update

doc/src/How2ReadData/How2ReadData.do.txt

@@ -317,7 +317,7 @@ from sklearn.linear_model import LinearRegression
 from sklearn.metrics import mean_squared_error, r2_score, mean_squared_log_error, mean_absolute_error
 
 x = np.random.rand(100,1)
-y = 2.0+ 5*x+0.5np.random.randn(100,1)
+y = 2.0+ 5*x+0.5*np.random.randn(100,1)
 linreg = LinearRegression()
 linreg.fit(x,y)
 ypredict = linreg.predict(x)
@@ -430,7 +430,7 @@ print (error(y))
 !ec
 
 Similarly, using _R_, we can perform similar studies. The following _R_ code illustrates this.
-
+(more details on _R_ will be inserted later).
 
 ===== Non-Linear Least squares in R  =====
 !bblock
@@ -478,7 +478,7 @@ display(data_pandas)
 ===== Examples =====
 
 We present here several examples, with pertinent Python codes that we
-will us to illustrate various machine learning methods and ways to
+will use to illustrate various machine learning methods and ways to
 analyze, from simple to complex, various data sets. Many of these
 examples allow us to generate the data we want to analyze, following
 much of the same philosophy we discussed above when
@@ -502,7 +502,7 @@ Here we will construct a model for cell growth based on a simple difference equa
    interval $\Delta t$ as $N$ cells would: $\Delta N \propto N$
  o $N$ cells result in twice as many new individuals $\Delta N$ in
    time $2\Delta t$ as in time $\Delta t$: $\Delta N \propto\Delta t$
- o Same proportionality wrt death 
+ o Same proportionality with respect to  death 
  o Proposed model: $\Delta N = b\Delta t N - d\Delta tN$ for some unknown
    constants $b$ (births) and $d$ (deaths)
  o Describe evolution in discrete time: $t_n=n\Delta t$
@@ -511,7 +511,7 @@ Here we will construct a model for cell growth based on a simple difference equa
  o Program model: `N[n+1] = N[n] + r*dt*N[n]`
 !eblock
 
-The difference equation can be programmed in a simple was, and in order to get started we
+The difference equation can be programmed in a simple way, and in order to get started we
 set $r=1.5$, $N^0=1$, $\Delta t=0.5$. The program reads
 
 !bc pycod 
@@ -520,13 +520,12 @@ import numpy as np
 t = np.linspace(0, 10, 21)  # 20 intervals in [0, 10]
 dt = t[1] - t[0]
 N = np.zeros(t.size)
-
 N[0] = 1
 r = 0.5
 
 for n in range(0, N.size-1, 1):
     N[n+1] = N[n] + r*dt*N[n]
-    print 'N[%d]=%.1f' % (n+1, N[n+1])
+    print('N[%d]=%.1f' % (n+1, N[n+1]))
 !ec
 and it generates the following output
 !bc
@@ -553,7 +552,7 @@ N[20]=86.7
 !ec
 This forms our data which later will define our training set. 
 In this case we defined the value of the parameter $r$. We could alternatively assume that we just received the 
-above data file and where asked to use find $r$. How can we estimate $r$ from data?
+above data file and where asked to find $r$. How can we estimate $r$ from data? This will be one of our tasks later.
 
 We can use the difference equation with the experimental data
 !bt
@@ -564,10 +563,11 @@ Suppose now that  $N^{n+1}$ and $N^n$ are known from data. Then we could solve w
 \[ r = \frac{N^{n+1}-N^n}{N^n\Delta t} \]
 !et
 Suppose we set $t_1=600$, $t_2=1200$,
-$N^1=140$ and $N^2=250$. We obtain then $r=0.0013$. The exact value is $r = 0.000694$
-The following code plot 
+$N^1=140$ and $N^2=250$. 
+The following code plots the data 
 !bc pycod 
 import numpy as np
+import matplotlib.pyplot as plt
 
 # Estimate r
 data = np.loadtxt('ecoli.csv', delimiter=',')
@@ -575,10 +575,9 @@ t_e = data[:,0]
 N_e = data[:,1]
 i = 2  # Data point (i,i+1) used to estimate r
 r = (N_e[i+1] - N_e[i])/(N_e[i]*(t_e[i+1] - t_e[i]))
-print 'Estimated r=%.5f' % r
+print('Estimated r=%.5f' % r)
 # Can experiment with r values and see if the model can
 # match the data better
-
 T = 1200     # cell can divide after T sec
 t_max = 5*T  # 5 generations in experiment
 t = np.linspace(0, t_max, 1000)
@@ -589,7 +588,6 @@ N[0] = 100
 for n in range(0, len(t)-1, 1):
     N[n+1] = N[n] + r*dt*N[n]
 
-import matplotlib.pyplot as plt
 plt.plot(t, N, 'r-', t_e, N_e, 'bo')
 plt.xlabel('time [s]');  plt.ylabel('N')
 plt.legend(['model', 'experiment'], loc='upper left')
@@ -767,7 +765,7 @@ parameters result in a slightly modified initial conditions, namely
 $H(0) = 34.91$ and $L(0)=3.857$. 
 
 
-The following Python demonstrates how we can use linear regression to fit for example the population of lynx.
+The following Python code demonstrates how we can use linear regression to fit for example the population of lynx.
 Similarly, we have also used a decision tree algorithm to fit the lynx population data. As expected, the linear regression is not exactly impressive 
 !bc pycod
 import numpy as np
@@ -792,7 +790,7 @@ plt.show()
 
 
 
-The similar code for linear regression in _R_ reads
+The similar code for linear regression in _R_ reads (more details to come)
 !bc r
 HudsonBay = read.csv("src/Hudson_Bay.csv",header=T)
 fix(HudsonBay)
@@ -890,7 +888,6 @@ Our task is to first set up an algorithm which simulates the above transactions
   $w_m\Delta m$. You will need to set up a value for the interval $\Delta m$  (typically $0.01-0.05$).
   That means you need to account for the number of times you register an income in the interval
   $m,m+\Delta m$. The number of times you register this income, represents the value that enters the histogram.
-  You will also need to find a criterion for when the equilibrium situation has been reached.
 
 !bc pycod
 #!/usr/bin/env python