Series (FsODE)

FsODE

Documentation for 0.0.2

Series Type

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

Contains series calculations.

Constructors

Constructor	Description
`Series()` Full Usage: `Series()`

Static members

Static member Description

Static member	Description
`Series.dcsevl (x, cs, n)` Full Usage: `Series.dcsevl (x, cs, n)` Parameters: x : `float` - Value at which the series is to be evaluated. cs : `float[]` - cs array of n terms of a Chebyshev series. In evaluating cs, only half the first coefficient is summed. n : `int` - number of terms in array cs. Returns: `float` The n-term Chebyshev series cs at x.	Evaluate the n-term Chebyshev series cs at x. Adapted from a method presented in the paper by Broucke referenced below. References: R. Broucke, Ten subroutines for the manipulation of Chebyshev series, Algorithm 446, Communications of the A.C.M. 16, (1973) pp. 254-256. L. Fox and I. B. Parker, Chebyshev Polynomials in Numerical Analysis, Oxford University Press, 1968, page 56. This is a translation from the Fortran version of SLATEC, FNLIB, CATEGORY C3A2, REVISION 920501, originally written by Fullerton W., (LANL) to C++. x : `float` Value at which the series is to be evaluated. cs : `float[]` cs array of n terms of a Chebyshev series. In evaluating cs, only half the first coefficient is summed. n : `int` number of terms in array cs. Returns: `float` The n-term Chebyshev series cs at x.
`Series.initds (os, nos, eta)` Full Usage: `Series.initds (os, nos, eta)` Parameters: os : `float[]` - Double precision array of NOS coefficients in an orthogonal series. nos : `int` - Number of coefficients in OS. eta : `float` - single precision scalar containing requested accuracy of series. Returns: `int` The number of terms neccessary to insure the error is not larger than eta.	Initialize the orthogonal series, represented by the array os, so that initds is the number of terms needed to insure the error is no larger than eta. Ordinarily, eta will be chosen to be one-tenth machine precision. This is a translation from the Fortran version of SLATEC, FNLIB, CATEGORY C3A2, REVISION 900315, originally written by Fullerton W., (LANL) to C++. os : `float[]` Double precision array of NOS coefficients in an orthogonal series. nos : `int` Number of coefficients in OS. eta : `float` single precision scalar containing requested accuracy of series. Returns: `int` The number of terms neccessary to insure the error is not larger than eta.


                
                  
                    
                      Series.dcsevl (x, cs, n)

Full Usage: Series.dcsevl (x, cs, n)

Parameters:

x : float - Value at which the series is to be evaluated.

cs : float[] - cs array of n terms of a Chebyshev series. In evaluating cs, only half the first coefficient is summed.

n : int - number of terms in array cs.

Returns: float The n-term Chebyshev series cs at x.

Evaluate the n-term Chebyshev series cs at x. Adapted from a method presented in the paper by Broucke referenced below.

References: R. Broucke, Ten subroutines for the manipulation of Chebyshev series, Algorithm 446, Communications of the A.C.M. 16, (1973) pp. 254-256. L. Fox and I. B. Parker, Chebyshev Polynomials in Numerical Analysis, Oxford University Press, 1968, page 56. This is a translation from the Fortran version of SLATEC, FNLIB, CATEGORY C3A2, REVISION 920501, originally written by Fullerton W., (LANL) to C++.

x : float: Value at which the series is to be evaluated.
cs : float[]: cs array of n terms of a Chebyshev series. In evaluating cs, only half the first coefficient is summed.
n : int: number of terms in array cs.

Returns: float: The n-term Chebyshev series cs at x.


                
                  
                    
                      Series.initds (os, nos, eta)

Full Usage: Series.initds (os, nos, eta)

Parameters:

os : float[] - Double precision array of NOS coefficients in an orthogonal series.

nos : int - Number of coefficients in OS.

eta : float - single precision scalar containing requested accuracy of series.

Returns: int The number of terms neccessary to insure the error is not larger than eta.

Initialize the orthogonal series, represented by the array os, so that initds is the number of terms needed to insure the error is no larger than eta. Ordinarily, eta will be chosen to be one-tenth machine precision.

This is a translation from the Fortran version of SLATEC, FNLIB, CATEGORY C3A2, REVISION 900315, originally written by Fullerton W., (LANL) to C++.

os : float[]: Double precision array of NOS coefficients in an orthogonal series.
nos : int: Number of coefficients in OS.
eta : float: single precision scalar containing requested accuracy of series.

Returns: int: The number of terms neccessary to insure the error is not larger than eta.