import csv
def mean(L):
return n(sum(L)/len(L))
def LinReg(L):
X = [x for (x, y) in L]
Y = [y for (x, y) in L]
XY = [x*y for (x, y) in L]
XX = [x^2 for (x, y) in L]
YY = [y^2 for (x, y) in L]
n = len(L)
m = (mean(XY) - mean(X)*mean(Y))/(mean(XX) - mean(X)^2).n()
b = (mean(Y) - m * mean(X)).n()
d_m = sqrt(n/(n-2)*(sum(YY)-m*sum(XY)-b*sum(Y))/(n*sum(XX)-sum(X)^2)).n()
d_b = (d_m*sqrt(mean(XX))).n()
return [m, b, d_m, d_b, max(X).n(), max(Y).n()]
def LogY(L):
return [(n(x), ln(y).n()) for (x, y) in L]
def getData():
files = []
data = []
for i in range(0,5):
files.append(csv.reader(open(DATA+str(i+1)+".csv"), delimiter=',', quotechar='"'))
data.append([row for row in files[i]])
data[i] = [(n(x),n(y)) for [x,y] in data[i]]
return data
def getMetaData():
data = []
file = csv.reader(open(DATA+"meta.csv"), delimiter=',', quotechar='"')
for row in file:
data.append(row)
data = [(n(x),n(y),n(z)) for [x,y,z] in data]
return data
def ConvertToAt(Data, MetaData):
Calculated = []
for i in range(0, len(MetaData)):
Calculated.append([(x * 60 / MetaData[i][2],y * 0.01) for (x,y) in Data[i]])
return Calculated
def getTemperatures(M):
Temperatures = []
for m in M:
Temperatures.append((m[0] + m[1])/2 + 273.15)
return Temperatures
RawData = getData()
RawMetaData = getMetaData()
Data = ConvertToAt(RawData, RawMetaData)
Temperatures = getTemperatures(RawMetaData)
def ShiftRight(L, first="XXX"):
l = len(L)
for i in range(l,1):
L[i] = L[i-1]
L.append(L[l-1])
L[0] = first
return L
def DisplayData(RawData, Data, Temperatures, sig = 3):
for i in range(0,5):
lines = ["T = " + str(Temperatures[i].round()) + " K"]
lines.append(ShiftRight([(x).n(digits=sig) for (x,y) in RawData[i]], "x [mm]"))
lines.append(ShiftRight([(y*2).n(digits=sig) for (x,y) in RawData[i]], "y [mm]"))
lines.append(ShiftRight([t.round() for (t, A) in Data[i]],"t [s]"))
lines.append(ShiftRight([A.n(digits=(sig-1)) for (t, A) in Data[i]],"A [ ]"))
#show("Messung bei T = " + str(Temperatures[i].round()) + " K")
html.table(lines)
DisplayData(RawData, Data, Temperatures)
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def RawGraph(Data, Temp, labels, sig = 4, hueoffset = 0.28):
graph = text("", (0,0))
l = len(Data)
latexlabels = ["$"+labels[0]+"$", "$"+labels[1]+"$"]
maxesx = []
maxesy = []
for i in range(0, l):
graph += scatter_plot(Data[i], facecolor=hue(i/(l+1)+hueoffset))
maxesx.append(max([x for x,y in Data[i]]))
maxesy.append(max([y for x,y in Data[i]]))
maxes = (max(maxesx), max(maxesy))
for i in range(0, l):
graph += text("$T = " + str(Temp[i].n(digits=sig)) + " K$", (maxes[0], maxes[1] - i * maxes[1]/(6*72) * 10 * 1.2), fontsize=10, rgbcolor=hue(i/(l+1)+hueoffset), horizontal_alignment='right')
graph.axes_labels(latexlabels)
graph.show(figsize=[10, 6])
RawGraph(Data, Temperatures, ["t [s]", "A"])
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def LNGraphsTables(Data, Temp, labels, sig = 4, hueoffset = 0.28):
latexlabels = ["$"+labels[0]+"$", "$"+labels[1]+"$"]
graphs = []
data = []
regs = []
l = len(Data)
for i in range(0,l):
x = var('x')
data.append(LogY(Data[i]))
regs.append(LinReg(data[i]))
graphs.append(plot(regs[i][0] * x + regs[i][1], x, 0, max([x for x,y in data[i]])))
graphs[i] += scatter_plot(data[i], facecolor=hue(i/(l+1)+hueoffset))
Text = "$T = " + str(Temp[i].n(digits=sig)) + " K$\n"
Text += "$y = mx + b = $" + regs[i][0].n(digits=sig).str(no_sci=False) + "$ x + $" + regs[i][1].n(digits=sig).str(no_sci=False) +"\n"
Text += "$\Delta$ $m = $"+ regs[i][2].n(digits=sig).str(no_sci=False) + "$, $$\Delta$$b = $" + regs[i][3].n(digits=sig).str(no_sci=False)
graphs[i] += text(Text, (max([x for x,y in data[i]]), max([y for x,y in data[i]])), fontsize=10, rgbcolor='black', horizontal_alignment='right', vertical_alignment='top')
graphs[i].axes_labels(latexlabels)
tabledata = []
tabledata.append(("t [s]", "A", "ln(A)"))
for x,y in Data[i]:
tabledata.append((x.n(digits=sig), y.n(digits=sig), ln(y).n(digits=sig)))
show(latex("Messung " + str(i+1) + " bei $T = $" + str(Temp[i].n(digits=sig)) + ""))
html.table(tabledata, header=True)
graphs[i].show(figsize=[10, 6], gridlines=("minor", "major"))
return regs
Regressions = LNGraphsTables(Data, Temperatures, ["t [s]", "ln(A)"])
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def getEnergy(Regressions, T, labels, sig = 4):
latexlabels = ["$"+labels[0]+"$", "$"+labels[1]+"$"]
M = [n(m) for (m,b,x,y,z,a) in Regressions]
l = len(T)
table = [("T [K]", "k [s^-1]", "T [K^-1]", "ln(k)")]
data = []
for i in range(0,l):
table.append((T[i].n(digits=sig), M[i].n(digits=sig).str(no_sci=false), (1/T[i]).n(digits=sig).str(no_sci=false), ln(M[i]).real().n(digits=sig)))
data.append((1/T[i], ln(M[i]).real()))
reg = LinReg(data)
E_a = var('E_a')
E_a = (-reg[0] * 8.31447).n(digits=sig)
# html.table(reg)
buffer = scatter_plot(data, facecolor=hue(0.8))
Text = "$y = mx + b = $" + reg[0].n(digits=sig).str(no_sci=False) + "$ x + $" + reg[1].n(digits=sig).str(no_sci=False) +"\n"
Text += "$\Delta$ $m = $"+ reg[2].n(digits=sig).str(no_sci=False) + "$, $$\Delta$$b = $" + reg[3].n(digits=sig).str(no_sci=False) + "\n"
Text += "$E_a = -m R = " + str(round(E_a)) + "$ $J/mol $"
buffer += text(Text, (max([x for x,y in data]), max([y for x,y in data])), fontsize=10, rgbcolor='black', horizontal_alignment='right', vertical_alignment='top')
x = var('x')
buffer += plot(reg[0] * x + reg[1], x, min([x for x,y in data]), max([x for x,y in data]))
buffer.axes_labels(latexlabels)
html.table(table, header=true)
buffer.show(figsize=[10, 6])
show(E_a)
getEnergy(Regressions, Temperatures, ["1/T [K^-1]", "ln(k)"])
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