Linear Algebra Operations &lt; T &gt; . Triangular Multiply 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 operation to be performed as
             follows:
                TRANS = 'N' or 'n'   x := A*x.
                TRANS = 'T' or 't'   x := A^T*x.
                TRANS = 'C' or 'c'   x := A^T*x.

             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 vector x. On exit, X is overwritten with the
             tranformed vector x.

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

Remarks

Further Details:

            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- 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

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

Performs one of the matrix-vector operations x := A*x, or x := A^T*x, or x := A^H*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

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

Visual Basic

Public Sub TriangularMultiplyInPlace ( 
	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 TriangularMultiplyInPlace(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	Array2D<Complex<T>> a, 
	ArraySlice<Complex<T>> x
)

member TriangularMultiplyInPlace : 
        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 operation to be performed as
             follows:
                TRANS = 'N' or 'n'   x := A*x.
                TRANS = 'T' or 't'   x := A^T*x.
                TRANS = 'C' or 'c'   x := A^H*x.

             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 (input/output) complex array of dimension at least
             ( 1 + ( n - 1 )*abs( INCX ) ).
             Before entry, the incremented array X must contain the n
             element vector x. On exit, X is overwritten with the
             tranformed vector x.

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

Remarks

Further Details:

            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- 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

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

Performs one of the matrix-vector operations x := A*x, or x := A^T*x, or x := A^H*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

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

Visual Basic

Public Sub TriangularMultiplyInPlace ( 
	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 TriangularMultiplyInPlace(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	ReadOnlySpan2D<Complex<T>> a, 
	SpanSlice<Complex<T>> x
)

member TriangularMultiplyInPlace : 
        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 operation to be performed as
             follows:
                TRANS = 'N' or 'n'   x := A*x.
                TRANS = 'T' or 't'   x := A^T*x.
                TRANS = 'C' or 'c'   x := A^H*x.

             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 (input/output) complex array of dimension at least
             ( 1 + ( n - 1 )*abs( INCX ) ).
             Before entry, the incremented array X must contain the n
             element vector x. On exit, X is overwritten with the
             tranformed vector x.

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

Remarks

Further Details:

            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- 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

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

Performs one of the matrix-vector operations x := A*x, or x := A^T*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

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

Visual Basic

Public MustOverride Sub TriangularMultiplyInPlace ( 
	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 TriangularMultiplyInPlace(
	MatrixTriangle uplo, 
	TransposeOperation trans, 
	MatrixDiagonal diag, 
	int n, 
	ReadOnlySpan<T> a, 
	int lda, 
	Span<T> x, 
	int incx
) abstract

abstract TriangularMultiplyInPlace : 
        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 operation to be performed as
             follows:
                TRANS = 'N' or 'n'   x := A*x.
                TRANS = 'T' or 't'   x := A^T*x.
                TRANS = 'C' or 'c'   x := A^T*x.

             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>.TriangularMultiplyInPlace(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 vector x. On exit, X is overwritten with the
             tranformed vector x.

incx Int32

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

Implements

Remarks

Further Details:

            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- 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

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

Performs one of the matrix-vector operations x := A*x, or x := A^T*x, or x := A^H*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

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

abstract TriangularMultiplyInPlace : 
        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 operation to be performed as
             follows:
                TRANS = 'N' or 'n'   x := A*x.
                TRANS = 'T' or 't'   x := A^T*x.
                TRANS = 'C' or 'c'   x := A^H*x.

             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>.TriangularMultiplyInPlace(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 (input/output) complex array of dimension at least
             ( 1 + ( n - 1 )*abs( INCX ) ).
             Before entry, the incremented array X must contain the n
             element vector x. On exit, X is overwritten with the
             tranformed vector x.

incx Int32

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

Implements

Remarks

Further Details:

            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- 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

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

Performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ), where alpha is a scalar, B is an m by n matrix, 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 TriangularMultiplyInPlace(
	MatrixOperationSide side,
	MatrixTriangle uplo,
	TransposeOperation transa,
	MatrixDiagonal diag,
	int m,
	int n,
	T alpha,
	Array2D<T> a,
	Array2D<T> b
)

Visual Basic

Public Sub TriangularMultiplyInPlace ( 
	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 TriangularMultiplyInPlace(
	MatrixOperationSide side, 
	MatrixTriangle uplo, 
	TransposeOperation transa, 
	MatrixDiagonal diag, 
	int m, 
	int n, 
	T alpha, 
	Array2D<T> a, 
	Array2D<T> b
)

member TriangularMultiplyInPlace : 
        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 ) multiplies B from
             the left or right as follows:
                SIDE = 'L' or 'l'   B := alpha*op( A )*B.
                SIDE = 'R' or 'r'   B := alpha*B*op( A ).

             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 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 matrix  B,  and  on exit  is overwritten  by the
             transformed matrix.

             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

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

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

Performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, 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 or op( A ) = A^H.

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

member TriangularMultiplyInPlace : 
        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 ) multiplies B from
             the left or right as follows:
                SIDE = 'L' or 'l'   B := alpha*op( A )*B.
                SIDE = 'R' or 'r'   B := alpha*B*op( A ).

             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 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 (input/output) complex array of DIMENSION ( LDB, n ).
             Before entry,  the leading  m by n part of the array  B must
             contain the matrix  B,  and  on exit  is overwritten  by the
             transformed matrix.

             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

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

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

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

member TriangularMultiplyInPlace : 
        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 ) multiplies B from
             the left or right as follows:
                SIDE = 'L' or 'l'   B := alpha*op( A )*B.
                SIDE = 'R' or 'r'   B := alpha*B*op( A ).

             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 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 (input/output) complex array of DIMENSION ( LDB, n ).
             Before entry,  the leading  m by n part of the array  B must
             contain the matrix  B,  and  on exit  is overwritten  by the
             transformed matrix.

             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

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

TriangularMultiplyInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, ReadOnlySpan<T>, Int32, Span<T>, Int32)

public abstract void TriangularMultiplyInPlace(
	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 TriangularMultiplyInPlace ( 
	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 TriangularMultiplyInPlace(
	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 TriangularMultiplyInPlace : 
        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 ) multiplies B from
             the left or right as follows:
                SIDE = 'L' or 'l'   B := alpha*op( A )*B.
                SIDE = 'R' or 'r'   B := alpha*B*op( A ).

             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>.TriangularMultiplyInPlace(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 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 matrix  B,  and  on exit  is overwritten  by the
             transformed matrix.

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

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

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

public abstract void TriangularMultiplyInPlace(
	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 TriangularMultiplyInPlace ( 
	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 TriangularMultiplyInPlace(
	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 TriangularMultiplyInPlace : 
        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 ) multiplies B from
             the left or right as follows:
                SIDE = 'L' or 'l'   B := alpha*op( A )*B.
                SIDE = 'R' or 'r'   B := alpha*B*op( A ).

             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.