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--- seminar:plot_curvefit [2019/10/10 13:00] – [Special Functions] kimi
+++ seminar:plot_curvefit [2022/08/23 13:34] (現在) – 外部編集 127.0.0.1
@@ 行 33: / 行 33: @@
 $$
-R.M.S.D. =\sqrt{\sum_i}
+R.M.S.D. =\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left\{y_i-f(x_i)\right\}^2}
 $$
 Chi²:
@@ 行 57: / 行 57: @@
 column in a previous row
 Examples: 284 1234~ 10.7~0.2 1-2.3 5*0.12
+Plot functions which allow mathematical expressions supports the following functions:
+|''+, -, *, /''|	arithmetic operations|
+%, mod	modulo
+( )	grouping
+^, **	power
+rad(x), deg(x)	conversion between radians and degrees
+sin(x),cos(x),tan(x)	trigonometric functions
+asin(x),acos(x),atan(x)	inverse trigonometric functions
+sinh(x),cosh(x),tanh(x)	hyperbolic functions
+rnd(h)	random number (h = height)
+ln(x),log(x)	natural and logarithm to base 10
+sqrt(x)	square root
+cbrt(x)	cubic root
+frac(x)	returns the fraction of x
+int(x)	returns the integer of x
+round(x;n)	round up and down to the nth place on the right of the decimal point
+gau(x;x0;a;w)	Gauss (x0 = position, a = amplitude, w = width)
+lor(x;x0;a;w)	Lorentz (x0 = position, a = amplitude, w = width)
+galo(x;x0;a;w;r)	Gauss-Lorentz (x0 = position, a = amplitude, w = width, r =Gauss-Lorentz ratio (1.0=pure Gauss,0.0 = pure Lorentz))
+tail(x;x0;a;w;r;t)	Gauss-Lorentz with exponential Tail (x0 = position, a = amplitude, w = width, r = Gauss-Lorentz ratio(1.0=pure Gauss,0.0 = pure Lorentz)), t = tail exponent factor
+j0(x), j1(x), jn(x;n)	bessel functions
+y0(x), y1(x), yn(x;n)	bessel functions
+pi	3.14159265359
+e	2.71828182846
+xval(b;i)	x value of point i in buffer b
+yval(b;i)	y value of point i in buffer b
+xerr(b;i)	x error value of point i in buffer b
+yerr(b;i)	y error value of point i in buffer b
+xnval(b;i)	normalized x value (0.0-1.0) of point i in buffer b
+ynval(b;i)	normalized y value (0.0-1.0) of point i in buffer b
+xnerr(b;i)	normalized x error value (0.0-1.0) of point i in buffer b
+ynerr(b;i)	normalized y error value (0.0-1.0) of point i in buffer b
+xvf(b)	x value of the first point in buffer b
+xvl(b)	x value of the last point in buffer b
+yvf(b)	y value of the first point in buffer b
+yvl(b)	y value of the last point in buffer b
+xmin(b)	minimum x value in buffer b
+xmax(b)	maximum x value in buffer b
+ymin(b)	minimum y value in buffer b
+ymax(b)	maximum y value in buffer b
+exmin(b)	minimum x error value in buffer b
+exmax(b)	maximum x error value in buffer b
+eymin(b)	minimum y error value in buffer b
+eymax(b)	maximum y error value in buffer b
+txmin	minimum x value over all buffers
+txmax	maximum x value over all buffers
+tymin	minimum y value over all buffers
+tymax	maximum y value over all buffers
+vxmin(b)	minimum x value over all visible buffer
+vxmax(b)	maximum x value over all visible buffer
+vymin(b)	minimum y value over all visible buffer
+vymax(b)	maximum y value over all visible buffer
+points(b)	number of points in buffer b
+xpoint(v;a)	x screen coordinate of v (a can be 1 for the first or 2 for the second axis).
+xvalue(v;a)	x value of the screen coordinate v (a can be 1 for the first or 2 for the second axis).
+ypoint(v;a)	y screen coordinate of v (a can be 1 for the first or 2 for the second axis).
+yvalue(v;a)	y value of the screen coordinate v (a can be 1 for the first or 2 for the second axis).
+findx(v;b)	x value which depends to y in buffer b. If there are more than one it returns the first it found.
+findy(v;b)	y value which depends to x in buffer b. If there are more than one it returns the first it found.
+fnx(v;b)	normalized x value (0.0-1.0) which depends to y in buffer b. If there are more than one it returns the first it found.
+fny(v;b)	normalized y value (0.0-1.0) which depends to x in buffer b. If there are more than one it returns the first it found.
 ===== Special Functions =====
@@ 行 67: / 行 134: @@
 D =	Gauss-Lorentz ratio ( M ,1.0=pure Gauss, 0.0 = pure Lorentz)
 E	=	unused
-DS (Doniach-Sunjic curve)
+==== DS (Doniach-Sunjic curve) ====
-A =	position (x0)
+$$
-B = height (l0)
+\displaystyle I(E)={\frac {\Gamma (1-\alpha )}{[(E-E_{0})^{2}+\gamma ^{2}]^{(1-\alpha )/2}}}\cos \left\lbrace {\frac {\pi \alpha }{2}}+(1-\alpha )\arctan \left[{\frac {E-E_{0}}{\gamma }}\right]\right\rbrace
-C	= width ( γ, Lorentzian FWHM)
+$$
-D	=	Anderson's exponent ( α, -0.5 ... 0.5)
+|A| position | $E_0$|
-E	=	unused
+|B| height |$l0$|
-ET (Gauss-Lorentz mix curve with exponential Tail)
+|C| width |( γ, Lorentzian FWHM)|
+|D| Anderson's exponent | ( α, -0.5 ... 0.5)|
+|E| unused | |
+==== ET (Gauss-Lorentz mix curve with exponential Tail) ====
 A =	position (x0)
 B = height (I0)
@@ 行 79: / 行 150: @@
 D	=	Gauss-Lorentz ratio ( M ,1.0=pure Gauss, 0.0 = pure Lorentz)
 E	=	tail exponent factor ( α, -infinity - +infinity)
-GL* (Gauss convoluted Lorentz curve)
+==== GL* (Gauss convoluted Lorentz curve) ====
 A =	position
 B = height
@@ 行 85: / 行 157: @@
 D	=	Gauss-Lorentz ratio (must be set to 0.0)
 E	=	Gauss FWHM (0 - +infinity)
-DS* (Gauss convoluted Doniach-Sunjic curve)
+==== DS* (Gauss convoluted Doniach-Sunjic curve) ====
 A =	position
 B = height