MatrixMath (FsODE)

FsODE

Documentation for 0.0.2

MatrixMath Type

Namespace: Altaxo.Calc.LinearAlgebra
Assembly: AltaxoCore.Redist.dll
Base Type: obj

Class MatrixMath provides common static methods for matrix manipulation and arithmetic in tow dimensions. Class MatrixMath provides common static methods for matrix manipulation and arithmetic in tow dimensions.

Static members

Static member	Description
`MatrixMath.Add(a, b, c)` Full Usage: `MatrixMath.Add(a, b, c)` Parameters: a : `IROMatrix<float>` - First matrix to add.. b : `IROMatrix<float>` - Second operand.. c : `IMatrix<float>` - The resultant matrix a+b. Has to be of same dimension as a and b.	Calculates a+b and stores the result in matrix c. a : `IROMatrix<float>` First matrix to add.. b : `IROMatrix<float>` Second operand.. c : `IMatrix<float>` The resultant matrix a+b. Has to be of same dimension as a and b.
`MatrixMath.AddRow(a, b, c)` Full Usage: `MatrixMath.AddRow(a, b, c)` Parameters: a : `IROMatrix<float>` - The source matrix. b : `IReadOnlyList<float>` - The vector to add. c : `IMatrix<float>` - The destination matrix. Can be equivalent to matrix a (but not to vector b).	Add the vector `b` to all rows of matrix a. a : `IROMatrix<float>` The source matrix. b : `IReadOnlyList<float>` The vector to add. c : `IMatrix<float>` The destination matrix. Can be equivalent to matrix a (but not to vector b).
`MatrixMath.AddRow(a, b, brow, c)` Full Usage: `MatrixMath.AddRow(a, b, brow, c)` Parameters: a : `IROMatrix<float>` - The source matrix. b : `IROMatrix<float>` - The matrix which contains the row to add. brow : `int` - The row number of matrix b. c : `IMatrix<float>` - The destination matrix. Can be equivalent to matrix a (but not to matrix b).	Add the row `rowb` of matrix b to all rows of matrix a. a : `IROMatrix<float>` The source matrix. b : `IROMatrix<float>` The matrix which contains the row to add. brow : `int` The row number of matrix b. c : `IMatrix<float>` The destination matrix. Can be equivalent to matrix a (but not to matrix b).
`MatrixMath.Any(a, predicate)` Full Usage: `MatrixMath.Any(a, predicate)` Parameters: a : `IROMatrix<float>` - The matrix. predicate : `Func<int, int, float, bool>` - The predicate to fulfill. 1st argument is the row number, 2nd arg is the column number, 3rd arg is the element value at row and column. The return value is the predicate. Returns: `bool` True if any element of the provided matrix a fulfills the given predicate; otherwise false.	Determines whether any element of the provided matrix a fulfills the given predicate. a : `IROMatrix<float>` The matrix. predicate : `Func<int, int, float, bool>` The predicate to fulfill. 1st argument is the row number, 2nd arg is the column number, 3rd arg is the element value at row and column. The return value is the predicate. Returns: `bool` True if any element of the provided matrix a fulfills the given predicate; otherwise false.
`MatrixMath.Clear(matrix)` Full Usage: `MatrixMath.Clear(matrix)` Parameters: matrix : `IMatrix<'T>`	matrix : `IMatrix<'T>`
`MatrixMath.Clear_DefaultImpl(matrix)` Full Usage: `MatrixMath.Clear_DefaultImpl(matrix)` Parameters: matrix : `IMatrix<'T>`	matrix : `IMatrix<'T>`
`MatrixMath.ColumnToROVector(x, column)` Full Usage: `MatrixMath.ColumnToROVector(x, column)` Parameters: x : `IROMatrix<'T>` - The matrix. column : `int` - The column number of the matrix that is wrapped to a vector. Returns: `IROVector<'T>`	Returns a read-only vector representing a matrix column by providing the matrix and the row number of that matrix that is wrapped. x : `IROMatrix<'T>` The matrix. column : `int` The column number of the matrix that is wrapped to a vector. Returns: `IROVector<'T>`
`MatrixMath.ColumnToVector(x, column)` Full Usage: `MatrixMath.ColumnToVector(x, column)` Parameters: x : `IMatrix<'T>` - The matrix. column : `int` - The column number of the matrix that is wrapped to a vector. Returns: `IVector<'T>`	Returns a vector representing a matrix column by providing the matrix and the row number of that matrix that is wrapped. x : `IMatrix<'T>` The matrix. column : `int` The column number of the matrix that is wrapped to a vector. Returns: `IVector<'T>`
`MatrixMath.ColumnsToZeroMean(a, mean)` Full Usage: `MatrixMath.ColumnsToZeroMean(a, mean)` Parameters: a : `IMatrix<float>` - The matrix where the columns should be centered. mean : `IVector<float>` - You can provide a matrix of dimension(1,a.Cols) where the mean row vector is stored, or null if not interested in this vector.	This will center the matrix so that the mean of each column is null. Calling this function will change the matrix a to a column centered matrix. The original matrix data are lost. a : `IMatrix<float>` The matrix where the columns should be centered. mean : `IVector<float>` You can provide a matrix of dimension(1,a.Cols) where the mean row vector is stored, or null if not interested in this vector.
`MatrixMath.ColumnsToZeroMeanAndUnitVariance(a, meanvec, scalevec)` Full Usage: `MatrixMath.ColumnsToZeroMeanAndUnitVariance(a, meanvec, scalevec)` Parameters: a : `IMatrix<float>` - The matrix where the columns should be centered and normalized to standard variance. meanvec : `IVector<float>` - You can provide a vector of length(a.Cols) where the mean row vector is stored, or null if not interested in this vector. scalevec : `IVector<float>` - You can provide a vector of length(a.Cols) where the inverse of the variance of the columns is stored, or null if not interested in this vector.	This will center the matrix so that the mean of each column is null, and the variance of each column is one. Calling this function will change the matrix a to a column centered matrix. The original matrix data are lost. a : `IMatrix<float>` The matrix where the columns should be centered and normalized to standard variance. meanvec : `IVector<float>` You can provide a vector of length(a.Cols) where the mean row vector is stored, or null if not interested in this vector. scalevec : `IVector<float>` You can provide a vector of length(a.Cols) where the inverse of the variance of the columns is stored, or null if not interested in this vector.
`MatrixMath.Copy(src, dest)` Full Usage: `MatrixMath.Copy(src, dest)` Parameters: src : `IROMatrix<float>` - The source matrix to copy. dest : `IMatrix<float>` - The destination matrix to copy to.	Copies matrix src to matrix dest. Both matrizes must have the same dimensions. src : `IROMatrix<float>` The source matrix to copy. dest : `IMatrix<float>` The destination matrix to copy to.
`MatrixMath.Copy(src, dest, destrow, destcol)` Full Usage: `MatrixMath.Copy(src, dest, destrow, destcol)` Parameters: src : `IROMatrix<float>` - The source matrix. dest : `IMatrix<float>` - The destination matrix. Must have equal or higher dim than the source matrix. destrow : `int` - The vertical origin of copy operation in the destination matrix. destcol : `int` - The horizontal origin of copy operation in the destination matrix.	Copies the matrix src into the matrix dest. Matrix dest must have equal or greater dimension than src. You can provide a destination row/column into the destination matrix where the origin of the copy operation is located. src : `IROMatrix<float>` The source matrix. dest : `IMatrix<float>` The destination matrix. Must have equal or higher dim than the source matrix. destrow : `int` The vertical origin of copy operation in the destination matrix. destcol : `int` The horizontal origin of copy operation in the destination matrix.
`MatrixMath.CopyColumn(sourceMatrix, columnNumber, destinationVector)` Full Usage: `MatrixMath.CopyColumn(sourceMatrix, columnNumber, destinationVector)` Parameters: sourceMatrix : `IROMatrix<float>` - Matrix to copy from columnNumber : `int` - Number of column of the matrix to be copied. destinationVector : `float[]` - Vector to copy the column data to.	Gets the column of a matrix copied into a vector. sourceMatrix : `IROMatrix<float>` Matrix to copy from columnNumber : `int` Number of column of the matrix to be copied. destinationVector : `float[]` Vector to copy the column data to.
`MatrixMath.CopyColumn(sourceMatrix, columnNumber, destinationVector)` Full Usage: `MatrixMath.CopyColumn(sourceMatrix, columnNumber, destinationVector)` Parameters: sourceMatrix : `IROMatrix<float>` - Matrix to copy from columnNumber : `int` - Number of column of the matrix to be copied. destinationVector : `IVector<float>` - Vector to copy the column data to.	Gets the column of a matrix copied into a vector. sourceMatrix : `IROMatrix<float>` Matrix to copy from columnNumber : `int` Number of column of the matrix to be copied. destinationVector : `IVector<float>` Vector to copy the column data to.
`MatrixMath.DivideRow(a, b, brow, resultIfNull, c)` Full Usage: `MatrixMath.DivideRow(a, b, brow, resultIfNull, c)` Parameters: a : `IROMatrix<float>` - The source matrix. b : `IROMatrix<float>` - The matrix which contains the denominator row. brow : `int` - The row number of matrix b which serves as denominator. resultIfNull : `float` - If the denominator is null, the result is set to this number. c : `IMatrix<float>` - The destination matrix. Can be equivalent to matrix a (but not to matrix b).	Divides all rows of matrix a by the row `rowb` of matrix b (element by element). a : `IROMatrix<float>` The source matrix. b : `IROMatrix<float>` The matrix which contains the denominator row. brow : `int` The row number of matrix b which serves as denominator. resultIfNull : `float` If the denominator is null, the result is set to this number. c : `IMatrix<float>` The destination matrix. Can be equivalent to matrix a (but not to matrix b).
`MatrixMath.EnumerateElementsIndexed(matrix, ?zeros)` Full Usage: `MatrixMath.EnumerateElementsIndexed(matrix, ?zeros)` Parameters: matrix : `IROMatrix<'T>` ?zeros : `Zeros` Returns: `IEnumerable<int * int * 'T>`	matrix : `IROMatrix<'T>` ?zeros : `Zeros` Returns: `IEnumerable<int * int * 'T>`
`MatrixMath.GetMatrixArray(n, m)` Full Usage: `MatrixMath.GetMatrixArray(n, m)` Parameters: n : `int` - First matrix dimension. m : `int` - Second matrix dimension. Returns: `float[][]` Array of dimensions n x m.	Allocates an array of n x m values. n : `int` First matrix dimension. m : `int` Second matrix dimension. Returns: `float[][]` Array of dimensions n x m.
`MatrixMath.GetSingularValueDecomposition(input, output)` Full Usage: `MatrixMath.GetSingularValueDecomposition(input, output)` Parameters: input : `IROMatrix<float>` - The input matrix (is preserved). output : `IMatrix<float>` - The resulting matrix. Has to be of same dimensions as the input matrix. Returns: `SingularValueDecomposition`	Returns the singular value decomposition for this matrix. input : `IROMatrix<float>` The input matrix (is preserved). output : `IMatrix<float>` The resulting matrix. Has to be of same dimensions as the input matrix. Returns: `SingularValueDecomposition`
`MatrixMath.GetSingularValueDecomposition(inout)` Full Usage: `MatrixMath.GetSingularValueDecomposition(inout)` Parameters: inout : `IMatrix<float>` - The input matrix, on return the resulting decomposed matrix. Returns: `SingularValueDecomposition`	Returns the singular value decomposition for this matrix. inout : `IMatrix<float>` The input matrix, on return the resulting decomposed matrix. Returns: `SingularValueDecomposition`
`MatrixMath.Hypotenuse(a, b)` Full Usage: `MatrixMath.Hypotenuse(a, b)` Parameters: a : `float` - First parameter. b : `float` - Second parameter. Returns: `float` The square root of (a^2+b^2).	Calculates the hypotenuse length of a and b, i.e. the sqrt(a^2+b^2), avoiding overflow at large values. a : `float` First parameter. b : `float` Second parameter. Returns: `float` The square root of (a^2+b^2).
`MatrixMath.InvertDiagonalMatrix(a)` Full Usage: `MatrixMath.InvertDiagonalMatrix(a)` Parameters: a : `IMatrix<float>` - The matrix to invert. After calling the matrix is inverted, i.e. the diagonal elements are replaced by their inverses, and the outer diagonal elements are set to zero.	This inverts the provided diagonal matrix. There is no check that the matrix is really diagonal, but the algorithm sets the elements outside the diagonal to zero, assuming that this are small arithmetic errors. a : `IMatrix<float>` The matrix to invert. After calling the matrix is inverted, i.e. the diagonal elements are replaced by their inverses, and the outer diagonal elements are set to zero.
`MatrixMath.IsEqual(a, b, accuracy)` Full Usage: `MatrixMath.IsEqual(a, b, accuracy)` Parameters: a : `IROMatrix<float>` - The first matrix. b : `IROMatrix<float>` - The second matrix. Basis for calculation of threshold. accuracy : `float` - The accuracy. Returns: `bool`	Compares matrix a and matrix b. Takes the norm of matrix b times accuracy as threshold basis for comparing the elements. a : `IROMatrix<float>` The first matrix. b : `IROMatrix<float>` The second matrix. Basis for calculation of threshold. accuracy : `float` The accuracy. Returns: `bool`
`MatrixMath.IsZeroMatrix(a)` Full Usage: `MatrixMath.IsZeroMatrix(a)` Parameters: a : `IROMatrix<float>` - The matrix to test. Returns: `bool` True if all elements are zero or if one of the two dimensions of the matrix is zero. False if the matrix contains nonzero elements.	Tests if all elements of the matrix a are equal to zero. a : `IROMatrix<float>` The matrix to test. Returns: `bool` True if all elements are zero or if one of the two dimensions of the matrix is zero. False if the matrix contains nonzero elements.
`MatrixMath.LengthOf(a)` Full Usage: `MatrixMath.LengthOf(a)` Parameters: a : `IROMatrix<float>` - The matrix. Returns: `float` The square root of the sum of the squares of the matrix a.	Returns the square root of the sum of the squares of the matrix a. a : `IROMatrix<float>` The matrix. Returns: `float` The square root of the sum of the squares of the matrix a.
`MatrixMath.Map(src1, function, result)` Full Usage: `MatrixMath.Map(src1, function, result)` Parameters: src1 : `IROMatrix<float>` - Matrix to use the values from. function : `Func<float, float>` - Function to be applied to each element of the matrix. The argument is the element of the source matrix. result : `IMatrix<float>` - Matrix to store the result. This may be the same instance as the source matrix.	Elementwise application of a function to each element of a matrix. The result is stored in another matrix or in the same matrix. src1 : `IROMatrix<float>` Matrix to use the values from. function : `Func<float, float>` Function to be applied to each element of the matrix. The argument is the element of the source matrix. result : `IMatrix<float>` Matrix to store the result. This may be the same instance as the source matrix.
`MatrixMath.Map(src1, src2, function, result)` Full Usage: `MatrixMath.Map(src1, src2, function, result)` Parameters: src1 : `IROMatrix<float>` - First matrix to use the values from. src2 : `IROMatrix<float>` - Second matrix to use the values from. function : `Func<float, float, float>` - Function to be applied to each element of src1 and src2. result : `IMatrix<float>` - Matrix to store the result. This may be the same instance as one of the matrices src1 or src2.	Elementwise application of a function to each element of two matrices. The result is stored in another matrix or in the same matrix. src1 : `IROMatrix<float>` First matrix to use the values from. src2 : `IROMatrix<float>` Second matrix to use the values from. function : `Func<float, float, float>` Function to be applied to each element of src1 and src2. result : `IMatrix<float>` Matrix to store the result. This may be the same instance as one of the matrices src1 or src2.
`MatrixMath.MapIndexed(src1, parameter1, function, result, ?zeros)` Full Usage: `MatrixMath.MapIndexed(src1, parameter1, function, result, ?zeros)` Parameters: src1 : `IROMatrix<'T>` parameter1 : `'T1` function : `Func<int, int, 'T, 'T1, 'T>` result : `IMatrix<'T>` ?zeros : `Zeros`	src1 : `IROMatrix<'T>` parameter1 : `'T1` function : `Func<int, int, 'T, 'T1, 'T>` result : `IMatrix<'T>` ?zeros : `Zeros`
`MatrixMath.MapIndexed(src1, function, result)` Full Usage: `MatrixMath.MapIndexed(src1, function, result)` Parameters: src1 : `IROMatrix<float>` - Matrix to use the values from. function : `Func<int, int, float, float>` - Function to be applied to each element of the matrix. 1st argument is the row number, 2nd argument the column number, 3rd argument the element of the src matrix,. result : `IMatrix<float>` - Matrix to store the result. This may be the same instance as the source matrix.	Elementwise application of a function to each element of a matrix. The result is stored in another matrix or in the same matrix. src1 : `IROMatrix<float>` Matrix to use the values from. function : `Func<int, int, float, float>` Function to be applied to each element of the matrix. 1st argument is the row number, 2nd argument the column number, 3rd argument the element of the src matrix,. result : `IMatrix<float>` Matrix to store the result. This may be the same instance as the source matrix.
`MatrixMath.MapIndexed(src1, src2, function, result)` Full Usage: `MatrixMath.MapIndexed(src1, src2, function, result)` Parameters: src1 : `IROMatrix<float>` - First matrix to use the values from. src2 : `IROMatrix<float>` - Second matrix to use the values from. function : `Func<int, int, float, float, float>` - Function to be applied to each element of src1 and src2. 1st argument is the row number, 2nd argument is the column number, 3rd argument is the element of matrix src1, 4th argument is the element of matrix src2. result : `IMatrix<float>` - Matrix to store the result. This may be the same instance as one of the matrices src1 or src2.	Elementwise application of a function to each element of two matrices. The result is stored in another matrix or in the same matrix. src1 : `IROMatrix<float>` First matrix to use the values from. src2 : `IROMatrix<float>` Second matrix to use the values from. function : `Func<int, int, float, float, float>` Function to be applied to each element of src1 and src2. 1st argument is the row number, 2nd argument is the column number, 3rd argument is the element of matrix src1, 4th argument is the element of matrix src2. result : `IMatrix<float>` Matrix to store the result. This may be the same instance as one of the matrices src1 or src2.
`MatrixMath.MapIndexed(src1, parameter1, function, result)` Full Usage: `MatrixMath.MapIndexed(src1, parameter1, function, result)` Parameters: src1 : `IROMatrix<float>` - Matrix to use the values from. parameter1 : `'T1` - An auxillary parameter. function : `Func<int, int, float, 'T1, float>` - Function to be applied to each element of the matrix. 1st argument is the row number, 2nd argument the column number, 3rd argument the element of the src matrix, 4th argument the auxillary parameter1. result : `IMatrix<float>` - Matrix to store the result. This may be the same instance as the source matrix.	Elementwise application of a function to each element of a matrix. The result is stored in another matrix or in the same matrix. src1 : `IROMatrix<float>` Matrix to use the values from. parameter1 : `'T1` An auxillary parameter. function : `Func<int, int, float, 'T1, float>` Function to be applied to each element of the matrix. 1st argument is the row number, 2nd argument the column number, 3rd argument the element of the src matrix, 4th argument the auxillary parameter1. result : `IMatrix<float>` Matrix to store the result. This may be the same instance as the source matrix.
`MatrixMath.MatrixToString(name, a)` Full Usage: `MatrixMath.MatrixToString(name, a)` Parameters: name : `string` a : `IROMatrix<'T>` Returns: `string`	name : `string` a : `IROMatrix<'T>` Returns: `string`
`MatrixMath.MatrixToString(name, a)` Full Usage: `MatrixMath.MatrixToString(name, a)` Parameters: name : `string` a : `IROMatrix<float32>` Returns: `string`	name : `string` a : `IROMatrix<float32>` Returns: `string`
`MatrixMath.MatrixToString(name, a)` Full Usage: `MatrixMath.MatrixToString(name, a)` Parameters: name : `string` a : `IROComplexDoubleMatrix` Returns: `string`	name : `string` a : `IROComplexDoubleMatrix` Returns: `string`
`MatrixMath.MatrixToString(name, a)` Full Usage: `MatrixMath.MatrixToString(name, a)` Parameters: name : `string` a : `IROComplexFloatMatrix` Returns: `string`	name : `string` a : `IROComplexFloatMatrix` Returns: `string`
`MatrixMath.Max(a)` Full Usage: `MatrixMath.Max(a)` Parameters: a : `IROMatrix<float>` - The matrix. Returns: `float` Maximum value of all elements of the specified matrix a.	Get the maximum value of all elements of the specified matrix a. a : `IROMatrix<float>` The matrix. Returns: `float` Maximum value of all elements of the specified matrix a.
`MatrixMath.Min(a)` Full Usage: `MatrixMath.Min(a)` Parameters: a : `IROMatrix<float>` - The matrix. Returns: `float` Minimum value of all elements of the specified matrix a.	Get the minimum value of all elements of the specified matrix a. a : `IROMatrix<float>` The matrix. Returns: `float` Minimum value of all elements of the specified matrix a.
`MatrixMath.Multiply(a, b, c)` Full Usage: `MatrixMath.Multiply(a, b, c)` Parameters: a : `IROMatrix<float>` - First multiplicant. b : `IROMatrix<float>` - Second multiplicant. c : `IMatrix<float>` - The matrix where to store the result. Has to be of dimension (a.Rows, b.Columns).	Multiplies matrix a with matrix b and stores the result in matrix c. a : `IROMatrix<float>` First multiplicant. b : `IROMatrix<float>` Second multiplicant. c : `IMatrix<float>` The matrix where to store the result. Has to be of dimension (a.Rows, b.Columns).
`MatrixMath.Multiply(a, b, c)` Full Usage: `MatrixMath.Multiply(a, b, c)` Parameters: a : `IROMatrix<float>` - First multiplicant. b : `IReadOnlyList<float>` - Second multiplicant. The vector must have the length of a.Columns. c : `IVector<float>` - The vector where to store the result. Has to be of dimension (a.Rows).	Multiplies matrix a with vector b and stores the result in vector c. a : `IROMatrix<float>` First multiplicant. b : `IReadOnlyList<float>` Second multiplicant. The vector must have the length of a.Columns. c : `IVector<float>` The vector where to store the result. Has to be of dimension (a.Rows).
`MatrixMath.MultiplyFirstTransposed(a, b, c)` Full Usage: `MatrixMath.MultiplyFirstTransposed(a, b, c)` Parameters: a : `IROMatrix<float>` - First multiplicant. b : `IROMatrix<float>` - Second multiplicant. c : `IMatrix<float>` - The matrix where to store the result. Has to be of dimension (a.Rows, b.Columns).	Multiplies matrix a_transposed with matrix b and stores the result in matrix c. a : `IROMatrix<float>` First multiplicant. b : `IROMatrix<float>` Second multiplicant. c : `IMatrix<float>` The matrix where to store the result. Has to be of dimension (a.Rows, b.Columns).