Defines methods for the solution of a system of
simultaneous linear equations and related operations.
| Name | Description |
---|
 | AddProductToVector | Obsolete.
Multiplies a VectorT by this instance
and stores the result in a second vector of type DenseVectorT.
|
 | Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
 | EstimateConditionNumber |
Calculates an estimate for the condition number of a matrix.
|
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) |
 | GetDeterminant |
Calculates the determinant of a matrix.
|
 | GetHashCode | Serves as the default hash function. (Inherited from Object.) |
 | GetInverse |
Calculates the inverse matrix..
|
 | GetInverse(Boolean) |
Calculates the inverse of the factorized
matrix.
|
 | GetObjectData | |
 | GetType | Gets the Type of the current instance. (Inherited from Object.) |
 | IsSingular |
Gets a value indicating whether the matrix
is singular.
|
 | LeastSquaresSolve(MatrixT) |
Solves the system of linear equations for the specified
right-hand side matrix in the least squares sense.
|
 | LeastSquaresSolve(VectorT) |
Solves the system of linear equations for the specified
right-hand side vector.
|
 | LeastSquaresSolve(DenseMatrixT, Boolean) |
Solves the system of linear equations for the specified
right-hand side dense matrix in the least squares sense and optionally overwrites the
right-hand side with the solution.
|
 | LeastSquaresSolve(DenseVectorT, Boolean) |
Solves the system of linear equations for the specified
right-hand side dense vector in the least squares sense and optionally
overwrites the right-hand side with the solution.
|
 | LeastSquaresSolveInto(MatrixT, MatrixT) |
Solves a system of equations defined by the matrix and multiple right-hand sides in the least squares sense.
|
 | LeastSquaresSolveInto(VectorT, VectorT) |
Solves a system of equations defined by the matrix and the specified right-hand side in the least squares sense.
|
 | MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
 | Multiply(MatrixT) | Applies the linear operator to a matrix. |
 | Multiply(VectorT) | Applies the linear operator to a vector. |
 | Multiply(TransposeOperation, MatrixT) | Obsolete.
Multiplies a matrix on the left by this matrix.
|
 | Multiply(TransposeOperation, VectorT) | Obsolete.
Multiplies a vector on the left by this vector.
|
 | MultiplyAndAddAsLeftFactorCore |
Multiplies the matrix with a vector, adds the scaled result to another scaled
vector, and returns the result.
|
  | MultiplyAndAddInto |
Multiplies the matrix with a vector, adds the scaled result to another scaled
vector, and returns the result.
|
 | MultiplyAsLeftCore(TransposeOperation, MatrixT, MatrixT) |
Multiplies a matrix by the linear operator and returns the result.
|
 | MultiplyAsLeftCore(TransposeOperation, VectorT, VectorT) |
Multiplies a vector by the linear operator and returns the result.
|
  | MultiplyInto(LinearOperatorT, MatrixT, MatrixT) |
Multiplies a matrix and a matrix.
|
  | MultiplyInto(LinearOperatorT, VectorT, VectorT) |
Multiplies a matrix and a vector.
|
  | MultiplyInto(LinearOperatorT, TransposeOperation, MatrixT, MatrixT) |
Multiplies a possibly transposed matrix and a matrix.
|
  | MultiplyInto(LinearOperatorT, TransposeOperation, VectorT, VectorT) |
Multiplies a possibly transposed matrix and a vector.
|
 | MultiplyTranspose(MatrixT) | Applies the transpose of the linear operator to a matrix. |
 | MultiplyTranspose(VectorT) | Applies the (conjugate) transpose of the linear operator to a vector. |
 | Rank |
Returns the numerical rank of a matrix.
|
 | Rank(T) |
Returns the numerical rank of a matrix using the specified tolerance.
|
 | Solve(MatrixT) |
Solves the system of linear equations for the specified
right-hand side matrix.
|
 | Solve(VectorT) |
Solves the system of linear equations for the specified
right-hand side vector.
|
 | Solve(DenseMatrixT, Boolean) |
Solves the system of linear equations for the specified
right-hand side dense matrix and optionally overwrites the
right-hand side with the solution.
|
 | Solve(DenseVectorT, Boolean) |
Solves the system of linear equations for the specified
right-hand side dense vector and optionally
overwrites the right-hand side with the solution.
|
 | SolveInto(MatrixT, MatrixT) |
Solves a system of equations defined by the matrix and multiple right-hand sides.
|
 | SolveInto(VectorT, VectorT) |
Solves a system of equations defined by the matrix and the specified right-hand side.
|
 | SolveInto(TransposeOperation, MatrixT, MatrixT) |
Solves a system of equations defined by the matrix and multiple right-hand sides.
|
 | SolveInto(TransposeOperation, VectorT, VectorT) |
Solves a system of equations defined by the matrix and the specified right-hand side.
|
 | SolveTranspose(MatrixT) |
Solves the transposed system of linear equations for the specified
right-hand side matrix.
|
 | SolveTranspose(VectorT) |
Solves the system of linear equations for the specified
right-hand side vector.
|
 | SolveTranspose(DenseMatrixT, Boolean) |
Solves the transposed system of linear equations for the specified
right-hand side dense matrix and optionally overwrites the
right-hand side with the solution.
|
 | SolveTranspose(DenseVectorT, Boolean) |
Solves the transposed system of linear equations for the specified
right-hand side dense vector and optionally
overwrites the right-hand side with the solution.
|
 | SolveTransposeInto(MatrixT, MatrixT) |
Solves a system of equations defined by the matrix and multiple right-hand sides.
|
 | SolveTransposeInto(VectorT, VectorT) |
Solves a system of equations defined by the matrix and the specified right-hand side.
|
 | ToString | Returns a string that represents the current object. (Inherited from Object.) |
The solution of a system of simultaneous linear equations represented by a
MatrixT is one of the most common tasks in linear algebra.
The [o:Solve] mechanism, which is overloaded, defines a common method
for all classes that can represent matrices. This not only includes the
MatrixT class and its descendants, but also the DecompositionT
class and its descendants.