fisx
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Common fluorescence spectroscopy math functions. More...
#include <fisx_math.h>
Static Public Member Functions | |
static double | E1 (const double &x) |
static double | En (const int &n, const double &x) |
static double | deBoerD (const double &x) |
static double | deBoerL0 (const double &mu1, const double &mu2, const double &muj, const double &density, const double &thickness) |
static double | deBoerX (const double &p, const double &q, const double &d1, const double &d2, const double &mu_1_j, const double &mu_2_j, const double &mu_b_j_d_t=0.0) |
static double | deBoerV (const double &p, const double &q, const double &d1, const double &d2, const double &mu_1_j, const double &mu_2_j, const double &mu_b_j_d_t) |
static bool | isNumber (const double &x) |
static bool | isFiniteNumber (const double &x) |
static double | deBoerY (const double &a, const double &b, const double &c, const double &d) |
static double | deBoerW (const double &a, const double &b, const double &d) |
static double | AS_5_1_53 (const double &x) |
static double | AS_5_1_56 (const double &x) |
static double | getFWHM (const double &energy, const double &noise, const double &fano, const double &quantumEnergy=0.00385) |
static double | erf (const double &x) |
static double | erfc (const double &x) |
Common fluorescence spectroscopy math functions.
De Boer Formulae for secondary excitation corrections
This class implements the formulae contained in the article: D.K.G. de Boer, X-Ray Spectrometry, Vol. 19, (1990) 145 - 154.
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Abramowitz and Stegun formula 5.1.53 Returns E1(x) + log(x) Formula is valid for 0 <= x <= 1
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Abramowitz and Stegun formula 5.1.56 Returns x * exp(x) * E1(x) Formula is valid for 1 <= x < +inf
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Calculates exp(x) * E1(x) Used in D.K.G. de Boer, X-Ray Spectrometry, Vol. 19, (1990) 145 - 154 and needed to calculate secondary excitation.
Implemented following Abramowitz and Stegun
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Calculates the integral part of expression 6 of the article D.K.G. de Boer, X-Ray Spectrometry, Vol. 19, (1990) 145 - 154 and needed to calculate secondary excitation. muj is the matrix mass attenuation coefficient at the matrix emitted line j mui is the matrix mass attenuation coefficient at the fluorescent line i mul is the matrix mass attenuation coefficient at the incident energy
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Help function, see formula A2b appendix
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For multilayers p and q following article d1 is the product density * thickness of fluorescing layer d2 is the product density * thickness of layer j originating the secondary excitation mu_1_j is the mass attenuation coefficient of fluorescing layer at j excitation energy mu_2_j is the mass attenuation coefficient of layer j at j excitation energy mu_b_d_t is the sum of the products mu * density * thickness of layers between layer i and j
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Help function, see formula A2a appendix
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Calculate the exponential integral of order 1 on x.
|inf | dy
E1(x) = | exp(y) -— |x y
Only the real part is calculated
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Calculate the exponential integral of order n on x
|inf | dy
En(x) = | exp(y) -— |x y^n
Only the real part is calculated
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Error function
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Complementary error function
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Get FWHM from energy, noise, fano and average energy needed to create a signal
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Returns false is x is NaN or an infinite number
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Returns false is x is NaN