ErrorFunction Type
Hosts the direct and the complementary error function.
Constructors
| Constructor | Description |
Full Usage:
ErrorFunction()
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Static members
| Static member | Description |
Full Usage:
ErrorFunction.Dawson(x)
Parameters:
float
-
The function argument
Returns: float
Dawson's integral for argument x.
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Dawson(x) evaluates Dawson's integral for a double precision real argument x.
2 / x 2
-x | t
F(x) = e | e dt
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/ 0
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Full Usage:
ErrorFunction.Dawson(x, bDebug)
Parameters:
float
-
The function argument
bDebug : bool
-
If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors.
Returns: float
Dawson's integral for argument x.
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Dawson(x) evaluates Dawson's integral for a double precision real argument x.
2 / x 2
-x | t
F(x) = e | e dt
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/ 0
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Full Usage:
ErrorFunction.Erf(x)
Parameters:
float
-
The argument x.
Returns: float
The error function value of the argument x.
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Erf(x) calculates the double precision error function for double precision argument x.
This is a translation from the Fortran version of SLATEC, FNLIB,
CATEGORY C8A, L5A1E, REVISION 920618, originally written by Fullerton W.,(LANL)
to C++.
Series for erf on the interval 0. to 1.00000E+00
with weighted error 1.28E-32
log weighted error 31.89
significant figures required 31.05
decimal places required 32.55
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Full Usage:
ErrorFunction.Erf(x, bDebug)
Parameters:
float
-
The argument x.
bDebug : bool
-
If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors.
Returns: float
The error function value of the argument x.
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Erf(x) calculates the double precision error function for double precision argument x.
This is a translation from the Fortran version of SLATEC, FNLIB,
CATEGORY C8A, L5A1E, REVISION 920618, originally written by Fullerton W.,(LANL)
to C++.
Series for erf on the interval 0. to 1.00000E+00
with weighted error 1.28E-32
log weighted error 31.89
significant figures required 31.05
decimal places required 32.55
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Full Usage:
ErrorFunction.Erfc(x)
Parameters:
float
-
The argument x.
Returns: float
The complementary error function of the argument x.
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Erfc(x) calculates the double precision complementary error function for double precision argument x.
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Full Usage:
ErrorFunction.Erfc(x, bDebug)
Parameters:
float
-
The argument x.
bDebug : bool
-
If true, an exception is thrown if serious errors occur. If false, NaN is returned on errors.
Returns: float
The complementary error function of the argument x.
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Erfc(x) calculates the double precision complementary error function for double precision argument x.
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Given a complex number z = (x,y), this subroutine computes the value of the Faddeeva function w(z) = exp(-z^2)*erfc(-i*z), where erfc is the complex complementary error function and i means sqrt(-1).
The accuracy of the algorithm for z in the 1st and 2nd quadrant
is 14 significant digits; in the 3rd and 4th it is 13 significant
digits outside a circular region with radius 0.126 around a zero
of the function.
All real variables in the program are double precision.
The parameter M_2_SQRTPI equals 2/sqrt(pi).
The routine is not underflow-protected but any variable can be
put to 0 upon underflow;
The routine is overflow-protected: Matpack::Error() is called.
References:
(1) G.P.M. Poppe, C.M.J. Wijers; More Efficient Computation of
the Complex Error-Function, ACM Trans. Math. Software,
Vol. 16, no. 1, pp. 47.
(2) Algorithm 680, collected algorithms from ACM.
The Fortran source code was translated to C++ by B.M. Gammel
and added to the Matpack library, 1992.
Last change: B. M. Gammel, 18.03.1996 error handling
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Given a complex number z = (x,y), this subroutine computes the value of the Faddeeva function w(z) = exp(-z^2)*erfc(-i*z), where erfc is the complex complementary error function and i means sqrt(-1).
The accuracy of the algorithm for z in the 1st and 2nd quadrant
is 14 significant digits; in the 3rd and 4th it is 13 significant
digits outside a circular region with radius 0.126 around a zero
of the function.
All real variables in the program are double precision.
The parameter M_2_SQRTPI equals 2/sqrt(pi).
The routine is not underflow-protected but any variable can be
put to 0 upon underflow;
The routine is overflow-protected: Matpack::Error() is called.
References:
(1) G.P.M. Poppe, C.M.J. Wijers; More Efficient Computation of
the Complex Error-Function, ACM Trans. Math. Software,
Vol. 16, no. 1, pp. 47.
(2) Algorithm 680, collected algorithms from ACM.
The Fortran source code was translated to C++ by B.M. Gammel
and added to the Matpack library, 1992.
Last change: B. M. Gammel, 18.03.1996 error handling
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Full Usage:
ErrorFunction.InverseErf(y)
Parameters:
float
-
Argument.
Returns: float
A value x so that Erf(x)==y.
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Inverse of the error function Erf(x).
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Full Usage:
ErrorFunction.QuantileOfNormalDistribution01(y)
Parameters:
float
-
Returns: float
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Quantile of the normal distribution function NormalDistribution[0,1].
Adopted from Cephes library; Cephes name: ndtri
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