, or A^H*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 void TriangularSolveInPlace(
	MatrixTriangle uplo,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan2D<Complex<T>> a,
	SpanSlice<Complex<T>> x
)

Visual Basic

Public Sub TriangularSolveInPlace ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	a As ReadOnlySpan2D(Of Complex(Of T)),
	x As SpanSlice(Of Complex(Of T))
)

C++/CLI

public:
void TriangularSolveInPlace(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	ReadOnlySpan2D<Complex<T>> a, 
	SpanSlice<Complex<T>> x
)

member TriangularSolveInPlace : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        a : ReadOnlySpan2D<Complex<'T>> * 
        x : SpanSlice<Complex<'T>> -> unit

Parameters

             On entry, UPLO specifies whether the matrix is an upper or
             lower triangular matrix as follows:
                UPLO = 'U' or 'u'   A is an upper triangular matrix.
                UPLO = 'L' or 'l'   A is a lower triangular matrix.

             On entry, TRANS specifies the equations to be solved as
             follows:
                TRANS = 'N' or 'n'   A*x = b.
                TRANS = 'T' or 't'   A^T*x = b.
                TRANS = 'C' or 'c'   A^H*x = b.

             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.

             On entry, N specifies the order of the matrix A.
             N must be at least zero.

a ReadOnlySpan2D<Complex<T>>

            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.

             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 SpanSlice<Complex<T>>

            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.

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.

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<T>, Int32, Span<T>, Int32)

Solves one of the systems of equations A*x = b, or A^T*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 abstract void TriangularSolveInPlace(
	MatrixTriangle uplo,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan<T> a,
	int lda,
	Span<T> x,
	int incx
)

Visual Basic

Public MustOverride Sub TriangularSolveInPlace ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	a As ReadOnlySpan(Of T),
	lda As Integer,
	x As Span(Of T),
	incx As Integer
)

C++/CLI

public:
virtual void TriangularSolveInPlace(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	ReadOnlySpan<T> a, 
	int lda, 
	Span<T> x, 
	int incx
) abstract

abstract TriangularSolveInPlace : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        a : ReadOnlySpan<'T> * 
        lda : int * 
        x : Span<'T> * 
        incx : int -> unit

Parameters

             On entry, UPLO specifies whether the matrix is an upper or
             lower triangular matrix as follows:
                UPLO = 'U' or 'u'   A is an upper triangular matrix.
                UPLO = 'L' or 'l'   A is a lower triangular matrix.

             On entry, TRANS specifies the equations to be solved as
             follows:
                TRANS = 'N' or 'n'   A*x = b.
                TRANS = 'T' or 't'   A^T*x = b.
                TRANS = 'C' or 'c'   A^T*x = b.

             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.

ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)

             On entry, N specifies the order of the matrix A.
             N must be at least zero.

a ReadOnlySpan<T>

            A is DOUBLE PRECISION 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<T>

            X is DOUBLE PRECISION 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.
            2 LinearAlgebra routine.
            itten on 22-October-1986.
            ack Dongarra, Argonne National Lab.
            Jeremy Du Croz, Nag Central Office.
            Sven Hammarling, Nag Central Office.
            Richard Hanson, Sandia National Labs.

Implements

Remarks

            No test for singularity or near-singularity is included in this
            routine. Such tests must be performed before calling this routine.

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

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

Solves one of the systems of equations A*x = b, or A^T*x = b, or A^H*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 abstract void TriangularSolveInPlace(
	MatrixTriangle uplo,
	TransposeOperation trans,
	MatrixDiagonal diag,
	int n,
	ReadOnlySpan<Complex<T>> a,
	int lda,
	Span<Complex<T>> x,
	int incx
)

Visual Basic

Public MustOverride Sub TriangularSolveInPlace ( 
	uplo As MatrixTriangle,
	trans As TransposeOperation,
	diag As MatrixDiagonal,
	n As Integer,
	a As ReadOnlySpan(Of Complex(Of T)),
	lda As Integer,
	x As Span(Of Complex(Of T)),
	incx As Integer
)

C++/CLI

public:
virtual void TriangularSolveInPlace(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	ReadOnlySpan<Complex<T>> a, 
	int lda, 
	Span<Complex<T>> x, 
	int incx
) abstract

abstract TriangularSolveInPlace : 
        uplo : MatrixTriangle * 
        trans : TransposeOperation * 
        diag : MatrixDiagonal * 
        n : int * 
        a : ReadOnlySpan<Complex<'T>> * 
        lda : int * 
        x : Span<Complex<'T>> * 
        incx : int -> unit

Parameters

             On entry, UPLO specifies whether the matrix is an upper or
             lower triangular matrix as follows:
                UPLO = 'U' or 'u'   A is an upper triangular matrix.
                UPLO = 'L' or 'l'   A is a lower triangular matrix.

             On entry, TRANS specifies the equations to be solved as
             follows:
                TRANS = 'N' or 'n'   A*x = b.
                TRANS = 'T' or 't'   A^T*x = b.
                TRANS = 'C' or 'c'   A^H*x = b.

             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.

ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32)

             On entry, N specifies the order of the matrix A.
             N must be at least zero.

a ReadOnlySpan<Complex<T>>

            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<T>>

            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

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, 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 ) = A^T.

public void TriangularSolveInPlace(
	MatrixOperationSide side,
	MatrixTriangle uplo,
	TransposeOperation transa,
	MatrixDiagonal diag,
	int m,
	int n,
	T alpha,
	Array2D<T> a,
	Array2D<T> b
)

Visual Basic

Public Sub TriangularSolveInPlace ( 
	side As MatrixOperationSide,
	uplo As MatrixTriangle,
	transa As TransposeOperation,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	alpha As T,
	a As Array2D(Of T),
	b As Array2D(Of T)
)

C++/CLI

public:
void TriangularSolveInPlace(
	MatrixOperationSide side, 
	MatrixTriangle uplo, 
	TransposeOperation transa, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	T alpha, 
	Array2D<T> a, 
	Array2D<T> b
)

member TriangularSolveInPlace : 
        side : MatrixOperationSide * 
        uplo : MatrixTriangle * 
        transa : TransposeOperation * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        alpha : 'T * 
        a : Array2D<'T> * 
        b : Array2D<'T> -> unit

Parameters

             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.

             On entry, UPLO specifies whether the matrix A is an upper or
             lower triangular matrix as follows:
                UPLO = 'U' or 'u'   A is an upper triangular matrix.
                UPLO = 'L' or 'l'   A is a lower triangular matrix.

             On entry, TRANSA specifies the form of op( A ) to be used in
             the matrix multiplication as follows:
                TRANSA = 'N' or 'n'   op( A ) = A.
                TRANSA = 'T' or 't'   op( A ) = A^T.
                TRANSA = 'C' or 'c'   op( A ) = A^T.

             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.

             On entry, M specifies the number of rows of B. M must be at
             least zero.

             On entry, N specifies the number of columns of B.  N must be
             at least zero.

alpha T

            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 Array2D<T>

            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.

             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 Array2D<T>

            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.

             On entry, LDB specifies the first dimension of B as declared
             in  the  calling  (sub)  program.   LDB  must  be  at  least
             max( 1, m ).

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, Complex<T>, Array2D<Complex<T>>, Array2D<Complex<T>>)

public void TriangularSolveInPlace(
	MatrixOperationSide side,
	MatrixTriangle uplo,
	TransposeOperation transa,
	MatrixDiagonal diag,
	int m,
	int n,
	Complex<T> alpha,
	Array2D<Complex<T>> a,
	Array2D<Complex<T>> b
)

Visual Basic

Public Sub TriangularSolveInPlace ( 
	side As MatrixOperationSide,
	uplo As MatrixTriangle,
	transa As TransposeOperation,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	alpha As Complex(Of T),
	a As Array2D(Of Complex(Of T)),
	b As Array2D(Of Complex(Of T))
)

C++/CLI

public:
void TriangularSolveInPlace(
	MatrixOperationSide side, 
	MatrixTriangle uplo, 
	TransposeOperation transa, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	Complex<T> alpha, 
	Array2D<Complex<T>> a, 
	Array2D<Complex<T>> b
)

member TriangularSolveInPlace : 
        side : MatrixOperationSide * 
        uplo : MatrixTriangle * 
        transa : TransposeOperation * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        alpha : Complex<'T> * 
        a : Array2D<Complex<'T>> * 
        b : Array2D<Complex<'T>> -> unit

Parameters

             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.

             On entry, UPLO specifies whether the matrix A is an upper or
             lower triangular matrix as follows:
                UPLO = 'U' or 'u'   A is an upper triangular matrix.
                UPLO = 'L' or 'l'   A is a lower triangular matrix.

             On entry, TRANSA specifies the form of op( A ) to be used in
             the matrix multiplication as follows:
                TRANSA = 'N' or 'n'   op( A ) = A.
                TRANSA = 'T' or 't'   op( A ) = A^T.
                TRANSA = 'C' or 'c'   op( A ) = A^H.

             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.

             On entry, M specifies the number of rows of B. M must be at
             least zero.

             On entry, N specifies the number of columns of B.  N must be
             at least zero.

alpha Complex<T>

             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 Array2D<Complex<T>>

            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.

             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 Array2D<Complex<T>>

            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.

             On entry, LDB specifies the first dimension of B as declared
             in  the  calling  (sub)  program.   LDB  must  be  at  least
             max( 1, m ).

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, Complex<T>, ReadOnlySpan2D<Complex<T>>, Span2D<Complex<T>>)

public void TriangularSolveInPlace(
	MatrixOperationSide side,
	MatrixTriangle uplo,
	TransposeOperation transa,
	MatrixDiagonal diag,
	int m,
	int n,
	Complex<T> alpha,
	ReadOnlySpan2D<Complex<T>> a,
	Span2D<Complex<T>> b
)

Visual Basic

Public Sub TriangularSolveInPlace ( 
	side As MatrixOperationSide,
	uplo As MatrixTriangle,
	transa As TransposeOperation,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan2D(Of Complex(Of T)),
	b As Span2D(Of Complex(Of T))
)

C++/CLI

public:
void TriangularSolveInPlace(
	MatrixOperationSide side, 
	MatrixTriangle uplo, 
	TransposeOperation transa, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	Complex<T> alpha, 
	ReadOnlySpan2D<Complex<T>> a, 
	Span2D<Complex<T>> b
)

member TriangularSolveInPlace : 
        side : MatrixOperationSide * 
        uplo : MatrixTriangle * 
        transa : TransposeOperation * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan2D<Complex<'T>> * 
        b : Span2D<Complex<'T>> -> unit

Parameters

             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.

             On entry, UPLO specifies whether the matrix A is an upper or
             lower triangular matrix as follows:
                UPLO = 'U' or 'u'   A is an upper triangular matrix.
                UPLO = 'L' or 'l'   A is a lower triangular matrix.

             On entry, TRANSA specifies the form of op( A ) to be used in
             the matrix multiplication as follows:
                TRANSA = 'N' or 'n'   op( A ) = A.
                TRANSA = 'T' or 't'   op( A ) = A^T.
                TRANSA = 'C' or 'c'   op( A ) = A^H.

             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.

             On entry, M specifies the number of rows of B. M must be at
             least zero.

             On entry, N specifies the number of columns of B.  N must be
             at least zero.

alpha Complex<T>

             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 ReadOnlySpan2D<Complex<T>>

            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.

             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 Span2D<Complex<T>>

            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.

             On entry, LDB specifies the first dimension of B as declared
             in  the  calling  (sub)  program.   LDB  must  be  at  least
             max( 1, m ).

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, T, ReadOnlySpan<T>, Int32, Span<T>, Int32)

public abstract void TriangularSolveInPlace(
	MatrixOperationSide side,
	MatrixTriangle uplo,
	TransposeOperation transa,
	MatrixDiagonal diag,
	int m,
	int n,
	T alpha,
	ReadOnlySpan<T> a,
	int lda,
	Span<T> b,
	int ldb
)

Visual Basic

Public MustOverride Sub TriangularSolveInPlace ( 
	side As MatrixOperationSide,
	uplo As MatrixTriangle,
	transa As TransposeOperation,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	alpha As T,
	a As ReadOnlySpan(Of T),
	lda As Integer,
	b As Span(Of T),
	ldb As Integer
)

C++/CLI

public:
virtual void TriangularSolveInPlace(
	MatrixOperationSide side, 
	MatrixTriangle uplo, 
	TransposeOperation transa, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	T alpha, 
	ReadOnlySpan<T> a, 
	int lda, 
	Span<T> b, 
	int ldb
) abstract

abstract TriangularSolveInPlace : 
        side : MatrixOperationSide * 
        uplo : MatrixTriangle * 
        transa : TransposeOperation * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        alpha : 'T * 
        a : ReadOnlySpan<'T> * 
        lda : int * 
        b : Span<'T> * 
        ldb : int -> unit

Parameters

             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.

             On entry, UPLO specifies whether the matrix A is an upper or
             lower triangular matrix as follows:
                UPLO = 'U' or 'u'   A is an upper triangular matrix.
                UPLO = 'L' or 'l'   A is a lower triangular matrix.

             On entry, TRANSA specifies the form of op( A ) to be used in
             the matrix multiplication as follows:
                TRANSA = 'N' or 'n'   op( A ) = A.
                TRANSA = 'T' or 't'   op( A ) = A^T.
                TRANSA = 'C' or 'c'   op( A ) = A^T.

             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.

             On entry, M specifies the number of rows of B. M must be at
             least zero.

ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, ReadOnlySpan<T>, Int32, Span<T>, Int32)

             On entry, N specifies the number of columns of B.  N must be
             at least zero.

alpha T

            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<T>

            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<T>

            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

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, Complex<T>, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32)

public abstract void TriangularSolveInPlace(
	MatrixOperationSide side,
	MatrixTriangle uplo,
	TransposeOperation transa,
	MatrixDiagonal diag,
	int m,
	int n,
	Complex<T> alpha,
	ReadOnlySpan<Complex<T>> a,
	int lda,
	Span<Complex<T>> b,
	int ldb
)

Visual Basic

Public MustOverride Sub TriangularSolveInPlace ( 
	side As MatrixOperationSide,
	uplo As MatrixTriangle,
	transa As TransposeOperation,
	diag As MatrixDiagonal,
	m As Integer,
	n As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan(Of Complex(Of T)),
	lda As Integer,
	b As Span(Of Complex(Of T)),
	ldb As Integer
)

C++/CLI

public:
virtual void TriangularSolveInPlace(
	MatrixOperationSide side, 
	MatrixTriangle uplo, 
	TransposeOperation transa, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	Complex<T> alpha, 
	ReadOnlySpan<Complex<T>> a, 
	int lda, 
	Span<Complex<T>> b, 
	int ldb
) abstract

abstract TriangularSolveInPlace : 
        side : MatrixOperationSide * 
        uplo : MatrixTriangle * 
        transa : TransposeOperation * 
        diag : MatrixDiagonal * 
        m : int * 
        n : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan<Complex<'T>> * 
        lda : int * 
        b : Span<Complex<'T>> * 
        ldb : int -> unit

Parameters

             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.

             On entry, UPLO specifies whether the matrix A is an upper or
             lower triangular matrix as follows:
                UPLO = 'U' or 'u'   A is an upper triangular matrix.
                UPLO = 'L' or 'l'   A is a lower triangular matrix.

             On entry, TRANSA specifies the form of op( A ) to be used in
             the matrix multiplication as follows:
                TRANSA = 'N' or 'n'   op( A ) = A.
                TRANSA = 'T' or 't'   op( A ) = A^T.
                TRANSA = 'C' or 'c'   op( A ) = A^H.

             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.

             On entry, M specifies the number of rows of B. M must be at
             least zero.