From 4fd9efa17d9a6094875a6e319b7819f8f97e04bc Mon Sep 17 00:00:00 2001 From: Tim Skov Jacobsen Date: Mon, 2 Sep 2019 16:22:06 +0200 Subject: [PATCH] First commit --- .../Session 7 - Exercise solutions.html | 12208 ++++++++++++++ ...ession 7 - Explanations and exercises.html | 13652 ++++++++++++++++ .../Session 8 - Exercise (Interpolation).html | 11929 ++++++++++++++ .../Session 8 - Exercise solutions.html | 11896 ++++++++++++++ .../base_slab_nodes.xlsx | Bin 0 -> 335736 bytes .../known_sections_plaxis.xlsx | Bin 0 -> 17827 bytes ...ettlement_field_generated_code_example.dat | 6917 ++++++++ .../settlement_interpolation.py | 82 + .../Crack_width_Seg7_y_direction.csv | 1201 ++ .../Session 9 - Exercise Solutions.html | 12419 ++++++++++++++ ...n 9 - Heatmaps and merging operations.html | 12132 ++++++++++++++ .../piles.csv | 7 + .../steel_profiles.csv | 23 + 13 files changed, 82466 insertions(+) create mode 100644 Session 7 - Coordinate Transformation/Session 7 - Exercise solutions.html create mode 100644 Session 7 - Coordinate Transformation/Session 7 - Explanations and exercises.html create mode 100644 Session 8 - Interpolation/Session 8 - Exercise (Interpolation).html create mode 100644 Session 8 - Interpolation/Session 8 - Exercise solutions.html create mode 100644 Session 8 - Interpolation/base_slab_nodes.xlsx create mode 100644 Session 8 - Interpolation/known_sections_plaxis.xlsx create mode 100644 Session 8 - Interpolation/settlement_field_generated_code_example.dat create mode 100644 Session 8 - Interpolation/settlement_interpolation.py create mode 100644 Session 9 - Heatmaps and merging operation/Crack_width_Seg7_y_direction.csv create mode 100644 Session 9 - Heatmaps and merging operation/Session 9 - Exercise Solutions.html create mode 100644 Session 9 - Heatmaps and merging operation/Session 9 - Heatmaps and merging operations.html create mode 100644 Session 9 - Heatmaps and merging operation/piles.csv create mode 100644 Session 9 - Heatmaps and merging operation/steel_profiles.csv diff --git a/Session 7 - Coordinate Transformation/Session 7 - Exercise solutions.html b/Session 7 - Coordinate Transformation/Session 7 - Exercise solutions.html new file mode 100644 index 0000000..b96daa3 --- /dev/null +++ b/Session 7 - Coordinate Transformation/Session 7 - Exercise solutions.html @@ -0,0 +1,12208 @@ + + + +Session 7 - Exercise solutions + + + + + + + + + + + + + + + + + + + +
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+ +
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+

Session 7 - Exercise solutions

+
+
+
+
+
+
In [1]:
+
+
+
import numpy as np
+from math import cos, sin, atan, pi
+import matplotlib.pyplot as plt
+
+
+def rotate(x, y, theta=90):
+    '''
+    Rotate coordinate lists/arrays x and y rotated angle theta [deg] clockwise. 
+    Returns the rotated coordinates as arrays.
+    '''
+    
+    # Convert angle to radians
+    theta = pi * theta / 180
+    
+    # Define rotation matrix    
+    R = np.array([[cos(theta), sin(theta), 0],
+                  [-sin(theta), cos(theta), 0],
+                  [0, 0, 1]])
+
+    # Define array of original coordinates 
+    xy1 = np.array([x, y, np.ones(len(x))])
+    
+    # Compute rotated coordinates
+    xr, yr, _ = np.matmul(R, xy1)
+
+    return xr, yr
+
+
+
+# Test arrays to transform
+x = np.array([-5, 5, 5, 0.5, 0.5, 5, 5, -5, -5, -0.5, -0.5, -5, -5])
+y = np.array([-8, -8, -6, -6, 6, 6, 8, 8, 6, 6, -6, -6, -8])
+
+# Call the function with test arrays
+xr, yr = rotate(x, y, theta=45)
+
+# Display the rotated x-coordinates
+xr
+
+ +
+
+
+ +
+
+ + +
+
Out[1]:
+ + + +
+
array([-9.19238816, -2.12132034, -0.70710678, -3.8890873 ,  4.59619408,
+        7.77817459,  9.19238816,  2.12132034,  0.70710678,  3.8890873 ,
+       -4.59619408, -7.77817459, -9.19238816])
+
+ +
+ +
+
+ +
+
+
+
In [2]:
+
+
+
# Display the rotated y-coordinates
+yr
+
+ +
+
+
+ +
+
+ + +
+
Out[2]:
+ + + +
+
array([-2.12132034, -9.19238816, -7.77817459, -4.59619408,  3.8890873 ,
+        0.70710678,  2.12132034,  9.19238816,  7.77817459,  4.59619408,
+       -3.8890873 , -0.70710678, -2.12132034])
+
+ +
+ +
+
+ +
+
+
+
In [3]:
+
+
+
def plot_transform(xt, yt, x=None, y=None, title=None):
+    ''' 
+    Plot the transformed coordinates (xr, yr). Optionally plot the original coordinates (x, y).
+    All four inputs are of type list or array and should all have same length. 
+    Optionally give a title tp the plot as a string.
+    '''
+    
+    # Plot transformed coordintes
+    plt.plot(xt, yt, '.-', color='limegreen')
+    
+    # Plot original coordinates if they were input
+    if x is not None and y is not None:
+        plt.plot(x, y, '.-', color='black')
+        
+    # Set title if that was input
+    if title is not None:
+        plt.title(title, fontsize=15)
+        
+    # Set same scaling on x- and y-axis and show the plot
+    plt.axis('equal')    
+    plt.show()
+    
+    
+# Plot rotated coordinates from previosly
+rotate_title = 'Rotated coordinates with $\\theta = 45 ^{\circ} $'
+plot_transform(xr, yr, x, y, title=rotate_title)
+
+ +
+
+
+ +
+
+ + +
+
+ + + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+
+

Note: An optional title parameter is also implemented here, even though it was not required by the exercise text.

+ +
+
+
+
+
+
In [4]:
+
+
+
def translate(x, y, x_translate, y_translate):
+    ''' 
+    Translate coordinate lists/arrays x and y the distance x_translate in the x-direction 
+    and the distance y_translate in the y-direction. Returns the translated coordinates as arrays. 
+    '''
+    
+    # Define translation matrix
+    T = np.array([[1, 0, x_translate],
+                  [0, 1, y_translate],
+                  [0, 0, 1]])
+    
+    # Define array of original coordinates
+    xy1 = np.array([x, y, np.ones(len(x))])
+    
+    # Compute translated coordinates
+    xt, yt, _ = np.matmul(T, xy1)
+    
+    return xt, yt
+
+
+# Call the function with test arrays
+xt, yt = translate(x, y, 10, 8)
+
+# Plot the translated coordinates
+translate_title = 'Translated coordinates with $(\Delta x, \Delta y) = (10, 8)$'
+plot_transform(xt, yt, x, y, title=translate_title)
+
+ +
+
+
+ +
+
+ + +
+
+ + + +
+ +
+ +
+ +
+
+ +
+
+
+
In [5]:
+
+
+
def scale(x, y, x_scale, y_scale):
+    ''' 
+    Scale coordinate lists/arrays x and y the by factors x_scale and y_scale in the x-direction 
+    and y_translate, respectively. Returns the scaled coordinates as arrays.  
+    '''
+    
+    # Define scaling matrix
+    S = np.array([[x_scale, 0, 0],
+                  [0, y_scale, 0],
+                  [0, 0, 1]])
+    
+    # Define array of original coordinates
+    xy1 = np.array([x, y, np.ones(len(x))])
+    
+    # Compute scaled coordinates
+    xs, ys, _ = np.matmul(S, xy1)
+    
+    return xs, ys
+
+
+# Call the function with test arrays
+xs, ys = scale(x, y, 2, 1.5)
+
+# Plot the scaled coordinates
+scale_title = 'Scaled coordinates with $(x_{scaled}, y_{scaled}) = (2, 1.5)$'
+plot_transform(xs, ys, x, y, title=scale_title)
+
+ +
+
+
+ +
+
+ + +
+
+ + + +
+ +
+ +
+ +
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+ +
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+
In [6]:
+
+
+
def mirror(x, y):
+    ''' 
+    Mirror coordinate lists/arrays x and y about the y-axis. Returns the mirrored 
+    coordinates as arrays. 
+    '''
+    
+    # Define translation matrix
+    M = np.array([[-1, 0, 0],
+                  [0, 1, 0],
+                  [0, 0, 1]])
+    
+    # Define array of original coordinates
+    xy1 = np.array([x, y, np.ones(len(x))])
+    
+    # Compute new coordinates
+    xm, ym, _ = np.matmul(M, xy1)
+    
+    return xm, ym
+
+
+# Call the function with test arrays with 20 added to all x-values
+xm, ym = mirror(x+20, y)
+
+# Plot the mirrored coordinates
+mirror_title = 'Mirrored coordinates'
+plot_transform(xm, ym, x, y, title=mirror_title)
+
+ +
+
+
+ +
+
+ + +
+
+ + + +
+ +
+ +
+ +
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+ +
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+
In [7]:
+
+
+
def transform(x, y, rotation=0, scaling=(1, 1), translation=(0, 0), mirroring=False):
+    '''
+    Perform a combined coordinate tranformation according to given inputs. 
+    Returns the transformed coordinates as arrays.
+    If no inputs are given, returns the unchanged coordinates.
+
+    Args:
+        x (array)                   : x-values to transform.
+        y (array)                   : y-values to transform.
+        rotate (float, optional)    : Clockwise rotation angle in [deg]. Defaults to no rotation.
+        scale (float, optional)     : Scaling factor in axes directions (cx, cy). Defaults to no scaling.
+        translate (tuple, optional) : Translation in axes directions (dx, dy). Defaults to no translation.
+        mirror (bool, optional)     : Whether or not to mirror the coordinates, Defaults to no mirroring.
+    '''
+    
+    # Rotate coordinates 
+    xt, yt = rotate(x, y, theta=rotation)
+    
+    # Scale coordinates
+    xt, yt = scale(xt, yt, scaling[0], scaling[1])
+    
+    # Translate coordinates
+    xt, yt = translate(xt, yt, translation[0], translation[1])
+    
+    # Mirror coordinates if input parameter mirroring is set to True
+    if mirroring:
+        xt, yt = mirror(xt, yt)
+
+    # Return transformed coordinates as numpy arrays
+    return xt, yt
+
+
+# Call the function with test arrays
+xt, yt = transform(x, y, rotation=45, scaling=(1.5, 2), translation=(10, 8), mirroring=True)
+
+# Plot the transformed coordinates
+transform_title = 'Transformed coordinates'
+plot_transform(xt, yt, x, y, title=transform_title)
+
+ +
+
+
+ +
+
+ + +
+
+ + + +
+ +
+ +
+ +
+
+ +
+
+
+ + + + + + diff --git a/Session 7 - Coordinate Transformation/Session 7 - Explanations and exercises.html b/Session 7 - Coordinate Transformation/Session 7 - Explanations and exercises.html new file mode 100644 index 0000000..9bd3b39 --- /dev/null +++ b/Session 7 - Coordinate Transformation/Session 7 - Explanations and exercises.html @@ -0,0 +1,13652 @@ + + + + +Session 7 - Explanations and exercises + + + + + + + + + + + + + + + + + + + + + + + +
+
+ +
+
+
+ +
+
+
+
+
+
+

Session 7 - Tranformation functions

Coordinate transformations can be performed by matrix operations. Some common ones are:

+\begin{equation} +\tag{Rotation about Origin} +\begin{bmatrix} +x_{\text{rotated}}\\y_{\text{rotated}}\\1 +\end{bmatrix} = +\begin{bmatrix} +\cos(\theta) & \sin(\theta) & 0 \\ +-\sin(\theta) & \cos(\theta) & 0 \\ +0 & 0 & 1 +\end{bmatrix} +\begin{bmatrix} x \\ y \\ 1 \end{bmatrix} +\end{equation}\begin{equation} +\tag{Translation} +\begin{bmatrix} +x_{\text{translated}}\\y_{\text{translated}}\\1 +\end{bmatrix} = +\begin{bmatrix} +1 & 0 & \Delta x \\ +0 & 1 & \Delta y \\ +0 & 0 & 1 +\end{bmatrix} +\begin{bmatrix} x \\ y \\ 1 \end{bmatrix} +\end{equation}\begin{equation} +\tag{Scale about Origin} +\begin{bmatrix} +x_{\text{scaled}}\\y_{\text{scaled}}\\1 +\end{bmatrix} = +\begin{bmatrix} +C_x & 0 & 0 \\ +0 & C_y & 0 \\ +0 & 0 & 1 +\end{bmatrix} +\begin{bmatrix} x \\ y \\ 1 \end{bmatrix} +\end{equation}\begin{equation} +\tag{Mirror about $y$-axis} +\begin{bmatrix} +x_{\text{mirrored}}\\y_{\text{mirrored}}\\1 +\end{bmatrix} = +\begin{bmatrix} +-1 & 0 & 0 \\ +0 & 1 & 0 \\ +0 & 0 & 1 +\end{bmatrix} +\begin{bmatrix} x \\ y \\ 1 \end{bmatrix} +\end{equation}
    +
  • In the rotation matrix it is assumed that the angle $\theta$ is a clockwise rotation.
    • +
+
    +
  • In the translation matrix $\Delta x$ and $\Delta y$ denote the absolute translation in the $x$- and $y$-direction, respectively.
    • +
+
    +
  • In the scaling matrix $C_x$ and $C_y$ denote the scaling in the $x$- and $y$-direction, respectively.
    • +
+
    +
  • The mirroring matrix has no inputs and can bee seen as a boolean operation. It can be done in exactly one way or not done at all.
    • +
+

See more here: https://upload.wikimedia.org/wikipedia/commons/2/2c/2D_affine_transformation_matrix.svg

+ +
+
+
+
+
+
+

Vectorization in numpy

numpy can perform calculation in a vectorized manner meaning that vector and matrix operations can be done on entire arrays at a time as opposed to value by value.

+

Vectorization can eliminate the use of for loops in many scenarios, which makes the code easier to read and write. As an added bonus, vectorized calculations are also much faster than their looping counterparts.

+

For the equations above, we can utilize vectorization by using a arrays (or lists) of values for $x$ and $y$ instead of single values. That implies that $1$ also must be an array of ones with the same size.

+

Thus, the vector $[x, y, 1]^T$ on the right hand side of the is actually an array of arrays.

+

The resulting vector $[x_{\text{transformed}}, y_{\text{transformed}}, 1]^T$ is of course also an array or arrays.

+

Unpacking values

A small example that demontrates unpacking of variables from a function output:

+ +
+
+
+
+
+
In [1]:
+
+
+
def f():
+    '''
+    Define function that takes no input and returns three values
+    '''
+    return 1, 2, 3
+
+# Call function and save result in variable
+result = f()
+result
+
+ +
+
+
+ +
+
+ + +
+ +
Out[1]:
+ + + + +
+
(1, 2, 3)
+
+ +
+ +
+
+ +
+
+
+
+
    +
  • Note: When returning multiple values from a function, they will by default be a tuple. This is basically the same as if the last line of the function would have been return (1, 2)
    • +
+

Unpacking the result to two variables:

+ +
+
+
+
+
+
In [2]:
+
+
+
# Unpack function output to two variables
+a, b, c = f()
+a
+
+ +
+
+
+ +
+
+ + +
+ +
Out[2]:
+ + + + +
+
1
+
+ +
+ +
+
+ +
+
+
+
In [3]:
+
+
+
b
+
+ +
+
+
+ +
+
+ + +
+ +
Out[3]:
+ + + + +
+
2
+
+ +
+ +
+
+ +
+
+
+
In [4]:
+
+
+
c
+
+ +
+
+
+ +
+
+ + +
+ +
Out[4]:
+ + + + +
+
3
+
+ +
+ +
+
+ +
+
+
+
+

As we see, if we do not unpack, all values are saved in a tuple.

+

But if we decide to unpack, we have to account for all outputs. If we try to unpack only 2 values when the function returns 3 we get this error:

+ +
+
+
+
+
+
In [5]:
+
+
+
# ValueError, function returns 3 values, but only 2 unpacked
+h, i = f()
+
+ +
+
+
+ +
+
+ + +
+ +
+ + +
+
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+<ipython-input-5-393f2c6eb4f0> in <module>
+      1 # ValueError, function returns 3 values, but only 2 unpacked
+----> 2 h, i = f()
+
+ValueError: too many values to unpack (expected 2)
+
+
+ +
+
+ +
+
+
+
+

If we try to unpack too many:

+ +
+
+
+
+
+
In [6]:
+
+
+
# ValueError, function returns 3 values, but 4 were unpacked
+h, i, j, k = f()
+
+ +
+
+
+ +
+
+ + +
+ +
+ + +
+
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+<ipython-input-6-6809bb4f4bd8> in <module>
+      1 # ValueError, function returns 3 values, but 4 were unpacked
+----> 2 h, i, j, k = f()
+
+ValueError: not enough values to unpack (expected 4, got 3)
+
+
+ +
+
+ +
+
+
+
+

Note: When unpacking, the variables of the left side of the equal sign must exactly match the number of outputs, so all unpacked elements are accounted for.

+

There are fancier ways to unpack which can handle cases where it is not known how many elements are to be unpacked. See for example https://www.python.org/dev/peps/pep-3132/.

+ +
+
+
+
+
+
+

Unpacking values for the tranformation examples

The resulting array of arrays will have the code structure

+
# Define an array of arrays
+array_of_arrays = [ [x_values], [y_values], [ones] ]
+
+

Unpacking x-values and y_values to their own arrays can be done like this:

+
# Unpack an array of arrays
+x_values, y_values, ones = array_of_arrays
+
+

In this case, we don't care about the array of ones. It is a quite common scenario that a function returns some values that are not needed. In Python, it is common comvention to unpack unused variables to an underscore _ like this:

+
# Convention for unpacking unused variables
+x_transformed, y_transformed, _ = array_of_arrays
+
+

By following this convention, it is clear to anyvody reading the code that this value is not going to be used throughout the program.

+

Some numpy functions

numpy.matmul

This function will find the matrix product of two arrays:

+ +
+
+
+
+
+
In [7]:
+
+
+
import numpy as np
+
+# Define a vector
+a = np.array([1, 2, 3])
+
+# Define a matrix
+T = np.array([ [1, 1, 5], [3, 1, 1], [5, 0, 1] ])
+
+# Compute the matrix product {T}x{a}
+b = np.matmul(T, a) 
+b
+
+ +
+
+
+ +
+
+ + +
+ +
Out[7]:
+ + + + +
+
array([18,  8,  8])
+
+ +
+ +
+
+ +
+
+
+
+

np.ones

Creates an array of ones of a specifies shape

+ +
+
+
+
+
+
In [8]:
+
+
+
# Create 1x5 vector of ones (1D array)
+np.ones(5)
+
+ +
+
+
+ +
+
+ + +
+ +
Out[8]:
+ + + + +
+
array([1., 1., 1., 1., 1.])
+
+ +
+ +
+
+ +
+
+
+
In [9]:
+
+
+
# Create 5x5 matrix of ones (2D array)
+np.ones([5, 5])
+
+ +
+
+
+ +
+
+ + +
+ +
Out[9]:
+ + + + +
+
array([[1., 1., 1., 1., 1.],
+       [1., 1., 1., 1., 1.],
+       [1., 1., 1., 1., 1.],
+       [1., 1., 1., 1., 1.],
+       [1., 1., 1., 1., 1.]])
+
+ +
+ +
+
+ +
+
+
+
+

Exercise 1

Write a function that implements rotation of a array of coordinates x and y. The angle of rotation in clockwise direction should be an input parameter with default value of 90 degress. The function should return the rotated coordinates xr and yr.

+

Test the function with these arrays.

+
# Test arrays to transform
+x = np.array[-5, 5, 5, 0.5, 0.5, 5, 5, -5, -5, -0.5, -0.5, -5, -5])
+y = np.array[-8, -8, -6, -6, 6, 6, 8, 8, 6, 6, -6, -6, -8])
+
+

Exercise 2

Write a function that takes a pair of arrays of transformed coordinates xt and yt as input and plots them as a line plot. The function should be able to plot the orignal coordinates as well, but this should be optional and not plotted as default.

+

Plot the original shape from Exercise 1 together with the rotated shape.

+

A good way of setting default values for parameters that should not be present as default is by setting them equal to None in the function definition. The code inside the function can then check if they actual values were input

+

Exercise 3

Write a function that implements translation of an array of coordinates x and y. The translation shall be defined by values (not arrays) x_translate and y_translate, which are the distance the points will move in te $x$- and $y$-direction, respectively.

+

Test the function with the arrays given in Exercise 1. Plot the translation with the function written in Exercise 2.

+

Exercise 4

Implement the scaling transformation as a function. Test it by plotting it.

+

Exercise 5

Implement mirroring tranformation about the $y$-axis as a funcion.

+

Since the given coordinates in Exercise 1 are symmetic about the $y$-axis, the mirrored coordinates will lie on top of the orignal ones. Try to test it by plotting.

+

You can quickly make a more visible test by moving all the $x$-coordinates, say 20 units to the right. Since we are using numpy this can be done by simply adding 20 to the array itself x+20. This is a simple example of vectorization.

+

Exercise 6

Write a function that combines all of the above tranformations in one. When performing multiple transformations at once, the tranformation matrices can be multiplied by each other prior to multiplication with the orignal coordinates.

+

It could have a structure like this:

+
def tranform(x, y, rotatation=0, scaling=(1, 1), translation=(0, 0), mirroring=False)):
+    '''
+    Perform a combined coordinate tranformation according to given inputs. If no inputs are given, returns the unchanged coordinates.
+
+    Args:
+        x (array)                   : x-values to transform.
+        y (array)                   : y-values to transform.
+        rotate (float, optional)    : Clockwise rotation angle in [deg]. Defaults to no rotation.
+        scale (float, optional)     : Scaling factor in axes directions (cx, cy). Defaults to no scaling.
+        translate (tuple, optional) : Translation in axes directions (dx, dy). Defaults to no translation.
+        mirror (bool, optional)     : Whether or not to mirror the coordinates, Defaults to no mirroring.
+    '''
+
+    # Code here
+
+
    +
  • Remember that rotation and scaling are performed about the origin. So the order of operations will matter.
    • +
  • You can call the previously defined functions to perform the individual transformations if you want.
    • +
  • Return the tranformed coordinates xt, yt.
    • +
+

Addtional Exercise

Write a alternative function for translation where the translation input can be given as a distance that the points should move and the corresponding angle from the $x$-axis. This can often be useful instead of the one defined earlier where the distances are given parallel to the $x$- and $y$-axes.

+ +
+
+
+
+
+ + + + + + diff --git a/Session 8 - Interpolation/Session 8 - Exercise (Interpolation).html b/Session 8 - Interpolation/Session 8 - Exercise (Interpolation).html new file mode 100644 index 0000000..e2acf0e --- /dev/null +++ b/Session 8 - Interpolation/Session 8 - Exercise (Interpolation).html @@ -0,0 +1,11929 @@ + + + +Session 8 - Interpolation + + + + + + + + + + + + + + + + + + + +
+
+ +
+
+
+
+
+

Session 8 - Interpolation

If you haven't already installed the packages xlrd and scipy, you can install them by opening the Anaconda Prompt and type:

+
    +

  • pip install xlrd

    +
    • +

  • pip install scipy

    +
    • +
+

Exercise 1

This exercise is mostly about reading and understanding code written by others. Which is often just as important as being able to write it oneself.

+

Exercise 1.1

Read through the code given in the scipt below and try to understand what it does and how it does it.

+

Copy the script tot he editor and run it.

+

Add print statements if you are unsure about how a certain varaible looks at any point. Remember you can print the first five rows of a dataframe with df.head().

+

The script reads two Excel files. One limitation of this is that they cannot be read while they are open. If you want to inspect these files while running the script, create a copy.

+

Exercise 1.2

The variable settlements_interpolated is a numpy array (you can see this by type(settlements_interpolated) => <class 'numpy.ndarray'>).

+

The last part of the code creates a figure object and an axis object which enables 3D plots.

+

Continue the plotting code to add:

+
    +

  • 3D scatter points of the known points $(x_{known}, y_{known}, w_{known})$

    +
    • +

  • 3D scatter points of the interpoalted settlements in every base slab node $(x_{nodes}, y_{nodes}, w_{nodes})$

    +
    • +
+

In the above $w$ denotes the settlements.

+

Exercise 1.3

All the settlement values in the base slab are in this example to be transferred to and applied in a Sofistik calculation.

+

To this end, we can create a text file with the exact syntax that the Sofistik input language accepts (this language is called CADINP and is somewhat similar to IBDAS's input language). The file has to be a .dat-file.

+

To write data to a file we can use something called context managers. Basically, it allows us to open a file and write to it. See code snippet below:

+
+
# Use a context manager to open and write ('w') to file
+with open('file_name.dat', 'w') as file:
+
+    # The file can from here on out be referred to as file
+    file.write("This text will be written inside 'file_name.dat'")
+
+
+

By using the concept the file is automatically closed after our indented block is terminated. It also creates the file in case it doesn't already exist.

+

The Sofistik input file we want has the format:

+
+PROG SOFILOAD 
+
+LC 25 type 'P' fact 1.0 facd 0.0 titl 'LT settlement all nodes'
+
+  POIN NODE 'insert first node number' WIDE 0 TYPE WZZ 'insert first settlement value'
+  ... 'one line per base slab node' ... 
+  POIN NODE 'insert last node number' WIDE 0 TYPE WZZ 'insert last settlement value'
+
+END
+
+

The indented block should print all the node/settlement pairs. The three non-indented lines should only appear once. The output file should look like the file settlement_field_generated_code_example.dat in the folder.

+ +
+
+
+
+
+
+
+
+

The script

import pandas as pd
+import numpy as np
+from scipy.interpolate import griddata
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
+
+
+# Set name of Excel file to read
+file_known = 'known_sections_plaxis.xlsx'
+
+# Set name of sheet to read from Excel file
+sheet_known = 'known_sections_plaxis'
+
+# Read data from Excel sheet into a dataframe
+df = pd.read_excel(file_known, sheet_name=sheet_known, skiprows=7)
+
+# Extract columns whose names starts with a 'Y' into new dataframe of Y-coordinates
+df_y = df[df.columns[df.columns.str.startswith('Y')]]
+
+# Extract columns whose names starts with 'Z' into new dataframe of settlements
+df_settlements_known = df[df.columns[df.columns.str.startswith('Z')]]
+
+# Flatten dataframe values into 1D array
+y_known = df_y.values.flatten()
+settlements_known = df_settlements_known.values.flatten()
+
+# Extract known x-values
+x_known = df['X']
+
+# Create X-array by repeating itself as many times as there are Y-columns
+# This will create matching(x, y)-points between arrays x and y
+x_known = np.repeat(x_known, len(df_y.columns))
+
+# Set names and read Excel file with base slab nodes
+file_nodes = 'base_slab_nodes.xlsx'
+sheet_nodes = 'XLSX-Export'
+df_nodes = pd.read_excel(file_nodes, sheet_name=sheet_nodes)
+
+# Extract x- and y-coordinates of nodes
+x_nodes = df_nodes['X [m]']
+y_nodes = df_nodes['Y [m]']
+
+# Extract node numbers
+node_no = df_nodes['NR']
+
+# Mirror known y-values and add corresponding x-values and settlements
+x_known = np.append(x_known, x_known)
+y_known = np.append(y_known, -y_known)
+settlements_known = np.append(settlements_known, settlements_known)
+
+# Arrange known (x, y) points to fit input for interpolation
+xy_known = np.array(list(zip(x_known, y_known)))
+
+# Perform interpolation calculation
+settlements_interpolated = griddata(xy_known, settlements_known, (x_nodes, y_nodes), method='cubic')
+
+
+####################
+### Exercise 1.2 ###
+####################
+# Create figure object
+fig = plt.figure()
+
+# Create axis object for 3D plot
+ax = fig.add_subplot(111, projection='3d')
+
+# Plot known settlement points as 3D scatter plot (ax.scatter(...))
+    # <Put plotting code here!>
+
+# Plot interpolated field as 3D scatter plot
+    # <Put plotting code here!>
+
+# Show figure
+    # <Put plotting code here!>
+
+
+####################
+### Exercise 1.3 ###
+####################
+# Write Sofistik input code to .dat-file for applying settlements as imposed displacements
+    # <Put plotting code here!>
+
+ +
+
+
+
+
+ + + + + + diff --git a/Session 8 - Interpolation/Session 8 - Exercise solutions.html b/Session 8 - Interpolation/Session 8 - Exercise solutions.html new file mode 100644 index 0000000..018a7f0 --- /dev/null +++ b/Session 8 - Interpolation/Session 8 - Exercise solutions.html @@ -0,0 +1,11896 @@ + + + +Session 8 - Exercise solutions + + + + + + + + + + + + + + + + + + + +
+
+ +
+
+
+
+
+

Session 8 - Exercise solution

The full script is provided below.

+ +
+
+
+
+
+
+
+
+
import pandas as pd
+import numpy as np
+from scipy.interpolate import griddata
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
+
+
+# Set name of Excel file to read
+file_known = 'known_sections_plaxis.xlsx'
+
+# Set name of sheet to read from Excel file
+sheet_known = 'known_sections_plaxis'
+
+# Read data from Excel sheet into a dataframe
+df = pd.read_excel(file_known, sheet_name=sheet_known, skiprows=7)
+
+# Extract columns whose names starts with a 'Y' into new dataframe of Y-coordinates
+df_y = df[df.columns[df.columns.str.startswith('Y')]]
+
+# Extract columns whose names starts with 'Z' into new dataframe of settlements
+df_settlements_known = df[df.columns[df.columns.str.startswith('Z')]]
+
+# Flatten dataframe values into 1D array
+y_known = df_y.values.flatten()
+settlements_known = df_settlements_known.values.flatten()
+
+# Extract known x-values
+x_known = df['X']
+
+# Create X-array by repeating itself as many times as there are Y-columns
+# This will create matching(x, y)-points between arrays x and y
+x_known = np.repeat(x_known, len(df_y.columns))
+
+# Set names and read Excel file with base slab nodes
+file_nodes = 'base_slab_nodes.xlsx'
+sheet_nodes = 'XLSX-Export'
+df_nodes = pd.read_excel(file_nodes, sheet_name=sheet_nodes)
+
+# Extract x- and y-coordinates of nodes
+x_nodes = df_nodes['X [m]']
+y_nodes = df_nodes['Y [m]']
+
+# Extract node numbers
+node_no = df_nodes['NR']
+
+# Mirror known y-values and add corresponding x-values and settlements
+x_known = np.append(x_known, x_known)
+y_known = np.append(y_known, -y_known)
+settlements_known = np.append(settlements_known, settlements_known)
+
+# Arrange known (x, y) points to fit input for interpolation
+xy_known = np.array(list(zip(x_known, y_known)))
+
+# Perform interpolation calculation
+settlements_interpolated = griddata(xy_known, settlements_known, (x_nodes, y_nodes), method='cubic')
+
+
+####################
+### Exercise 1.2 ###
+####################
+# Create figure object
+fig = plt.figure()
+
+# Create axis object for 3D plot and put it on the figure
+ax = fig.add_subplot(111, projection='3d')
+
+# Plot known settlement points as 3D scatter plot (ax.scatter(...))
+ax.scatter(x_known, y_known, settlement_known, '-.', color='limegreen')
+
+# Plot interpolated field as 3D scatter plot
+ax.scatter(x_nodes, y_nodes, settlement_interpolated, '.', color='cornflowerblue', s=0.1)
+
+# Show figure
+plt.show()
+
+
+####################
+### Exercise 1.3 ###
+####################
+# Write Sofistik input code to .dat-file for applying settlements as imposed displacements
+with open(f'Generated_sofistik_code.dat', 'w') as file:
+
+    # Write the 'static' text to file 
+    file.write('''+PROG SOFILOAD 
+
+LC 25 type 'P' fact 1.0 facd 0.0 titl 'LT settlement all nodes'  \n''')
+
+    # Write the 'variable' text to file with node number/settlement pairs
+    for node, settlement in zip(node_no, settlement_interpolated):
+        file.write(f'  POIN NODE {node} WIDE 0 TYPE WZZ {settlement} \n')
+
+    # Write 'static' END statement to file
+    file.write('END')
+
+ +
+
+
+
+
+ + + + + + diff --git a/Session 8 - Interpolation/base_slab_nodes.xlsx b/Session 8 - Interpolation/base_slab_nodes.xlsx new file mode 100644 index 0000000000000000000000000000000000000000..868c626669384ac6472b7e82073d76a515fd298c GIT binary patch literal 335736 zcmeFYRd8l8&n6hg4l^@zhda#7dBe=i=`b^Mhnbm~=?yb=m^tY%)8?C*+S#r7ul8=X z#uul`b#!b?)+5QXj-m`W1Ud*52n+}a2non8_7_JjC*)*3H6 zOVJAC&6Mw*_~j0!fM&%$kMwYDE9`aX^={Lj_G91-v0QPy7iczSMW z5K4n=oFQ}zym#CAdgIl-7gwDU?7hD9Mt-4spY>%NSDSCGO897Y*3R?2K&w@!7pf)< zD$Ys9gWz0J$8kZb2R6@}=DiBa9fON^-&F_UnwNagr^&?wE=?Pcc`=Ct_s!sX4Vvx4 z>)kekpCPs{RQ8DF9P36_Voo0qWJ$pDwg*2w(-wD_vT8TmoxAHXZgE|KK7Gdtqo*?C>c zqD^F4Bm>l^xHX_sqR`VL1UW>CcqjPC-&}#OcbfH0uKT?hZ;Msh_Gu@YQ7ew>>J)Dp zBK0Tb;P7RGnLo+AO7We0uU2oed_XqzjAh6K9UH}lh&etGh|O7l5@QJtSK3E#;Qc*2 z*CN3(L?&-9_}97!CYpjHv-E3FdqM$kdy~g%W@W`vlerK6D3F!TA1JvTugRVJ*V|@+ zy+Bl7MRmT;SNag-MCVT(MHbbXj{N;oGqa*-5Q3iJUBZBdPk&w83VJ?H~vZT##P@_{uhw2Z1%uIOCT!qxLUR)gx9*jHg6q-REG59 zvcCZt@%ohVu*<=B`J%D=?de77-1+i(BMnZu705iI;>p`l9Hy 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z|8!gWKirn%cegc21$0|bO}OH3hYSYQ_tgL4w)nrht;?X5&&5P^_*6JMDVXRl#FZqL zzijW`Gy~n%gprz*+3Gv^pf&RepH+)IhEr6Ql45d>%HYkG=>yF0M7)8dJ)?ZovdJpf zw6gm;!pk~qU8e?iz0a&uTsTx4lYTtf_Ojkq6MRrXwwog;aSv!&OUduo)wEXNjLWO& z3ATm7FDng0&>dzJQ2Kt$lip1%VAtl9n@<@a*npD6plQl>wk z{Fv;&qx@cV`V(aU^N%P$0)XF9ey^kYi6Vgi1Lbd3Rlg(rUU&2pL7w0r2>(%q^n264 zCgy)O1OO~Z0f67r^uM?MJ>B`Uy&}brKmMO2KYs`PYYy!vBmkfYOsW3IEBz~@_IvZc zCO>{{K1&VwEh_t?KK{Cz^DBS^^REDZTHE>kW&XM*@GF)a>#tbfSBQSD5d4nv*BJU& z6eG6ZQGNtdzXSX=HvJVqmi>2tpONbCD1VLRenm0l_!Z@+V17n+zhnJ1Aovx_g6mhT z?}GW`-1{p5{uQ8!`*(mJUHT)+UkT%{C|`Mg9cw=lXy57M@BR2IQTP=Am;cw-_$ia0 Zv_W1P0%*y + +# Plot interpolated field as 3D scatter plot + # + +# Show figure + # + + +#################### +### Exercise 1.3 ### +#################### +# Write Sofistik input code to .dat-file for applying settlements as imposed displacements + # + diff --git a/Session 9 - Heatmaps and merging operation/Crack_width_Seg7_y_direction.csv b/Session 9 - Heatmaps and merging operation/Crack_width_Seg7_y_direction.csv new file mode 100644 index 0000000..cc77297 --- /dev/null +++ b/Session 9 - Heatmaps and merging operation/Crack_width_Seg7_y_direction.csv @@ -0,0 +1,1201 @@ +Criterion,x[m],y[m],N[kN/m],M[kNm/m],w_k[mm] +max Ny,22.115,7.603,711.1,-197.8,0.380247700783853 +min My,22.115,7.603,707.2,-198.6,0.380122188346953 +max My,22.115,7.603,-459.6,66.1,0.00255324050766829 +max Ny,22.25,7.603,413.4,-299.1,0.429457484438553 +min My,22.25,7.603,408,-302.2,0.432137439214522 +max My,22.25,7.603,-432.1,87.8,0.0134174317276819 +max Ny,22.25,7.747,401.3,-261.2,0.373611977572572 +min My,22.25,7.747,397.3,-262.8,0.374645662835818 +max My,22.25,7.747,-443.1,80.9,0.00909236008121159 +max Ny,22.115,7.747,692.6,-190.9,0.364905851035598 +min My,22.115,7.747,690.1,-191.4,0.364810361698549 +max My,22.115,7.747,-497,69,0.00206753049198065 +max Ny,22.115,8.159,533.3,-86.5,0.177915944998069 +min My,22.115,8.159,532,-86.7,0.177757785986583 +max My,22.115,8.159,-522.5,56.7,0 +max Ny,22.25,8.159,427.5,-93.2,0.159638363168645 +min My,22.25,8.159,425.7,-93.6,0.159554680807324 +max My,22.25,8.159,-441.8,65.6,0.00308087285039348 +max Ny,22.25,9.141,41.9,-2.3,0 +min My,22.25,9.141,39.9,-2.9,0 +max My,22.25,9.141,-339.4,43.2,0.00047771795801555 +max Ny,22.115,9.141,11,-7.9,0.00847625657598447 +min My,22.115,9.141,-11,-13.3,0.00901643050518952 +max My,22.115,9.141,-380.8,41.7,0 +max Ny,22.115,9.627,-64.7,5.5,0 +min My,22.115,9.627,-95.8,2.5,0 +max My,22.115,9.627,-371.5,31.9,0 +max Ny,22.25,9.627,-52.6,3.7,0 +min My,22.25,9.627,-90.4,-1.6,0 +max My,22.25,9.627,-264.4,29.9,0 +max Ny,22.25,9.973,-41.9,10.9,0.00277161362325132 +min My,22.25,9.973,-46.3,10.3,0.00194958258023449 +max My,22.25,9.973,-226.5,42.4,0.00515180040225427 +max Ny,22.115,9.973,-57.2,8.2,0.00031003670080999 +min My,22.115,9.973,-60.7,7.8,0.000101164668006097 +max My,22.115,9.973,-290.9,30.4,0 +max Ny,22.115,10.185,-23.9,4.1,0.00037184286615936 +min My,22.115,10.185,-31.1,3.2,0 +max My,22.115,10.185,-144.9,17.7,5.70525546540003E-05 +max Ny,22.25,10.185,6.1,3.9,0.00431113674172668 +min My,22.25,10.185,-48.6,1.7,0 +max My,22.25,10.185,-64.3,22.2,0.00816684523368165 +max Ny,22.25,10.415,51.8,0.5,0 +min My,22.25,10.415,3.5,-6.6,0.00603036844854252 +max My,22.25,10.415,24.5,4.1,0.00825876663452618 +max Ny,22.115,10.415,-27.7,1,0 +min My,22.115,10.415,-36.6,0.3,0 +max My,22.115,10.415,-117.5,9.2,0 +max Ny,22.115,10.585,6.1,-3.2,0.00374667801541056 +min My,22.115,10.585,0,-4.1,0.00353544682708009 +max My,22.115,10.585,-45.5,3.2,0 +max Ny,22.25,10.585,-47.1,-8.2,0.000784648994718016 +min My,22.25,10.585,-105.3,-17.3,0.00132518688997526 +max My,22.25,10.585,-130.5,-3.9,0 +max Ny,22.25,10.815,-34.6,-23.6,0.0135638229619693 +min My,22.25,10.815,-81.3,-47,0.0250935049824549 +max My,22.25,10.815,-110,-15.4,0.000492275331579074 +max Ny,22.115,10.815,20.8,-13.5,0.0148633222934274 +min My,22.115,10.815,16.8,-15.9,0.0160611720380014 +max My,22.115,10.815,-18.5,-5.5,0.00170059719303777 +max Ny,22.554,7.603,308.6,-252.4,0.334427932834407 +min My,22.554,7.603,306,-254.2,0.336165456650416 +max My,22.554,7.603,-336.8,93,0.0259477249962396 +max Ny,23.246,7.603,131.5,-194.4,0.204370545102888 +min My,23.246,7.603,127.7,-206.2,0.219639252388743 +max My,23.246,7.603,-139.4,113.6,0.0695979697540626 +max Ny,23.246,7.747,154.9,-170.6,0.177738887324946 +min My,23.246,7.747,151.2,-179.7,0.189373433210329 +max My,23.246,7.747,-138.7,105,0.0627552631440657 +max Ny,22.554,7.747,327.3,-202.2,0.270232915078139 +min My,22.554,7.747,325.5,-203.2,0.271103916428397 +max My,22.554,7.747,-340.4,83.2,0.0189926694084735 +max Ny,22.554,8.159,285.1,-115.7,0.148028887011356 +min My,22.554,8.159,283.7,-116.1,0.148071577264343 +max My,22.554,8.159,-333.6,70.7,0.0119886276234193 +max Ny,23.246,8.159,147,-131.4,0.134249101420092 +min My,23.246,8.159,145.9,-132.5,0.134939308056547 +max My,23.246,8.159,-137.9,81.5,0.0439843231638366 +max 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My,41.915,7.603,-138.1,186.8,0.129364720947079 +max Ny,41.915,7.747,264.2,-56.3,0.0976970677427843 +min My,41.915,7.747,250.5,-68.9,0.104365648637408 +max My,41.915,7.747,-114.7,143.1,0.0976177536947448 +max Ny,41.685,7.747,271.8,-64.3,0.105269266237631 +min My,41.685,7.747,264.9,-70.9,0.108858638120514 +max My,41.685,7.747,-67.3,130.7,0.0954498608714146 +max Ny,41.685,8.159,222.5,-37.6,0.0752525926919475 +min My,41.685,8.159,217.2,-40.1,0.0758306592806969 +max My,41.685,8.159,-92.6,66.6,0.0390715726344036 +max Ny,41.915,8.159,300.2,-33.4,0 +min My,41.915,8.159,294,-35.3,0 +max My,41.915,8.159,-168.3,69.2,0.0298153486654155 +max Ny,41.915,9.141,113.7,-12.2,0 +min My,41.915,9.141,36.9,-29.9,0.031192243228069 +max My,41.915,9.141,79.4,5.7,0 +max Ny,41.685,9.141,121.2,-9.1,0 +min My,41.685,9.141,29.8,-18.6,0.0206952632154996 +max My,41.685,9.141,53.3,8.3,0.0175534120322988 +max Ny,41.685,9.627,73.1,-9.9,0.0231738935950682 +min My,41.685,9.627,18.7,-17.5,0.0177162734897175 +max My,41.685,9.627,31.2,7.2,0.0119478086498383 +max Ny,41.915,9.627,137.4,-8.3,0 +min My,41.915,9.627,5.5,-18,0.0157193642810875 +max My,41.915,9.627,59.8,12.4,0.0218605092240314 +max Ny,41.915,9.973,48.2,-20.8,0.0260128664019971 +min My,41.915,9.973,31.9,-23.9,0.0253839203919317 +max My,41.915,9.973,-30.5,2.2,0 +max Ny,41.685,9.973,40.9,-11.6,0.0173103367822101 +min My,41.685,9.973,14.3,-15.8,0.0155173453759848 +max My,41.685,9.973,5.6,3.3,0.00373135578045392 +max Ny,41.685,10.185,55.5,-6.7,0 +min My,41.685,10.185,37.5,-10.4,0.0156895318759476 +max My,41.685,10.185,-9.5,3.7,0.00152449918835989 +max Ny,41.915,10.185,49.1,-6.5,0.015487139200699 +min My,41.915,10.185,-10.9,-13.1,0.0088700006375178 +max My,41.915,10.185,32.4,3.2,0 +max Ny,41.915,10.415,15.2,-2,0.00478828923150163 +min My,41.915,10.415,-4.1,-19.1,0.0149318541905585 +max My,41.915,10.415,9.4,2,0.00347368303733675 +max Ny,41.685,10.415,36.1,-6.1,0.0122091833024414 +min My,41.685,10.415,26.7,-8.5,0.0120210000364816 +max My,41.685,10.415,-5.2,2.5,0.0012035624359923 +max Ny,41.685,10.585,-1.1,-1.1,0.000714392248603697 +min My,41.685,10.585,-15.8,-4.4,0.00124302246445822 +max My,41.685,10.585,-4.9,0.7,2.58523535626257E-05 +max Ny,41.915,10.585,30.5,0.1,0 +min My,41.915,10.585,-3.2,-3.8,0.00256665339082853 +max My,41.915,10.585,12.5,2.4,0.00442999531653625 +max Ny,41.915,10.815,13,1.9,0.00420237263627688 +min My,41.915,10.815,-8.9,-0.8,0 +max My,41.915,10.815,12.5,2,0.00415184450166357 +max Ny,41.685,10.815,-3.2,-0.5,3.06476200165145E-05 +min My,41.685,10.815,-20.3,-1.9,0 +max My,41.685,10.815,-7.3,-0.1,0 +max Ny,42.127,7.603,288.3,-77.6,0.118810023624563 +min My,42.127,7.603,275.9,-90.3,0.12614639012712 +max My,42.127,7.603,-210.8,220.7,0.152204411595723 +max Ny,42.473,7.603,1014.1,-101.6,0 +min My,42.473,7.603,986.8,-109.5,0 +max My,42.473,7.603,-1117.7,362.3,0.135868452796775 +max Ny,42.473,7.747,960.2,-58.1,0 +min My,42.473,7.747,943.6,-61.9,0 +max My,42.473,7.747,-1139.8,248.8,0.0451648080027733 +max Ny,42.127,7.747,312.8,-54.5,0.106924471151734 +min My,42.127,7.747,298.9,-64.6,0.111198278471008 +max My,42.127,7.747,-173.9,155.9,0.0983192082339231 +max Ny,42.127,8.159,336.5,-28,0 +min My,42.127,8.159,326.4,-30.5,0 +max My,42.127,8.159,-186.8,65.3,0.0243285766398802 +max Ny,42.473,8.159,295.3,-4.9,0 +min My,42.473,8.159,205.4,-13,0 +max My,42.473,8.159,54.4,18.9,0.0257324547221352 +max Ny,42.473,9.141,261.9,-0.1,0 +min My,42.473,9.141,-30,-38.6,0.0264877641601258 +max My,42.473,9.141,213.3,13.2,0 +max Ny,42.127,9.141,162.2,-8.6,0 +min My,42.127,9.141,-2.8,-32,0.0257241275782756 +max My,42.127,9.141,125.3,6.2,0 +max Ny,42.127,9.627,77.8,-16.1,0.0284167955730797 +min My,42.127,9.627,19.6,-23.9,0.0230989531080712 +max My,42.127,9.627,46.9,2.1,0 +max Ny,42.473,9.627,41.7,-26.6,0.0294221753549645 +min My,42.473,9.627,-22.8,-44,0.0321087297084266 +max My,42.473,9.627,13.5,-10.4,0.0109741332174752 +max Ny,42.473,9.973,118.3,-16.8,0.0379456410024312 +min My,42.473,9.973,34.8,-41.9,0.0405761428029153 +max My,42.473,9.973,66.7,14.6,0.0249508320829654 +max Ny,42.127,9.973,33.5,-20.2,0.0226918685063538 +min My,42.127,9.973,7.3,-28.9,0.0249653189322768 +max My,42.127,9.973,22.4,-0.3,0 +max Ny,42.127,10.185,67.2,-11.6,0.0228958475950119 +min My,42.127,10.185,-20.1,-21.8,0.0144368606641429 +max My,42.127,10.185,42.8,2.7,0 +max Ny,42.473,10.185,101,-6.6,0 +min My,42.473,10.185,-113.3,-68.9,0.0376887020195537 +max My,42.473,10.185,55.2,-1.1,0 +max Ny,42.473,10.415,40.9,-0.8,0 +min My,42.473,10.415,-52.4,-23.7,0.0109576269194582 +max My,42.473,10.415,17.9,1.3,0 +max Ny,42.127,10.415,37.3,-9.5,0.0149586592956336 +min My,42.127,10.415,-0.4,-15.9,0.0129550254916192 +max My,42.127,10.415,16.4,2.1,0.00513953747167946 +max Ny,42.127,10.585,15.4,0,0 +min My,42.127,10.585,-9,-11.2,0.00763645883309824 +max My,42.127,10.585,9.6,1.7,0.00330063454318889 +max Ny,42.473,10.585,9.4,-1,0 +min My,42.473,10.585,-15.8,-10.7,0.00613202413813209 +max My,42.473,10.585,2.6,0.7,0.00107160749357407 +max Ny,42.473,10.815,2.8,0.1,0 +min My,42.473,10.815,-2.8,-0.8,0.000234425933624346 +max My,42.473,10.815,1.8,0.7,0.000910396888269344 +max Ny,42.127,10.815,11.8,0.8,0 +min My,42.127,10.815,-11,-3.7,0.00132431621173686 +max My,42.127,10.815,10,1.1,0 diff --git a/Session 9 - Heatmaps and merging operation/Session 9 - Exercise Solutions.html b/Session 9 - Heatmaps and merging operation/Session 9 - Exercise Solutions.html new file mode 100644 index 0000000..e3cde90 --- /dev/null +++ b/Session 9 - Heatmaps and merging operation/Session 9 - Exercise Solutions.html @@ -0,0 +1,12419 @@ + + + +Session 9 - Exercise Solutions + + + + + + + + + + + + + + + + + + + +

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+

Exercise 1

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+
In [13]:
+
+
+
# Read pile data from csv-file
+df_piles = pd.read_csv('piles.csv')
+
+# Read steel profile data from csv-file
+df_profiles = pd.read_csv('steel_profiles.csv')
+
+# Merge dataframes on "Profile" column (similar to Excel VLOOKUP)
+df_merged = df_piles.merge(df_profiles, on='Profile', how='left')
+
+ +
+
+
+ +
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+
In [15]:
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+
+
# Display first five rows of dataframe of steel profiles
+df_profiles.head()
+
+ +
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+ +
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+ + +
+
Out[15]:
+ + +
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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Profileh[mm]b[mm]Iy[mm4]Wel_y[mm3]g[kg/m]
0HE100A96100349000072.816.7
1HE120A1141206060000106.019.9
2HE140A13314010300000155.024.7
3HE160A15216016700000220.030.4
4HE180A17118025100000294.035.5
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In [14]:
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# Display dataframe of piles
+df_piles
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Out[14]:
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Pile_typeProfile
0P01HE200A
1P20HE220A
2P05HE240B
3P23NaN
4P04HE200A
5P01HE300B
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+ +
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+
In [16]:
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+
# Display merged dataframe 
+df_merged
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+ +
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+
Out[16]:
+ + +
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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Pile_typeProfileh[mm]b[mm]Iy[mm4]Wel_y[mm3]g[kg/m]
0P01HE200A190.0200.036900000.0389.042.3
1P20HE220A210.0220.054100000.0515.050.5
2P05HE240B240.0240.0112600000.0938.083.2
3P23NaNNaNNaNNaNNaNNaN
4P04HE200A190.0200.036900000.0389.042.3
5P01HE300B300.0300.0251700000.01680.0117.0
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+

Exercise 2

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+
In [55]:
+
+
+
import pandas as pd
+import matplotlib.pyplot as plt
+import seaborn as sns
+
+# Set filename for dataset of forces from an IBDAS shell element
+filename = 'Crack_width_Seg7_y_direction.csv'
+
+# Read CSV-file
+df = pd.read_csv(filename, skip_blank_lines=True)
+
+# Filter dataframe for load case and criterion for critical combination
+criterion = 'max My'
+df = df[df['Criterion'] == criterion]
+
+df.head()
+
+ +
+
+
+ +
+
+ + +
+
Out[55]:
+ + +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Criterionx[m]y[m]N[kN/m]M[kNm/m]w_k[mm]
2max My22.1157.603-459.666.10.002553
5max My22.2507.603-432.187.80.013417
8max My22.2507.747-443.180.90.009092
11max My22.1157.747-497.069.00.002068
14max My22.1158.159-522.556.70.000000
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In [56]:
+
+
+
# Round dataframe coordinate columns
+df['x[m]'] = round(df['x[m]'], 1)
+df['y[m]'] = round(df['y[m]'], 1)
+
+# Pivot data frame data into matrix form for heatmap plotting
+pivot_final = df.pivot(index='y[m]', columns='x[m]', values='w_k[mm]').sort_index(ascending=False)
+
+# Set max allowable crack with for concrete slab for use as max value of colorbar
+vmax = 0.3
+
+# Create figure
+plt.figure(figsize=(18, 8))
+
+# Plot heatmap wiht annotation
+sns.heatmap(pivot_final, annot=True, annot_kws={'size': 10}, vmax=vmax,
+                  fmt=".2f", square=True, cbar_kws={"orientation": "horizontal"}, cmap='Reds')
+
+# Set titles and axes labels
+plt.title(f'Crack width for Segment 7, Criterion: {criterion}', fontsize=20)
+plt.xlabel('Global x-coordinate [m]', fontsize=16)
+plt.ylabel('Global y-coordinate [m]', fontsize=16)
+
+ +
+
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+ +
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+ + +
+
Out[56]:
+ + + +
+
Text(142,0.5,'Global y-coordinate [m]')
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+

Some extra stuff - Conditional coloring of values

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In [61]:
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+
+
# Create figure
+plt.figure(figsize=(18, 8))
+
+# Plot heatmap wiht annotation, save axes object so it can be accessed later
+ax = sns.heatmap(pivot_final, annot=True, annot_kws={'size': 10}, vmax=vmax,
+                  fmt=".2f", square=True, cbar_kws={"orientation": "horizontal"}, cmap='Reds')
+
+# --- Color values that exceed the max value ---
+
+# Loop over all annotations of the axes object
+for annot in ax.texts:
+    
+    # Annot will now be an object which prints 'Text(x, y, w_k)'
+    
+    # Extract the crack width part of the Text object and convert from string to float 
+    wk = float(annot.get_text())
+    
+    # Set all values that exceed vmax to bold and a special color
+    if wk > vmax: 
+        annot.set_weight('bold')
+        annot.set_color('cyan')
+        annot.set_size(12)
+
+plt.show()
+
+ +
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In [ ]:
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In [ ]:
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In [ ]:
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+ + + + + + diff --git a/Session 9 - Heatmaps and merging operation/Session 9 - Heatmaps and merging operations.html b/Session 9 - Heatmaps and merging operation/Session 9 - Heatmaps and merging operations.html new file mode 100644 index 0000000..42f167c --- /dev/null +++ b/Session 9 - Heatmaps and merging operation/Session 9 - Heatmaps and merging operations.html @@ -0,0 +1,12132 @@ + + + +Session 9 - Heatmaps and merging operations + + + + + + + + + + + + + + + + + + + +
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+

Heatmaps from dataframes

A pandas dataframe can be visualized by means of a so-called heatmap. A heatmap consists of tiles at each data point that adheres to a chosen color palette.

+

Many plotting libraries offer the possibility of creating heatmaps. A common one is called seaborn, which is built on top of matplotlib to enhance certain plot types.

+

Before the dataframe can be plotted to a heatmap, it needs to be in the right format. +If we for example have a dataframe with $x$-values in one column, $y$-values in another and the values to be plotted in a third column we can pivot the data to a new dataframe:

+ +
+
+
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+
In [41]:
+
+
+
import pandas as pd
+
+# Creata a dummy dataframe to pivot
+df = pd.DataFrame({
+    'x': [1, 1, 1, 2, 2, 2, 3, 3, 3],
+    'y': ['a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c'],
+    'values': [34, 74, 1, 9, -36, -24, 47, -27, 47]})
+
+df
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+ +
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Out[41]:
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xyvalues
01a34
11b74
21c1
32a9
42b-36
52c-24
63a47
73b-27
83c47
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In [44]:
+
+
+
# Pivot the dataframe
+df_pivot = df.pivot(index='y', columns='x', values='values')
+df_pivot
+
+ +
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+ +
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+ + +
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Out[44]:
+ + +
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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
x123
y
a34947
b74-36-27
c1-2447
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+

A heatmap can be created from a dataframe like this:

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+
In [43]:
+
+
+
import seaborn as sns
+
+# Plot the pivotted dataframe as a heatmap
+sns.heatmap(df_pivot, annot=True)
+
+ +
+
+
+ +
+
+ + +
+
Out[43]:
+ + + +
+
<matplotlib.axes._subplots.AxesSubplot at 0x28d74e097b8>
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+ +
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+ +
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+ +
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+

Note: Make sure you have installed the seaborn library before using this. Otherwise a ModuleNotFoundError will be raised. +Recall that libraries are installed via the Anaconda Prompt by typing pip install <library_name>.

+

Heatmap parameters

seaborn.heatmap has many parameters for tweaking the appearance of the colormap. Often a bunch of them are needed to create a good looking plot.

+

Special attention should be paid to choosing a colormap that fits the dataset well. +A bad choice in colormap can be very misleading to the reader of the plot, while a well-chosen one can convey the overall message to the reader in very few seconds.

+

See https://seaborn.pydata.org/generated/seaborn.heatmap.html

+

Some of the parameters for seaborn.heatmap:

+
    +
  • annot=True for putting the value in each tile.
    • +
  • fmt to set the number of decimals for the annotated tiles. Set equal to ".0f" for 0 decimals.
    • +
  • annot_kws={'size': 10} for setting fontsize of annotated tiles to 10.
    • +
  • square=True for ensuring that tiles are square.
    • +
  • cmap=name_of_colormap for controlling the colomap (see available colormaps here: https://matplotlib.org/users/colormaps.html, be sure to choose one that fits the content of the data).
    • +
  • vmin and vmax to define the min and max values of the colormap (and colorbar).
    • +
  • cbar_kws={"orientation": "horizontal"} for orientation of the colorbar. Here set to horizontal but is vertical as default.
    • +
+ +
+
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+
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+
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+

Merge operations on dataframes

Merge operations provide very powerful manipulation techniques in pandas. We are only gonna look at a simple example here, which will perform an operation similar ti Excel's VLOOKUP.

+
# Merge df1 and df2 on <column_to_merge_on>, retain only rows from df1  (similar to Excel VLOOKUP)
+df_merged = df1.merge(df2, on='<column_to_merge_on>', how='left')
+
+

See this page of the pandas documentation for more on merging, joining and concatenating dataframes: https://pandas.pydata.org/pandas-docs/stable/user_guide/merging.html

+ +
+
+
+
+
+
+
+
+

Exercise 1

The file piles.csv in the session folder contains some piles and their profile type. Use steel_profiles.csv to insert the cross sectional parameters in each pile row. Use the merging operation described above.

+ +
+
+
+
+
+
+
+
+

Exercise 2

The file Crack_width_Seg7_y_direction.csv has results of a crack width calculation in a base slab from the ESS project.

+

The sectional forces from IBDAS were exported into Excel and each $(N, M)$ pair was run through our standard spreadsheet for calculating the crack with in the Quasi-Permanent load combination. +The results were exported to this csv-file in order to create a presentable plot for the documentation report.

+

While doing the exercises below, recall that df.head() will print the first five rows of df.

+

Exercise 2.1

Load the file Crack_width_Seg7_y_direction.csv into a dataframe. Filter the dataframe so it only contains rows where the criterion column has max My.

+

Exercise 2.2

Pivot the dataframe and save it to a new dataframe. Use column 'y[m]' as index, column 'x[m]' as columns and column 'w_k[mm]' as values.

+

Exercise 2.3

Create a heatmap of the pivotted dataframe. Use parameters of your choice from the ones described above or in the pandas documentation.

+

Be sure to choose a colormap, the default one is awful. The maximum allowable crack width for this concrete slab is $w_{k.max} = 0.30$mm.

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In [ ]:
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+
+
+ + + + + + diff --git a/Session 9 - Heatmaps and merging operation/piles.csv b/Session 9 - Heatmaps and merging operation/piles.csv new file mode 100644 index 0000000..6827b71 --- /dev/null +++ b/Session 9 - Heatmaps and merging operation/piles.csv @@ -0,0 +1,7 @@ +Pile_type,Profile +P01,HE200A +P20,HE220A +P05,HE240B +P23,NaN +P04,HE200A +P01,HE300B \ No newline at end of file diff --git a/Session 9 - Heatmaps and merging operation/steel_profiles.csv b/Session 9 - Heatmaps and merging operation/steel_profiles.csv new file mode 100644 index 0000000..70c24f8 --- /dev/null +++ b/Session 9 - Heatmaps and merging operation/steel_profiles.csv @@ -0,0 +1,23 @@ +Profile,h[mm],b[mm],Iy[mm4],Wel_y[mm3],g[kg/m] +HE100A,96,100,3490000,72.8,16.7 +HE120A,114,120,6060000,106,19.9 +HE140A,133,140,10300000,155,24.7 +HE160A,152,160,16700000,220,30.4 +HE180A,171,180,25100000,294,35.5 +HE200A,190,200,36900000,389,42.3 +HE220A,210,220,54100000,515,50.5 +HE240A,230,240,77600000,675,60.3 +HE260A,250,260,104500000,836,68.2 +HE280A,270,280,136700000,1010,76.4 +HE300A,290,300,182600000,1260,88.3 +HE100B,100,100,4500000,89.9,20.4 +HE120B,120,120,8640000,144,26.7 +HE140B,140,140,15100000,216,33.7 +HE160B,160,160,24900000,311,42.6 +HE180B,180,180,38300000,426,51.2 +HE200B,200,200,57000000,570,61.3 +HE220B,220,220,80900000,736,71.5 +HE240B,240,240,112600000,938,83.2 +HE260B,260,260,149200000,1150,93.0 +HE280B,280,280,192700000,1380,103.0 +HE300B,300,300,251700000,1680,117.0 \ No newline at end of file