[-0.32938847 -2.07110274 -0.2627588 0.68616263 1.65238878 -0.03750367
- 1.653702 0.71442781 0.2983233 -1.10327559]
+[ 0.63628911 0.14168589 0.80381774 -1.0333934 -0.30509508 0.43222125
+ 2.19605877 -0.10357077 -0.15968414 0.70924636]
The following examples show how to compute various quantities like the mean value of a matrix or a vector and how to use functions like reshape and ravel. These are all useful quantities when scaling the data and preparing the data for various machine learning algorithms and when calculating quantities like the mean squared error or the variance.
+"""
+Simple code that tests various numpy functions
+"""
+
+import numpy as np
+# Simple test-matrix of dim 3 x 4
+a = np.array([ [1, 2, 3], [4, 5, 6], [7, 8, 9],[10, 11, 12]],dtype=np.float64)
+print(f"The test matrix:{a}")
+# This is the total mean summed over all elements, which here has to be 6.5
+print(f"This is the total mean summed over all elements:{np.mean(a,dtype=np.float64)}")
+# This is the mean for each column, it returns an array with the mean values for each column. It returns a row-like vector
+print(f"This is the mean for each column:{np.mean(a, axis=0, keepdims=True,dtype=np.float64)}")
+# This is the mean value for each row, it returns an array via the keepdims option which is a column-like vector if
+# keepdims=True. Else it return a row-like vector
+# Try setting keepdims=False
+print(f"This is the mean value for each row:{np.mean(a, axis=1, keepdims=True,dtype=np.float64)}")
+# We print then the mean value for each row by setting keepdims=False
+print(f"This is the mean value for each row with keepdims false:{np.mean(a, axis=1, keepdims=False,dtype=np.float64)}")
+
+# Ravel return a contiguous flattened array.
+print(f"Flatten the matrix:{np.ravel(a)}")
+# It is the same as reshaping the matrix into a one-dimensional array
+print(f"Reshape the matrix to a one-dim array:{a.reshape(-1)}")
+# ‘C’ means to index the elements in row-major, C-style order, with the last axis index changing fastest, back to the first axis index changing slowest.
+# ‘F’ means to index the elements in column-major, Fortran-style order, with the first index changing fastest, and the last index changing slowest
+print(np.ravel(a, order='F'))
+# When order is ‘A’, it will preserve the array’s ‘C’ or ‘F’ ordering
+# ‘A’ means to read the elements in Fortran-like index order if a is Fortran contiguous in memory, C-like order otherwise.
+# ‘K’ means to read the elements in the order they occur in memory, except for reversing the data when strides are negative. By default, ‘C’ index order is used.
+# Transposing it
+print(np.ravel(a.T))
+print(np.ravel(a.T, order='A'))
+We start with the linear set of equations
Thereafter you call the function lubksb(double a, int n, int indx, double w) which uses the LU decomposed matrix \(\bf A\) and the vector \(\bf w\) and returns \(\bf x\) in the same place as \(\bf w\). Upon exit the original content in \(\bf w\) is destroyed. If you wish to keep this information, you should make a backup of it in your calling function.
If the inverse exists then
Lab Wednesday: Wrap up project 1
Lecture Thursday: Writing a feed-forward Neural Network code for regression and classification
Lecture Thursday: Stochastic gradient descent, automatic differentiation and start discussion of feed-forward Neural Network code for regression and classification
Lecture Friday: Deep Learning and Neural Networks
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