MatrixT Class |
Defines the base class for Matrix classes.
Inheritance HierarchySystemObject
Altaxo.Calc.LinearAlgebraMatrixT
Altaxo.Calc.LinearAlgebra.ComplexMatrix
Altaxo.Calc.LinearAlgebra.Complex32Matrix
Altaxo.Calc.LinearAlgebra.DoubleMatrix
Altaxo.Calc.LinearAlgebra.SingleMatrix
Altaxo.Calc.LinearAlgebraMatrixT
Altaxo.Calc.LinearAlgebra.ComplexMatrix
Altaxo.Calc.LinearAlgebra.Complex32Matrix
Altaxo.Calc.LinearAlgebra.DoubleMatrix
Altaxo.Calc.LinearAlgebra.SingleMatrix
Namespace: Altaxo.Calc.LinearAlgebra
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
SyntaxC#
[SerializableAttribute] public abstract class Matrix<T> : IFormattable, IEquatable<Matrix<T>>, ICloneable, IMatrix<T>, IROMatrix<T> where T : struct, new(), IEquatable<T>, IFormattable
Type Parameters
- T
- Supported data types are double, single, Altaxo.Calc.LinearAlgebra.Complex, and Altaxo.Calc.LinearAlgebra.Complex32.
The MatrixT type exposes the following members.
ConstructorsProperties| Name | Description | |
|---|---|---|
 | ColumnCount | Gets the number of columns. |
| Item | Gets or sets the value at the given row and column, with range checking. |
| RowCount | Gets the number of rows. |
| Storage | Gets the raw matrix data storage. |
Methods| Name | Description | |
|---|---|---|
  | Abs | Computes the absolute value of a matrix pointwise |
| Acos | Computes the acos of a matrix pointwise |
| Add(T) | Adds a scalar to each element of the matrix. |
| Add(MatrixT) | Adds another matrix to this matrix. |
| Add(T, MatrixT) | Adds a scalar to each element of the matrix and stores the result in the result matrix. |
| Add(MatrixT, MatrixT) | Adds another matrix to this matrix. |
| Append(MatrixT) | Concatenates this matrix with the given matrix. |
| Append(MatrixT, MatrixT) | Concatenates this matrix with the given matrix and places the result into the result matrix. |
| AsArray | Returns the internal multidimensional array of this matrix if, and only if, this matrix is stored by such an array internally. Otherwise returns null. Changes to the returned array and the matrix will affect each other. Use ToArray instead if you always need an independent array. |
| AsColumnArrays | Returns the internal column arrays of this matrix if, and only if, this matrix is stored by such arrays internally. Otherwise returns null. Changes to the returned arrays and the matrix will affect each other. Use ToColumnArrays instead if you always need an independent array. |
 | AsColumnMajorArray | Returns the internal column by column (column major) array of this matrix if, and only if, this matrix is stored by such arrays internally. Otherwise returns null. Changes to the returned arrays and the matrix will affect each other. Use ToColumnMajorArray instead if you always need an independent array. |
| Asin | Computes the asin of a matrix pointwise |
| AsRowArrays | Returns the internal row arrays of this matrix if, and only if, this matrix is stored by such arrays internally. Otherwise returns null. Changes to the returned arrays and the matrix will affect each other. Use ToRowArrays instead if you always need an independent array. |
| AsRowMajorArray | Returns the internal row by row (row major) array of this matrix if, and only if, this matrix is stored by such arrays internally. Otherwise returns null. Changes to the returned arrays and the matrix will affect each other. Use ToRowMajorArray instead if you always need an independent array. |
| At(Int32, Int32) | Retrieves the requested element without range checking. |
| At(Int32, Int32, T) | Sets the value of the given element without range checking. |
| Atan | Computes the atan of a matrix pointwise |
| Ceiling | Computes the ceiling of a matrix pointwise |
| Cholesky | Computes the Cholesky decomposition for a matrix. |
| Clear | Sets all values to zero. |
| ClearColumn | Sets all values of a column to zero. |
| ClearColumns | Sets all values for all of the chosen columns to zero. |
| ClearRow | Sets all values of a row to zero. |
| ClearRows | Sets all values for all of the chosen rows to zero. |
| ClearSubMatrix | Sets all values of a sub-matrix to zero. |
| Clone | Creates a clone of this instance. |
| CoerceZero(Double) | Set all values whose absolute value is smaller than the threshold to zero, in-place. |
| CoerceZero(FuncT, Boolean) | Set all values that meet the predicate to zero, in-place. |
| Column(Int32) | Copies a column into a new Vector>. |
| Column(Int32, VectorT) | Copies a column into to the given Vector. |
| Column(Int32, Int32, Int32) | Copies the requested column elements into a new Vector. |
| Column(Int32, Int32, Int32, VectorT) | Copies the requested column elements into the given vector. |
| ColumnAbsoluteSums | Calculates the absolute value sum of each column vector. |
| ColumnNorms | Calculates the p-norms of all column vectors. Typical values for p are 1.0 (L1, Manhattan norm), 2.0 (L2, Euclidean norm) and positive infinity (infinity norm) |
| ColumnSums | Calculates the value sum of each column vector. |
| ConditionNumber | Calculates the condition number of this matrix. |
| Conjugate | Complex conjugate each element of this matrix. |
| Conjugate(MatrixT) | Complex conjugate each element of this matrix and place the results into the result matrix. |
| ConjugateTranspose | Returns the conjugate transpose of this matrix. |
| ConjugateTranspose(MatrixT) | Puts the conjugate transpose of this matrix into the result matrix. |
| ConjugateTransposeAndMultiply(MatrixT) | Multiplies this matrix with the conjugate transpose of another matrix and returns the result. |
| ConjugateTransposeAndMultiply(MatrixT, MatrixT) | Multiplies this matrix with the conjugate transpose of another matrix and places the results into the result matrix. |
| ConjugateTransposeThisAndMultiply(MatrixT) | Multiplies the conjugate transpose of this matrix with another matrix and returns the result. |
| ConjugateTransposeThisAndMultiply(VectorT) | Multiplies the conjugate transpose of this matrix by a vector and returns the result. |
| ConjugateTransposeThisAndMultiply(MatrixT, MatrixT) | Multiplies the conjugate transpose of this matrix with another matrix and places the results into the result matrix. |
| ConjugateTransposeThisAndMultiply(VectorT, VectorT) | Multiplies the conjugate transpose of this matrix with a vector and places the results into the result vector. |
| CopyTo | Copies the elements of this matrix to the given matrix. |
| Cos | Computes the cos of a matrix pointwise |
| Cosh | Computes the cosh of a matrix pointwise |
| Determinant | Computes the determinant of this matrix. |
| Diagonal | Returns the elements of the diagonal in a Vector. |
| Diagonal(VectorT) | Returns the elements of the diagonal in a Vector. |
| DiagonalStack(MatrixT) | Diagonally stacks his matrix on top of the given matrix. The new matrix is a M-by-N matrix, where M = this.Rows + lower.Rows and N = this.Columns + lower.Columns. The values of off the off diagonal matrices/blocks are set to zero. |
| DiagonalStack(MatrixT, MatrixT) | Diagonally stacks his matrix on top of the given matrix and places the combined matrix into the result matrix. |
| Divide(T) | Divides each element of this matrix with a scalar. |
| Divide(T, MatrixT) | Divides each element of the matrix by a scalar and places results into the result matrix. |
| DivideByThis(T) | Divides a scalar by each element of the matrix. |
| DivideByThis(T, MatrixT) | Divides a scalar by each element of the matrix and places results into the result matrix. |
 | DoAdd(T, MatrixT) | Add a scalar to each element of the matrix and stores the result in the result vector. |
| DoAdd(MatrixT, MatrixT) | Adds another matrix to this matrix. |
| DoConjugate | Complex conjugates each element of this matrix and place the results into the result matrix. |
| DoConjugateTransposeAndMultiply | Multiplies this matrix with the conjugate transpose of another matrix and places the results into the result matrix. |
| DoConjugateTransposeThisAndMultiply(MatrixT, MatrixT) | Multiplies the transpose of this matrix with another matrix and places the results into the result matrix. |
| DoConjugateTransposeThisAndMultiply(VectorT, VectorT) | Multiplies the conjugate transpose of this matrix with a vector and places the results into the result vector. |
| DoDivide | Divides each element of the matrix by a scalar and places results into the result matrix. |
| DoDivideByThis | Divides a scalar by each element of the matrix and stores the result in the result matrix. |
| DoLeftMultiply | Left multiply a matrix with a vector ( = vector * matrix ) and place the result in the result vector. |
| DoModulus | Computes the canonical modulus, where the result has the sign of the divisor, for the given divisor each element of the matrix. |
| DoModulusByThis | Computes the canonical modulus, where the result has the sign of the divisor, for the given dividend for each element of the matrix. |
| DoMultiply(T, MatrixT) | Multiplies each element of the matrix by a scalar and places results into the result matrix. |
| DoMultiply(MatrixT, MatrixT) | Multiplies this matrix with another matrix and places the results into the result matrix. |
| DoMultiply(VectorT, VectorT) | Multiplies this matrix with a vector and places the results into the result vector. |
| DoNegate | Negate each element of this matrix and place the results into the result matrix. |
| DoPointwiseAbs | |
| DoPointwiseAbsoluteMaximum(T, MatrixT) | |
| DoPointwiseAbsoluteMaximum(MatrixT, MatrixT) | |
| DoPointwiseAbsoluteMinimum(T, MatrixT) | |
| DoPointwiseAbsoluteMinimum(MatrixT, MatrixT) | |
| DoPointwiseAcos | |
| DoPointwiseAsin | |
| DoPointwiseAtan | |
| DoPointwiseAtan2 | |
| DoPointwiseCeiling | |
| DoPointwiseCos | |
| DoPointwiseCosh | |
| DoPointwiseDivide | Pointwise divide this matrix by another matrix and stores the result into the result matrix. |
| DoPointwiseExp | Pointwise applies the exponential function to each value and stores the result into the result matrix. |
| DoPointwiseFloor | |
| DoPointwiseLog | Pointwise applies the natural logarithm function to each value and stores the result into the result matrix. |
| DoPointwiseLog10 | |
| DoPointwiseMaximum(T, MatrixT) | |
| DoPointwiseMaximum(MatrixT, MatrixT) | |
| DoPointwiseMinimum(T, MatrixT) | |
| DoPointwiseMinimum(MatrixT, MatrixT) | |
| DoPointwiseModulus | Pointwise canonical modulus, where the result has the sign of the divisor, of this matrix with another matrix and stores the result into the result matrix. |
| DoPointwiseMultiply | Pointwise multiplies this matrix with another matrix and stores the result into the result matrix. |
| DoPointwisePower(T, MatrixT) | Pointwise raise this matrix to an exponent and store the result into the result matrix. |
| DoPointwisePower(MatrixT, MatrixT) | Pointwise raise this matrix to an exponent matrix and store the result into the result matrix. |
| DoPointwiseRemainder | Pointwise remainder (% operator), where the result has the sign of the dividend, of this matrix with another matrix and stores the result into the result matrix. |
| DoPointwiseRound | |
| DoPointwiseSign | |
| DoPointwiseSin | |
| DoPointwiseSinh | |
| DoPointwiseSqrt | |
| DoPointwiseTan | |
| DoPointwiseTanh | |
| DoRemainder | Computes the remainder (% operator), where the result has the sign of the dividend, for the given divisor each element of the matrix. |
| DoRemainderByThis | Computes the remainder (% operator), where the result has the sign of the dividend, for the given dividend for each element of the matrix. |
| DoSubtract(T, MatrixT) | Subtracts a scalar from each element of the matrix and stores the result in the result matrix. |
| DoSubtract(MatrixT, MatrixT) | Subtracts another matrix from this matrix. |
| DoSubtractFrom | Subtracts each element of the matrix from a scalar and stores the result in the result matrix. |
| DoTransposeAndMultiply | Multiplies this matrix with the transpose of another matrix and places the results into the result matrix. |
| DoTransposeThisAndMultiply(MatrixT, MatrixT) | Multiplies the transpose of this matrix with another matrix and places the results into the result matrix. |
| DoTransposeThisAndMultiply(VectorT, VectorT) | Multiplies the transpose of this matrix with a vector and places the results into the result vector. |
| Enumerate | Returns an IEnumerable that can be used to iterate through all values of the matrix. |
| Enumerate(Zeros) | Returns an IEnumerable that can be used to iterate through all values of the matrix. |
| EnumerateColumns | Returns an IEnumerable that can be used to iterate through all columns of the matrix. |
| EnumerateColumns(Int32, Int32) | Returns an IEnumerable that can be used to iterate through a subset of all columns of the matrix. |
| EnumerateColumnsIndexed | Returns an IEnumerable that can be used to iterate through all columns of the matrix and their index. |
| EnumerateColumnsIndexed(Int32, Int32) | Returns an IEnumerable that can be used to iterate through a subset of all columns of the matrix and their index. |
| EnumerateIndexed | Returns an IEnumerable that can be used to iterate through all values of the matrix and their index. |
| EnumerateIndexed(Zeros) | Returns an IEnumerable that can be used to iterate through all values of the matrix and their index. |
| EnumerateRows | Returns an IEnumerable that can be used to iterate through all rows of the matrix. |
| EnumerateRows(Int32, Int32) | Returns an IEnumerable that can be used to iterate through a subset of all rows of the matrix. |
| EnumerateRowsIndexed | Returns an IEnumerable that can be used to iterate through all rows of the matrix and their index. |
| EnumerateRowsIndexed(Int32, Int32) | Returns an IEnumerable that can be used to iterate through a subset of all rows of the matrix and their index. |
| Equals(MatrixT) | Indicates whether the current object is equal to another object of the same type. |
| Equals(Object) |
Determines whether the specified Object is equal to this instance.
(Overrides ObjectEquals(Object)) |
| Evd | Computes the EVD decomposition for a matrix. |
| Exists | Returns true if at least one element satisfies a predicate. Zero elements may be skipped on sparse data structures if allowed (default). |
| Exists2TOther | Returns true if at least one element pairs of two matrices of the same size satisfies a predicate. Zero elements may be skipped on sparse data structures if allowed (default). |
| Exp | Computes the exponential of a matrix pointwise |
| Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
| Find | Returns a tuple with the index and value of the first element satisfying a predicate, or null if none is found. Zero elements may be skipped on sparse data structures if allowed (default). |
| Find2TOther | Returns a tuple with the index and values of the first element pair of two matrices of the same size satisfying a predicate, or null if none is found. Zero elements may be skipped on sparse data structures if allowed (default). |
| Floor | Computes the floor of a matrix pointwise |
| Fold2TOther, TState | Applies a function to update the status with each value pair of two matrices and returns the resulting status. |
| FoldByColumnTU | For each column, applies a function f to each element of the column, threading an accumulator argument through the computation. Returns an array with the resulting accumulator states for each column. |
| FoldByRowTU | For each row, applies a function f to each element of the row, threading an accumulator argument through the computation. Returns an array with the resulting accumulator states for each row. |
| FoldColumnsTU | Applies a function f to each column vector, threading an accumulator vector argument through the computation. Returns the resulting accumulator vector. |
| FoldRowsTU | Applies a function f to each row vector, threading an accumulator vector argument through the computation. Returns the resulting accumulator vector. |
| ForAll | Returns true if all elements satisfy a predicate. Zero elements may be skipped on sparse data structures if allowed (default). |
| ForAll2TOther | Returns true if all element pairs of two matrices of the same size satisfy a predicate. Zero elements may be skipped on sparse data structures if allowed (default). |
| FrobeniusNorm | Calculates the entry-wise Frobenius norm of this matrix. |
| GetHashCode |
Returns a hash code for this instance.
(Overrides ObjectGetHashCode) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| GramSchmidt | Computes the QR decomposition for a matrix using Modified Gram-Schmidt Orthogonalization. |
| InfinityNorm | Calculates the induced infinity norm of this matrix. |
| InsertColumn | Creates a new matrix and inserts the given column at the given index. |
| InsertRow | Creates a new matrix and inserts the given row at the given index. |
| Inverse | Computes the inverse of this matrix. |
| IsHermitian | Evaluates whether this matrix is Hermitian (conjugate symmetric). |
| IsSymmetric | Evaluates whether this matrix is symmetric. |
| Kernel | Computes an orthonormal basis for the null space of this matrix, also known as the kernel of the corresponding matrix transformation. |
| KroneckerProduct(MatrixT) | Computes the Kronecker product of this matrix with the given matrix. The new matrix is M-by-N with M = this.Rows * lower.Rows and N = this.Columns * lower.Columns. |
| KroneckerProduct(MatrixT, MatrixT) | Computes the Kronecker product of this matrix with the given matrix. The new matrix is M-by-N with M = this.Rows * lower.Rows and N = this.Columns * lower.Columns. |
| L1Norm | Calculates the induced L1 norm of this matrix. |
| L2Norm | Calculates the induced L2 norm of the matrix. |
| LeftMultiply(VectorT) | Left multiply a matrix with a vector ( = vector * matrix ). |
| LeftMultiply(VectorT, VectorT) | Left multiply a matrix with a vector ( = vector * matrix ) and place the result in the result vector. |
| Log | Computes the log of a matrix pointwise |
| Log10 | Computes the log10 of a matrix pointwise |
| LowerTriangle | Returns a new matrix containing the lower triangle of this matrix. |
| LowerTriangle(MatrixT) | Puts the lower triangle of this matrix into the result matrix. |
| LU | Computes the LU decomposition for a matrix. |
| Map(FuncT, T, MatrixT, Zeros) | Applies a function to each value of this matrix and replaces the value in the result matrix. If forceMapZero is not set to true, zero values may or may not be skipped depending on the actual data storage implementation (relevant mostly for sparse matrices). |
| MapTU(FuncT, TU, Zeros) | Applies a function to each value of this matrix and returns the results as a new matrix. If forceMapZero is not set to true, zero values may or may not be skipped depending on the actual data storage implementation (relevant mostly for sparse matrices). |
| Map2(FuncT, T, T, MatrixT, Zeros) | Applies a function to each value pair of two matrices and returns the results as a new vector. |
| Map2(FuncT, T, T, MatrixT, MatrixT, Zeros) | Applies a function to each value pair of two matrices and replaces the value in the result vector. |
| MapConvertTU | Applies a function to each value of this matrix and replaces the value in the result matrix. If forceMapZero is not set to true, zero values may or may not be skipped depending on the actual data storage implementation (relevant mostly for sparse matrices). |
| MapIndexed(FuncInt32, Int32, T, T, MatrixT, Zeros) | Applies a function to each value of this matrix and replaces the value in the result matrix. The index of each value (zero-based) is passed as first argument to the function. If forceMapZero is not set to true, zero values may or may not be skipped depending on the actual data storage implementation (relevant mostly for sparse matrices). |
| MapIndexedTU(FuncInt32, Int32, T, TU, Zeros) | Applies a function to each value of this matrix and returns the results as a new matrix. The index of each value (zero-based) is passed as first argument to the function. If forceMapZero is not set to true, zero values may or may not be skipped depending on the actual data storage implementation (relevant mostly for sparse matrices). |
| MapIndexedConvertTU | Applies a function to each value of this matrix and replaces the value in the result matrix. The index of each value (zero-based) is passed as first argument to the function. If forceMapZero is not set to true, zero values may or may not be skipped depending on the actual data storage implementation (relevant mostly for sparse matrices). |
| MapIndexedInplace | Applies a function to each value of this matrix and replaces the value with its result. The row and column indices of each value (zero-based) are passed as first arguments to the function. If forceMapZero is not set to true, zero values may or may not be skipped depending on the actual data storage implementation (relevant mostly for sparse matrices). |
| MapInplace | Applies a function to each value of this matrix and replaces the value with its result. If forceMapZero is not set to true, zero values may or may not be skipped depending on the actual data storage implementation (relevant mostly for sparse matrices). |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| Modulus(T) | Computes the canonical modulus, where the result has the sign of the divisor, for each element of the matrix. |
| Modulus(T, MatrixT) | Computes the canonical modulus, where the result has the sign of the divisor, for each element of the matrix. |
| ModulusByThis(T) | Computes the canonical modulus, where the result has the sign of the divisor, for each element of the matrix. |
| ModulusByThis(T, MatrixT) | Computes the canonical modulus, where the result has the sign of the divisor, for each element of the matrix. |
| Multiply(T) | Multiplies each element of this matrix with a scalar. |
| Multiply(MatrixT) | Multiplies this matrix with another matrix and returns the result. |
| Multiply(VectorT) | Multiplies this matrix by a vector and returns the result. |
| Multiply(T, MatrixT) | Multiplies each element of the matrix by a scalar and places results into the result matrix. |
| Multiply(MatrixT, MatrixT) | Multiplies this matrix with another matrix and places the results into the result matrix. |
| Multiply(VectorT, VectorT) | Multiplies this matrix with a vector and places the results into the result vector. |
| Negate | Negate each element of this matrix. |
| Negate(MatrixT) | Negate each element of this matrix and place the results into the result matrix. |
| NormalizeColumns | Normalizes all column vectors to a unit p-norm. Typical values for p are 1.0 (L1, Manhattan norm), 2.0 (L2, Euclidean norm) and positive infinity (infinity norm) |
| NormalizeRows | Normalizes all row vectors to a unit p-norm. Typical values for p are 1.0 (L1, Manhattan norm), 2.0 (L2, Euclidean norm) and positive infinity (infinity norm) |
| Nullity | Calculates the nullity of the matrix. |
| PermuteColumns | Permute the columns of a matrix according to a permutation. |
| PermuteRows | Permute the rows of a matrix according to a permutation. |
| PointwiseAbs | Pointwise applies the abs function to each value |
| PointwiseAbs(MatrixT) | Pointwise applies the abs function to each value |
| PointwiseAbsoluteMaximum(T) | Pointwise applies the absolute maximum with a scalar to each value. |
| PointwiseAbsoluteMaximum(MatrixT) | Pointwise applies the absolute maximum with the values of another matrix to each value. |
| PointwiseAbsoluteMaximum(T, MatrixT) | Pointwise applies the absolute maximum with a scalar to each value. |
| PointwiseAbsoluteMaximum(MatrixT, MatrixT) | Pointwise applies the absolute maximum with the values of another matrix to each value. |
| PointwiseAbsoluteMinimum(T) | Pointwise applies the absolute minimum with a scalar to each value. |
| PointwiseAbsoluteMinimum(MatrixT) | Pointwise applies the absolute minimum with the values of another matrix to each value. |
| PointwiseAbsoluteMinimum(T, MatrixT) | Pointwise applies the absolute minimum with a scalar to each value. |
| PointwiseAbsoluteMinimum(MatrixT, MatrixT) | Pointwise applies the absolute minimum with the values of another matrix to each value. |
| PointwiseAcos | Pointwise applies the acos function to each value |
| PointwiseAcos(MatrixT) | Pointwise applies the acos function to each value |
| PointwiseAsin | Pointwise applies the asin function to each value |
| PointwiseAsin(MatrixT) | Pointwise applies the asin function to each value |
| PointwiseAtan | Pointwise applies the atan function to each value |
| PointwiseAtan(MatrixT) | Pointwise applies the atan function to each value |
| PointwiseAtan2(MatrixT) | Pointwise applies the atan2 function to each value of the current matrix and a given other matrix being the 'x' of atan2 and the 'this' matrix being the 'y' |
| PointwiseAtan2(MatrixT, MatrixT) | Pointwise applies the atan2 function to each value of the current matrix and a given other matrix being the 'x' of atan2 and the 'this' matrix being the 'y' |
| PointwiseBinary(ActionMatrixT, MatrixT, MatrixT) | Helper function to apply a binary function which takes two matrices and modifies the latter in place. A copy of the "this" matrix is first made and then passed to f together with the other matrix. The copy is then returned as the result |
| PointwiseBinary(ActionMatrixT, MatrixT, MatrixT, MatrixT) | Helper function to apply a binary function which takes two matrices and modifies the second one in place |
| PointwiseCeiling | Pointwise applies the ceiling function to each value |
| PointwiseCeiling(MatrixT) | Pointwise applies the ceiling function to each value |
| PointwiseCos | Pointwise applies the cos function to each value |
| PointwiseCos(MatrixT) | Pointwise applies the cos function to each value |
| PointwiseCosh | Pointwise applies the cosh function to each value |
| PointwiseCosh(MatrixT) | Pointwise applies the cosh function to each value |
| PointwiseDivide(MatrixT) | Pointwise divide this matrix by another matrix. |
| PointwiseDivide(MatrixT, MatrixT) | Pointwise divide this matrix by another matrix and stores the result into the result matrix. |
| PointwiseExp | Pointwise applies the exponent function to each value. |
| PointwiseExp(MatrixT) | Pointwise applies the exponent function to each value. |
| PointwiseFloor | Pointwise applies the floor function to each value |
| PointwiseFloor(MatrixT) | Pointwise applies the floor function to each value |
| PointwiseLog | Pointwise applies the natural logarithm function to each value. |
| PointwiseLog(MatrixT) | Pointwise applies the natural logarithm function to each value. |
| PointwiseLog10 | Pointwise applies the log10 function to each value |
| PointwiseLog10(MatrixT) | Pointwise applies the log10 function to each value |
| PointwiseMaximum(T) | Pointwise applies the maximum with a scalar to each value. |
| PointwiseMaximum(MatrixT) | Pointwise applies the maximum with the values of another matrix to each value. |
| PointwiseMaximum(T, MatrixT) | Pointwise applies the maximum with a scalar to each value. |
| PointwiseMaximum(MatrixT, MatrixT) | Pointwise applies the maximum with the values of another matrix to each value. |
| PointwiseMinimum(T) | Pointwise applies the minimum with a scalar to each value. |
| PointwiseMinimum(MatrixT) | Pointwise applies the minimum with the values of another matrix to each value. |
| PointwiseMinimum(T, MatrixT) | Pointwise applies the minimum with a scalar to each value. |
| PointwiseMinimum(MatrixT, MatrixT) | Pointwise applies the minimum with the values of another matrix to each value. |
| PointwiseModulus(MatrixT) | Pointwise canonical modulus, where the result has the sign of the divisor, of this matrix by another matrix. |
| PointwiseModulus(MatrixT, MatrixT) | Pointwise canonical modulus, where the result has the sign of the divisor, of this matrix by another matrix and stores the result into the result matrix. |
| PointwiseMultiply(MatrixT) | Pointwise multiplies this matrix with another matrix. |
| PointwiseMultiply(MatrixT, MatrixT) | Pointwise multiplies this matrix with another matrix and stores the result into the result matrix. |
| PointwisePower(T) | Pointwise raise this matrix to an exponent and store the result into the result matrix. |
| PointwisePower(MatrixT) | Pointwise raise this matrix to an exponent and store the result into the result matrix. |
| PointwisePower(T, MatrixT) | Pointwise raise this matrix to an exponent. |
| PointwisePower(MatrixT, MatrixT) | Pointwise raise this matrix to an exponent. |
| PointwiseRemainder(MatrixT) | Pointwise remainder (% operator), where the result has the sign of the dividend, of this matrix by another matrix. |
| PointwiseRemainder(MatrixT, MatrixT) | Pointwise remainder (% operator), where the result has the sign of the dividend, of this matrix by another matrix and stores the result into the result matrix. |
| PointwiseRound | Pointwise applies the round function to each value |
| PointwiseRound(MatrixT) | Pointwise applies the round function to each value |
| PointwiseSign | Pointwise applies the sign function to each value |
| PointwiseSign(MatrixT) | Pointwise applies the sign function to each value |
| PointwiseSin | Pointwise applies the sin function to each value |
| PointwiseSin(MatrixT) | Pointwise applies the sin function to each value |
| PointwiseSinh | Pointwise applies the sinh function to each value |
| PointwiseSinh(MatrixT) | Pointwise applies the sinh function to each value |
| PointwiseSqrt | Pointwise applies the sqrt function to each value |
| PointwiseSqrt(MatrixT) | Pointwise applies the sqrt function to each value |
| PointwiseTan | Pointwise applies the tan function to each value |
| PointwiseTan(MatrixT) | Pointwise applies the tan function to each value |
| PointwiseTanh | Pointwise applies the tanh function to each value |
| PointwiseTanh(MatrixT) | Pointwise applies the tanh function to each value |
| PointwiseUnary(ActionMatrixT) | Helper function to apply a unary function to a matrix. The function f modifies the matrix given to it in place. Before its called, a copy of the 'this' matrix is first created, then passed to f. The copy is then returned as the result |
| PointwiseUnary(ActionMatrixT, MatrixT) | Helper function to apply a unary function which modifies a matrix in place. |
| Power(Int32) | Multiplies this square matrix with another matrix and returns the result. |
| Power(Int32, MatrixT) | Raises this square matrix to a positive integer exponent and places the results into the result matrix. |
| PseudoInverse | Computes the Moore-Penrose Pseudo-Inverse of this matrix. |
| QR | Computes the QR decomposition for a matrix. |
| Range | Computes an orthonormal basis for the column space of this matrix, also known as the range or image of the corresponding matrix transformation. |
| Rank | Calculates the rank of the matrix. |
| ReduceColumns | Reduces all column vectors by applying a function between two of them, until only a single vector is left. |
| ReduceRows | Reduces all row vectors by applying a function between two of them, until only a single vector is left. |
| Remainder(T) | Computes the remainder (matrix % divisor), where the result has the sign of the dividend, for each element of the matrix. |
| Remainder(T, MatrixT) | Computes the remainder (matrix % divisor), where the result has the sign of the dividend, for each element of the matrix. |
| RemainderByThis(T) | Computes the remainder (dividend % matrix), where the result has the sign of the dividend, for each element of the matrix. |
| RemainderByThis(T, MatrixT) | Computes the remainder (dividend % matrix), where the result has the sign of the dividend, for each element of the matrix. |
| RemoveColumn | Creates a new matrix with the given column removed. |
| RemoveRow | Creates a new matrix with the given row removed. |
| Resize | Creates a new matrix with the desired size and copies this matrix to it. Values which no longer exist in the new matrix are ignored, new values are set to zero. |
| Round | Computes the rounded value of a matrix pointwise |
| Row(Int32) | Copies a row into an Vector. |
| Row(Int32, VectorT) | Copies a row into to the given Vector. |
| Row(Int32, Int32, Int32) | Copies the requested row elements into a new Vector. |
| Row(Int32, Int32, Int32, VectorT) | Copies the requested row elements into a new Vector. |
| RowAbsoluteSums | Calculates the absolute value sum of each row vector. |
| RowNorms | Calculates the p-norms of all row vectors. Typical values for p are 1.0 (L1, Manhattan norm), 2.0 (L2, Euclidean norm) and positive infinity (infinity norm) |
| RowSums | Calculates the value sum of each row vector. |
| SetColumn(Int32, T) | Copies the values of the given array to the specified column. |
| SetColumn(Int32, VectorT) | Copies the values of the given Vector to the specified column. |
| SetColumn(Int32, Int32, Int32, VectorT) | Copies the values of the given Vector to the specified sub-column. |
| SetDiagonal(T) | Copies the values of the given array to the diagonal. |
| SetDiagonal(VectorT) | Copies the values of the given Vector to the diagonal. |
| SetRow(Int32, T) | Copies the values of the given array to the specified row. |
| SetRow(Int32, VectorT) | Copies the values of the given Vector to the specified row. |
| SetRow(Int32, Int32, Int32, VectorT) | Copies the values of the given Vector to the specified sub-row. |
| SetSubMatrix(Int32, Int32, MatrixT) | Copies the values of a given matrix into a region in this matrix. |
| SetSubMatrix(Int32, Int32, Int32, Int32, MatrixT) | Copies the values of a given matrix into a region in this matrix. |
| SetSubMatrix(Int32, Int32, Int32, Int32, Int32, Int32, MatrixT) | Copies the values of a given matrix into a region in this matrix. |
| Sin | Computes the sin of a matrix pointwise |
| Sinh | Computes the sinh of a matrix pointwise |
| Solve(MatrixT) | Solves a system of linear equations, AX = B, with A QR factorized. |
| Solve(VectorT) | Solves a system of linear equations, Ax = b, with A QR factorized. |
| Solve(MatrixT, MatrixT) | Solves a system of linear equations, AX = B, with A QR factorized. |
| Solve(VectorT, VectorT) | Solves a system of linear equations, Ax = b, with A QR factorized. |
| SolveIterative(MatrixT, IIterativeSolverT, IIterationStopCriterionT) | Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix. |
| SolveIterative(VectorT, IIterativeSolverT, IIterationStopCriterionT) | Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector. |
| SolveIterative(MatrixT, IIterativeSolverT, IPreconditionerT, IIterationStopCriterionT) | Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix. |
| SolveIterative(MatrixT, IIterativeSolverT, IteratorT, IPreconditionerT) | Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix. |
| SolveIterative(VectorT, IIterativeSolverT, IPreconditionerT, IIterationStopCriterionT) | Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector. |
| SolveIterative(VectorT, IIterativeSolverT, IteratorT, IPreconditionerT) | Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector. |
| Sqrt | Computes the sqrt of a matrix pointwise |
| Stack(MatrixT) | Stacks this matrix on top of the given matrix and places the result into the result matrix. |
| Stack(MatrixT, MatrixT) | Stacks this matrix on top of the given matrix and places the result into the result matrix. |
| StrictlyLowerTriangle | Returns a new matrix containing the lower triangle of this matrix. The new matrix does not contain the diagonal elements of this matrix. |
| StrictlyLowerTriangle(MatrixT) | Puts the strictly lower triangle of this matrix into the result matrix. |
| StrictlyUpperTriangle | Returns a new matrix containing the upper triangle of this matrix. The new matrix does not contain the diagonal elements of this matrix. |
| StrictlyUpperTriangle(MatrixT) | Puts the strictly upper triangle of this matrix into the result matrix. |
| SubMatrix | Creates a matrix that contains the values from the requested sub-matrix. |
| Subtract(T) | Subtracts a scalar from each element of the matrix. |
| Subtract(MatrixT) | Subtracts another matrix from this matrix. |
| Subtract(T, MatrixT) | Subtracts a scalar from each element of the matrix and stores the result in the result matrix. |
| Subtract(MatrixT, MatrixT) | Subtracts another matrix from this matrix. |
| SubtractFrom(T) | Subtracts each element of the matrix from a scalar. |
| SubtractFrom(T, MatrixT) | Subtracts each element of the matrix from a scalar and stores the result in the result matrix. |
| Svd | Computes the SVD decomposition for a matrix. |
| Tan | Computes the tan of a matrix pointwise |
| Tanh | Computes the tanh of a matrix pointwise |
| ToArray | Returns this matrix as a multidimensional array. The returned array will be independent from this matrix. A new memory block will be allocated for the array. |
| ToColumnArrays | Returns this matrix as array of column arrays. The returned arrays will be independent from this matrix. A new memory block will be allocated for the arrays. |
| ToColumnMajorArray | Returns the matrix's elements as an array with the data laid out column by column (column major). The returned array will be independent from this matrix. A new memory block will be allocated for the array. |
| ToMatrixString(String, IFormatProvider) | Returns a string that summarizes the content of this matrix. |
| ToMatrixString(Int32, Int32, String, IFormatProvider) | Returns a string that summarizes the content of this matrix. |
| ToMatrixString(Int32, Int32, Int32, Int32, String, String, String, String, String, FuncT, String) | |
| ToMatrixString(Int32, Int32, Int32, Int32, Int32, String, String, String, String, String, FuncT, String) | |
| ToMatrixStringArray(Int32, Int32, Int32, Int32, String, String, String, FuncT, String) | Returns a string 2D array that summarizes the content of this matrix. |
| ToMatrixStringArray(Int32, Int32, Int32, Int32, Int32, Int32, String, String, String, FuncT, String) | Returns a string 2D array that summarizes the content of this matrix. |
| ToRowArrays | Returns this matrix as array of row arrays. The returned arrays will be independent from this matrix. A new memory block will be allocated for the arrays. |
| ToRowMajorArray | Returns the matrix's elements as an array with the data laid row by row (row major). The returned array will be independent from this matrix. A new memory block will be allocated for the array. |
| ToString |
Returns a string that summarizes this matrix.
The maximum number of cells can be configured in the Control class.
(Overrides ObjectToString) |
| ToString(String, IFormatProvider) | Returns a string that summarizes this matrix. The maximum number of cells can be configured in the Control class. The format string is ignored. |
| ToString(Int32, Int32, String, IFormatProvider) | Returns a string that summarizes this matrix. |
| ToTypeString | Returns a string that describes the type, dimensions and shape of this matrix. |
| Trace | Computes the trace of this matrix. |
| Transpose | Returns the transpose of this matrix. |
| Transpose(MatrixT) | Puts the transpose of this matrix into the result matrix. |
| TransposeAndMultiply(MatrixT) | Multiplies this matrix with transpose of another matrix and returns the result. |
| TransposeAndMultiply(MatrixT, MatrixT) | Multiplies this matrix with transpose of another matrix and places the results into the result matrix. |
| TransposeThisAndMultiply(MatrixT) | Multiplies the transpose of this matrix with another matrix and returns the result. |
| TransposeThisAndMultiply(VectorT) | Multiplies the transpose of this matrix by a vector and returns the result. |
| TransposeThisAndMultiply(MatrixT, MatrixT) | Multiplies the transpose of this matrix with another matrix and places the results into the result matrix. |
| TransposeThisAndMultiply(VectorT, VectorT) | Multiplies the transpose of this matrix with a vector and places the results into the result vector. |
| TrySolveIterative(MatrixT, MatrixT, IIterativeSolverT, IIterationStopCriterionT) | Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix. |
| TrySolveIterative(VectorT, VectorT, IIterativeSolverT, IIterationStopCriterionT) | Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector. |
| TrySolveIterative(MatrixT, MatrixT, IIterativeSolverT, IPreconditionerT, IIterationStopCriterionT) | Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix. |
| TrySolveIterative(MatrixT, MatrixT, IIterativeSolverT, IteratorT, IPreconditionerT) | Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix. |
| TrySolveIterative(VectorT, VectorT, IIterativeSolverT, IPreconditionerT, IIterationStopCriterionT) | Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector. |
| TrySolveIterative(VectorT, VectorT, IIterativeSolverT, IteratorT, IPreconditionerT) | Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector. |
| UpperTriangle | Returns a new matrix containing the upper triangle of this matrix. |
| UpperTriangle(MatrixT) | Puts the upper triangle of this matrix into the result matrix. |
Operators| Name | Description | |
|---|---|---|
 | Addition(T, MatrixT) | Adds a scalar to each element of the matrix. |
| Addition(MatrixT, T) | Adds a scalar to each element of the matrix. |
| Addition(MatrixT, MatrixT) | Adds two matrices together and returns the results. |
| Division(T, MatrixT) | Divides a scalar with a matrix. |
| Division(MatrixT, T) | Divides a matrix with a scalar. |
| DotDivide(MatrixT, MatrixT) | |
| DotHat(MatrixT, T) | |
| DotHat(MatrixT, MatrixT) | |
| DotMultiply(MatrixT, MatrixT) | |
| DotPercent(MatrixT, MatrixT) | |
| Modulus(T, MatrixT) | Computes the pointwise remainder (% operator), where the result has the sign of the dividend, of the given dividend of each element of the matrix. |
| Modulus(MatrixT, T) | Computes the pointwise remainder (% operator), where the result has the sign of the dividend, of each element of the matrix of the given divisor. |
| Modulus(MatrixT, MatrixT) | Computes the pointwise remainder (% operator), where the result has the sign of the dividend, of each element of two matrices. |
| Multiply(T, MatrixT) | Multiplies a Matrix by a constant and returns the result. |
| Multiply(MatrixT, T) | Multiplies a Matrix by a constant and returns the result. |
| Multiply(MatrixT, MatrixT) | Multiplies two matrices. |
| Multiply(MatrixT, VectorT) | Multiplies a Matrix and a Vector. |
| Multiply(VectorT, MatrixT) | Multiplies a Vector and a Matrix. |
| Subtraction(T, MatrixT) | Subtracts each element of a matrix from a scalar. |
| Subtraction(MatrixT, T) | Subtracts a scalar from each element of a matrix. |
| Subtraction(MatrixT, MatrixT) | Subtracts two matrices together and returns the results. |
| UnaryNegation(MatrixT) | Negates each element of the matrix. |
| UnaryPlus(MatrixT) | Returns a Matrix containing the same values of rightSide. |
Fields
Extension Methods| Name | Description | |
|---|---|---|
 | AlmostEqualT |
Compares two matrices and determines if they are equal within the specified maximum error.
(Defined by Precision) |
| AlmostEqualT |
Compares two matrices and determines if they are equal to within the specified number
of decimal places or not, using the number of decimal places as an absolute measure.
(Defined by Precision) |
| AlmostEqualRelativeT |
Compares two matrices and determines if they are equal within the specified maximum error.
(Defined by Precision) |
| AlmostEqualRelativeT |
Compares two matrices and determines if they are equal to within the specified number of decimal places or not.
If the numbers are very close to zero an absolute difference is compared, otherwise the relative difference is compared.
(Defined by Precision) |
See Also