Implements the BLAS (Basic Linear Algebra Subroutines) for
generic element types.
Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 6.0.16073.0 (6.0.16312.0)
| Name | Description |
---|
 | AbsoluteMaxIndex(Int32, ArraySliceComplexT) |
Finds the index of element having max. |
 | AbsoluteMaxIndex(Int32, ArraySliceT) |
Finds the index of element having max. |
 | ApplyModifiedGivensRotation |
THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX
(DXT) , WHERE **T INDICATES TRANSPOSE. |
 | BandMultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Int32, Int32, ComplexT, Array2DComplexT, ArraySliceComplexT, ComplexT, ArraySliceComplexT) |
Performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*AT*x + beta*y, or
y := alpha*AH*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an
m by n band matrix, with kl sub-diagonals and ku super-diagonals. |
 | BandMultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Int32, Int32, T, Array2DT, ArraySliceT, T, ArraySliceT) |
Performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*AT*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an
m by n band matrix, with kl sub-diagonals and ku super-diagonals. |
 | BandSymmetricMultiplyAndAddInPlace |
Performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n symmetric band matrix, with k super-diagonals. |
 | BandTriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2DComplexT, ArraySliceComplexT) |
Performs one of the matrix-vector operations
x := A*x, or x := AT*x, or x := AH*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular band matrix, with ( k + 1 ) diagonals. |
 | BandTriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2DT, ArraySliceT) |
Performs one of the matrix-vector operations
x := A*x, or x := AT*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular band matrix, with ( k + 1 ) diagonals. |
 | BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2DComplexT, ArraySliceComplexT) |
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 band matrix, with ( k + 1 )
diagonals. |
 | BandTriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2DT, ArraySliceT) |
Solves one of the systems of equations
A*x = b, or AT*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 band matrix, with ( k + 1 )
diagonals. |
 | ComplexOneNorm |
Computes the sum of the absolute values of a complex number
|
 | ConjugateDotProduct(Int32, ArraySliceComplexT, ArraySliceComplexT) |
Forms the dot product of a vector. |
 | ConjugateDotProduct(Int32, ArraySliceT, ArraySliceT) |
Returns the inner product of two vectors.
|
 | ConjugateRankUpdate(Int32, Int32, ComplexT, ArraySliceComplexT, ArraySliceComplexT, Array2DComplexT) |
Performs the rank 1 operation
A := alpha*x*y**H + A,
where alpha is a scalar, x is an m element vector, y is an n element
vector and A is an m by n matrix. |
 | ConjugateRankUpdate(Int32, Int32, T, ArraySliceT, ArraySliceT, Array2DT) |
Performs a rank one update of a matrix.
|
 | Copy(Int32, ArraySliceComplexT, ArraySliceComplexT) |
Copies a vector, x, to a vector, y. |
 | Copy(Int32, ArraySliceT, ArraySliceT) |
Copies a vector, x, to a vector, y. |
 | Copy(MatrixTriangle, Int32, Int32, Array2DComplexT, Array2DComplexT) |
Copies the specified elements of a complex matrix.
|
 | Copy(MatrixTriangle, Int32, Int32, Array2DT, Array2DT) |
Copies all or part of a two-dimensional matrix A to another
matrix B. |
 | CreateGivensRotation(T, T, T, T) |
Construct givens plane rotation. |
 | CreateGivensRotation(ComplexT, ComplexT, T, ComplexT) |
Determines a complex Givens rotation. |
 | CreateModifiedGivensRotation |
THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS
THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)*> DY2)**T. |
 | DotProduct(Int32, ArraySliceComplexT, ArraySliceComplexT) |
Forms the dot product of two vectors. |
 | DotProduct(Int32, ArraySliceT, ArraySliceT) |
Forms the dot product of two vectors. |
 | Equals | Determines whether the specified Object is equal to the current Object. (Inherited from Object.) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) |
 | FullMatrixNorm(MatrixNorm, Int32, Int32, Array2DComplexT) |
Computes the norm of a general rectangular matrix.
|
 | FullMatrixNorm(MatrixNorm, Int32, Int32, Array2DT) |
Returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real matrix A. |
 | GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) |
 | GetType | Gets the Type of the current instance. (Inherited from Object.) |
 | HermitianMatrixNorm(MatrixNorm, MatrixTriangle, Int32, Array2DComplexT) |
Computes the norm of a Hermitian matrix.
|
 | HermitianMatrixNorm(MatrixNorm, MatrixTriangle, Int32, Array2DT) |
Computes the norm of a Hermitian matrix.
|
 | HermitianMultiplyAndAddInPlace(MatrixTriangle, Int32, ComplexT, Array2DComplexT, ArraySliceComplexT, ComplexT, ArraySliceComplexT) |
Performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n hermitian matrix. |
 | HermitianMultiplyAndAddInPlace(MatrixTriangle, Int32, T, Array2DT, ArraySliceT, T, ArraySliceT) |
Product of a hermitian matrix and a vector.
|
 | HermitianMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, ComplexT, Array2DComplexT, Array2DComplexT, ComplexT, Array2DComplexT) |
Performs one of the matrix-matrix operations
C := alpha*A*B + beta*C,
or
C := alpha*B*A + beta*C,
where alpha and beta are scalars, A is an hermitian matrix and B and
C are m by n matrices. |
 | HermitianMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, T, Array2DT, Array2DT, T, Array2DT) |
Sum of the product of a hermitian and a general matrix and a scaled matrix.
|
 | HermitianRankUpdate(MatrixTriangle, Int32, T, ArraySliceComplexT, Array2DComplexT) |
Performs the hermitian rank 1 operation
A := alpha*x*x**H + A,
where alpha is a real scalar, x is an n element vector and A is an
n by n hermitian matrix. |
 | HermitianRankUpdate(MatrixTriangle, Int32, T, ArraySliceT, Array2DT) |
Performs a rank one update of a hermitian.
|
 | HermitianRankUpdate(MatrixTriangle, Int32, ComplexT, ArraySliceComplexT, ArraySliceComplexT, Array2DComplexT) |
Performs the hermitian rank 2 operation
A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
where alpha is a scalar, x and y are n element vectors and A is an n
by n hermitian matrix. |
 | HermitianRankUpdate(MatrixTriangle, Int32, T, ArraySliceT, ArraySliceT, Array2DT) |
Performs a hermitian rank two update of a hermitian matrix.
|
 | HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2DComplexT, T, Array2DComplexT) |
Performs one of the hermitian rank k operations
C := alpha*A*AH + beta*C,
or
C := alpha*AH*A + beta*C,
where alpha and beta are real scalars, C is an n by n hermitian
matrix and A is an n by k matrix in the first case and a k by n
matrix in the second case. |
 | HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2DT, T, Array2DT) |
Performs a rank k update of a hermitian matrix.
|
 | HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, ComplexT, Array2DComplexT, Array2DComplexT, T, Array2DComplexT) |
Performs one of the hermitian rank 2k operations
C := alpha*A*BH + conjg( alpha )*B*AH + beta*C,
or
C := alpha*AH*B + conjg( alpha )*BH*A + beta*C,
where alpha and beta are scalars with beta real, C is an n by n
hermitian matrix and A and B are n by k matrices in the first case
and k by n matrices in the second case. |
 | HermitianRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2DT, Array2DT, T, Array2DT) |
Performs a rank 2k update of a hermitian matrix.
|
 | MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
 | MultiplyAndAddInPlace(Int32, ComplexT, ArraySliceComplexT, ArraySliceComplexT) |
Constant times a vector plus a vector. |
 | MultiplyAndAddInPlace(Int32, T, ArraySliceT, ArraySliceT) |
Constant times a vector plus a vector. |
 | MultiplyAndAddInPlace(TransposeOperation, Int32, Int32, ComplexT, Array2DComplexT, ArraySliceComplexT, ComplexT, ArraySliceComplexT) |
Performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*AT*x + beta*y, or
y := alpha*AH*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an
m by n matrix. |
 | MultiplyAndAddInPlace(TransposeOperation, Int32, Int32, T, Array2DT, ArraySliceT, T, ArraySliceT) |
Performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*AT*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an
m by n matrix. |
 | MultiplyAndAddInPlace(TransposeOperation, TransposeOperation, Int32, Int32, Int32, ComplexT, Array2DComplexT, Array2DComplexT, ComplexT, Array2DComplexT) |
Performs one of the matrix-matrix operations
C := alpha*op( A )*op( B ) + beta*C,
where op( X ) is one of
op( X ) = X or op( X ) = XT or op( X ) = XH,
alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. |
 | MultiplyAndAddInPlace(TransposeOperation, TransposeOperation, Int32, Int32, Int32, T, Array2DT, Array2DT, T, Array2DT) |
Performs one of the matrix-matrix operations
C := alpha*op( A )*op( B ) + beta*C,
where op( X ) is one of
op( X ) = X or op( X ) = XT,
alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. |
 | MultiplyInPlace(Int32, ComplexT, ArraySliceComplexT) |
Scales a vector by a constant. |
 | MultiplyInPlace(Int32, T, ArraySliceComplexT) |
Scales a vector by a constant. |
 | MultiplyInPlace(Int32, T, ArraySliceT) |
Scales a vector by a constant. |
 | OneNorm |
Takes the sum of the absolute values. |
 | RankUpdate(Int32, Int32, ComplexT, ArraySliceComplexT, ArraySliceComplexT, Array2DComplexT) |
Performs the rank 1 operation
A := alpha*x*y**T + A,
where alpha is a scalar, x is an m element vector, y is an n element
vector and A is an m by n matrix. |
 | RankUpdate(Int32, Int32, T, ArraySliceT, ArraySliceT, Array2DT) |
Performs the rank 1 operation
A := alpha*x*y**T + A,
where alpha is a scalar, x is an m element vector, y is an n element
vector and A is an m by n matrix. |
 | RealOneNorm(Int32, ArraySliceComplexT) |
Takes the sum of the absolute values. |
 | RealOneNorm(Int32, ArraySliceT) |
Returns the sum of the absolute values of
the elements of a vector.
|
 | Rotate(Int32, ArraySliceComplexT, ArraySliceComplexT, T, T) |
A plane rotation, where the cos and sin (c and s) are real
and the vectors cx and cy are complex. |
 | Rotate(Int32, ArraySliceT, ArraySliceT, T, T) |
Applies a plane rotation. |
 | Swap(Int32, ArraySliceComplexT, ArraySliceComplexT) |
Interchanges two vectors. |
 | Swap(Int32, ArraySliceT, ArraySliceT) |
Swaps the elements of two vectors. |
 | SymmetricMatrixNorm(MatrixNorm, MatrixTriangle, Int32, Array2DComplexT) |
Computes the norm of a symmetric matrix.
|
 | SymmetricMatrixNorm(MatrixNorm, MatrixTriangle, Int32, Array2DT) |
Returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real symmetric matrix A. |
 | SymmetricMultiplyAndAddInPlace(MatrixTriangle, Int32, T, Array2DT, ArraySliceT, T, ArraySliceT) |
Performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n symmetric matrix. |
 | SymmetricMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, ComplexT, Array2DComplexT, Array2DComplexT, ComplexT, Array2DComplexT) |
Performs one of the matrix-matrix operations
C := alpha*A*B + beta*C,
or
C := alpha*B*A + beta*C,
where alpha and beta are scalars, A is a symmetric matrix and B and
C are m by n matrices. |
 | SymmetricMultiplyAndAddInPlace(MatrixOperationSide, MatrixTriangle, Int32, Int32, T, Array2DT, Array2DT, T, Array2DT) |
Performs one of the matrix-matrix operations
C := alpha*A*B + beta*C,
or
C := alpha*B*A + beta*C,
where alpha and beta are scalars, A is a symmetric matrix and B and
C are m by n matrices. |
 | SymmetricRankUpdate(MatrixTriangle, Int32, T, ArraySliceT, Array2DT) |
Performs the symmetric rank 1 operation
A := alpha*x*x**T + A,
where alpha is a real scalar, x is an n element vector and A is an
n by n symmetric matrix. |
 | SymmetricRankUpdate(MatrixTriangle, Int32, T, ArraySliceT, ArraySliceT, Array2DT) |
Performs the symmetric rank 2 operation
A := alpha*x*y**T + alpha*y*x**T + A,
where alpha is a scalar, x and y are n element vectors and A is an n
by n symmetric matrix. |
 | SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, ComplexT, Array2DComplexT, ComplexT, Array2DComplexT) |
Performs one of the symmetric rank k operations
C := alpha*A*AT + beta*C,
or
C := alpha*AT*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A is an n by k matrix in the first case and a k by n matrix
in the second case. |
 | SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2DT, T, Array2DT) |
Performs one of the symmetric rank k operations
C := alpha*A*AT + beta*C,
or
C := alpha*AT*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A is an n by k matrix in the first case and a k by n matrix
in the second case. |
 | SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, ComplexT, Array2DComplexT, Array2DComplexT, ComplexT, Array2DComplexT) |
Performs one of the symmetric rank 2k operations
C := alpha*A*BT + alpha*B*AT + beta*C,
or
C := alpha*AT*B + alpha*BT*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A and B are n by k matrices in the first case and k by n
matrices in the second case. |
 | SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2DT, Array2DT, T, Array2DT) |
Performs one of the symmetric rank 2k operations
C := alpha*A*BT + alpha*B*AT + beta*C,
or
C := alpha*AT*B + alpha*BT*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A and B are n by k matrices in the first case and k by n
matrices in the second case. |
 | ToString | Returns a string that represents the current object. (Inherited from Object.) |
 | TriangularMatrixNorm(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, Int32, Array2DComplexT) |
Computes the norm of a triangular matrix.
|
 | TriangularMatrixNorm(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, Int32, Array2DT) |
Returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
trapezoidal or triangular matrix A. |
 | TriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array2DComplexT, ArraySliceComplexT) |
Performs one of the matrix-vector operations
x := A*x, or x := AT*x, or x := AH*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix. |
 | TriangularMultiplyInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array2DT, ArraySliceT) |
Performs one of the matrix-vector operations
x := A*x, or x := AT*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix. |
 | TriangularMultiplyInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ComplexT, Array2DComplexT, Array2DComplexT) |
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 ) = AT or op( A ) = AH. |
 | TriangularMultiplyInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, Array2DT, Array2DT) |
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 ) = AT. |
 | TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array2DComplexT, ArraySliceComplexT) |
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, Array2DT, ArraySliceT) |
Solves one of the systems of equations
A*x = b, or AT*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, ComplexT, Array2DComplexT, Array2DComplexT) |
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, T, Array2DT, Array2DT) |
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. |
 | TwoNorm(Int32, ArraySliceComplexT) |
Returns the euclidean norm of a vector via the function
name, so that
DZNRM2 := sqrt( x**H*x )
|
 | TwoNorm(Int32, ArraySliceT) |
Returns the euclidean norm of a vector via the function
name, so that
DNRM2 := sqrt( x'*x )
|