FastNonnegativeLeastSquares (FsODE)

FsODE

Documentation for 0.0.2

FastNonnegativeLeastSquares Type

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

Implementation of an algorithm that finds a vector x with all elements xi>=0 which minimizes |X*x-y|.

Literature: Rasmus Bro and Sijmen De Jong, 'A fast non-negativity-constrained least squares algorithm', Journal of Chemometrics, Vol. 11, 393-401 (1997)

Algorithm modified by Dirk Lellinger 2015 to allow a mixture of restricted and unrestricted parameters.

Static members

Static member Description

Static member	Description
`FastNonnegativeLeastSquares.Execution(XtX, Xty, isRestrictedToPositiveValues, tolerance, x, w)` Full Usage: `FastNonnegativeLeastSquares.Execution(XtX, Xty, isRestrictedToPositiveValues, tolerance, x, w)` Parameters: XtX : `IROMatrix<float>` - X transposed multiplied by X, thus a square matrix. Xty : `IROMatrix<float>` - X transposed multiplied by Y, thus a matrix with one column and same number of rows as X. isRestrictedToPositiveValues : `Func<int, bool>` - Function that takes the parameter index as argument and returns true if the parameter at this index is restricted to positive values; otherwise the return value must be false. tolerance : `Nullable<float>` - Used to decide if a solution element is less than or equal to zero. If this is null, a default tolerance of tolerance = MAX(SIZE(XtX)) * NORM(XtX,1) * EPS is used. x : `byref<IMatrix<float>>` - Output: solution vector (matrix with one column and number of rows according to dimension of X. w : `byref<IMatrix<float>>` - Output: Lagrange vector. Elements which take place in the fit are set to 0. Elements fixed to zero contain a negative number.	Execution of the fast nonnegative least squares algorithm. The algorithm finds a vector x with all elements xi>=0 which minimizes \|Xx-y\|. Literature: Rasmus Bro and Sijmen De Jong, 'A fast non-negativity-constrained least squares algorithm', Journal of Chemometrics, Vol. 11, 393-401 (1997) Algorithm modified by Dirk Lellinger 2015 to allow a mixture of restricted and unrestricted parameters. XtX : `IROMatrix<float>` X transposed multiplied by X, thus a square matrix. Xty : `IROMatrix<float>` X transposed multiplied by Y, thus a matrix with one column and same number of rows as X. isRestrictedToPositiveValues : `Func<int, bool>` Function that takes the parameter index as argument and returns true if the parameter at this index is restricted to positive values; otherwise the return value must be false. tolerance : `Nullable<float>` Used to decide if a solution element is less than or equal to zero. If this is null, a default tolerance of tolerance = MAX(SIZE(XtX)) NORM(XtX,1) * EPS is used. x : `byref<IMatrix<float>>` Output: solution vector (matrix with one column and number of rows according to dimension of X. w : `byref<IMatrix<float>>` Output: Lagrange vector. Elements which take place in the fit are set to 0. Elements fixed to zero contain a negative number.
`FastNonnegativeLeastSquares.Execution(XtX, Xty, tolerance, x, w)` Full Usage: `FastNonnegativeLeastSquares.Execution(XtX, Xty, tolerance, x, w)` Parameters: XtX : `IROMatrix<float>` - X transposed multiplied by X, thus a square matrix. Xty : `IROMatrix<float>` - X transposed multiplied by Y, thus a matrix with one column and same number of rows as X. tolerance : `Nullable<float>` - Used to decide if a solution element is less than or equal to zero. If this is null, a default tolerance of tolerance = MAX(SIZE(XtX)) * NORM(XtX,1) * EPS is used. x : `byref<IMatrix<float>>` - Output: solution vector (matrix with one column and number of rows according to dimension of X. w : `byref<IMatrix<float>>` - Output: Lagrange vector. Elements which take place in the fit are set to 0. Elements fixed to zero contain a negative number.	Execution of the fast nonnegative least squares algorithm. The algorithm finds a vector x with all elements xi>=0 which minimizes \|Xx-y\|. Literature: Rasmus Bro and Sijmen De Jong, 'A fast non-negativity-constrained least squares algorithm', Journal of Chemometrics, Vol. 11, 393-401 (1997) Algorithm modified by Dirk Lellinger 2015 to allow a mixture of restricted and unrestricted parameters. XtX : `IROMatrix<float>` X transposed multiplied by X, thus a square matrix. Xty : `IROMatrix<float>` X transposed multiplied by Y, thus a matrix with one column and same number of rows as X. tolerance : `Nullable<float>` Used to decide if a solution element is less than or equal to zero. If this is null, a default tolerance of tolerance = MAX(SIZE(XtX)) NORM(XtX,1) * EPS is used. x : `byref<IMatrix<float>>` Output: solution vector (matrix with one column and number of rows according to dimension of X. w : `byref<IMatrix<float>>` Output: Lagrange vector. Elements which take place in the fit are set to 0. Elements fixed to zero contain a negative number.


                
                  
                    
                      FastNonnegativeLeastSquares.Execution(XtX, Xty, isRestrictedToPositiveValues, tolerance, x, w)

Full Usage: FastNonnegativeLeastSquares.Execution(XtX, Xty, isRestrictedToPositiveValues, tolerance, x, w)

Parameters:

XtX : IROMatrix<float> - X transposed multiplied by X, thus a square matrix.

Xty : IROMatrix<float> - X transposed multiplied by Y, thus a matrix with one column and same number of rows as X.

isRestrictedToPositiveValues : Func<int, bool> - Function that takes the parameter index as argument and returns true if the parameter at this index is restricted to positive values; otherwise the return value must be false.

tolerance : Nullable<float> - Used to decide if a solution element is less than or equal to zero. If this is null, a default tolerance of tolerance = MAX(SIZE(XtX)) * NORM(XtX,1) * EPS is used.

x : byref<IMatrix<float>> - Output: solution vector (matrix with one column and number of rows according to dimension of X.

w : byref<IMatrix<float>> - Output: Lagrange vector. Elements which take place in the fit are set to 0. Elements fixed to zero contain a negative number.

Execution of the fast nonnegative least squares algorithm. The algorithm finds a vector x with all elements xi>=0 which minimizes |X*x-y|.

Literature: Rasmus Bro and Sijmen De Jong, 'A fast non-negativity-constrained least squares algorithm', Journal of Chemometrics, Vol. 11, 393-401 (1997)

Algorithm modified by Dirk Lellinger 2015 to allow a mixture of restricted and unrestricted parameters.

XtX : IROMatrix<float>: X transposed multiplied by X, thus a square matrix.
Xty : IROMatrix<float>: X transposed multiplied by Y, thus a matrix with one column and same number of rows as X.
isRestrictedToPositiveValues : Func<int, bool>: Function that takes the parameter index as argument and returns true if the parameter at this index is restricted to positive values; otherwise the return value must be false.
tolerance : Nullable<float>: Used to decide if a solution element is less than or equal to zero. If this is null, a default tolerance of tolerance = MAX(SIZE(XtX)) * NORM(XtX,1) * EPS is used.
x : byref<IMatrix<float>>: Output: solution vector (matrix with one column and number of rows according to dimension of X.
w : byref<IMatrix<float>>: Output: Lagrange vector. Elements which take place in the fit are set to 0. Elements fixed to zero contain a negative number.


                
                  
                    
                      FastNonnegativeLeastSquares.Execution(XtX, Xty, tolerance, x, w)

Full Usage: FastNonnegativeLeastSquares.Execution(XtX, Xty, tolerance, x, w)

Parameters: