Magnitude gradient along flowlines

Created by Mauro Alberti

Last run: 2019-06-16



In [1]:

    
import math



In [2]:

    
import numpy as np



In [3]:

    
from pygsf.spatial.rasters.fields import *

Test 1



In [4]:

    
fx = np.array([
    [1,1,1],
    [1,1,1],
    [1,1,1]
])



In [5]:

    
fx









    Out[5]:





array([[1, 1, 1],
       [1, 1, 1],
       [1, 1, 1]])



In [6]:

    
fy = np.array([
    [2,2,2],
    [2,2,2],
    [2,2,2]
])



In [7]:

    
magn = magnitude(fx, fy)



In [8]:

    
magn









    Out[8]:





array([[2.23606798, 2.23606798, 2.23606798],
       [2.23606798, 2.23606798, 2.23606798],
       [2.23606798, 2.23606798, 2.23606798]])



In [9]:

    
math.sqrt(1 + 2**2)









    Out[9]:





2.23606797749979



In [10]:

    
oriens_d = orients_d(fx, fy)



In [11]:

    
oriens_d









    Out[11]:





array([[26.56505118, 26.56505118, 26.56505118],
       [26.56505118, 26.56505118, 26.56505118],
       [26.56505118, 26.56505118, 26.56505118]])



In [12]:

    
math.degrees(math.atan(0.5))









    Out[12]:





26.56505117707799



In [13]:

    
magn_grad_along_flowlines(fx, fy, 10, 10)









    Out[13]:





array([[0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.]])

The previous result is correct.

Test 2



In [14]:

    
fx = np.array([
    [1,2,3],
    [1,2,3],
    [1,2,3]
])



In [15]:

    
fy = np.array([
    [0,0,0],
    [0,0,0],
    [0,0,0]
])



In [16]:

    
oriens_d = orients_d(fx, fy)



In [17]:

    
oriens_d









    Out[17]:





array([[90., 90., 90.],
       [90., 90., 90.],
       [90., 90., 90.]])



In [18]:

    
magnitude(fx, fy)









    Out[18]:





array([[1., 2., 3.],
       [1., 2., 3.],
       [1., 2., 3.]])



In [19]:

    
np.sqrt(fx**2 + fy**2)









    Out[19]:





array([[1., 2., 3.],
       [1., 2., 3.],
       [1., 2., 3.]])



In [20]:

    
magn_grad_along_flowlines(
        fld_x=fx,
        fld_y=fy,
        cell_size_x=10,
        cell_size_y=10)









    Out[20]:





array([[0.1, 0.1, 0.1],
       [0.1, 0.1, 0.1],
       [0.1, 0.1, 0.1]])



In [21]:

    
orien_rad = orients_r(fx, fy)



In [22]:

    
dm_dx, dm_dy = magn_grads(
    fld_x=fx,
    fld_y=fy,
    dir_cell_sizes=[1, 1])



In [23]:

    
dm_dx









    Out[23]:





array([[1., 1., 1.],
       [1., 1., 1.],
       [1., 1., 1.]])



In [24]:

    
dm_dy









    Out[24]:





array([[-0., -0., -0.],
       [-0., -0., -0.],
       [-0., -0., -0.]])



In [25]:

    
velocity_gradient = dm_dx * np.sin(orien_rad) + dm_dy * np.cos(orien_rad)



In [26]:

    
velocity_gradient









    Out[26]:





array([[1., 1., 1.],
       [1., 1., 1.],
       [1., 1., 1.]])

Results correct.

Test 3



In [27]:

    
fx = np.array([
    [1,2,3],
    [2,3,4],
    [3,4,5]
])



In [28]:

    
fy = -fx



In [29]:

    
magn = magnitude(fx, fy)



In [30]:

    
magn









    Out[30]:





array([[1.41421356, 2.82842712, 4.24264069],
       [2.82842712, 4.24264069, 5.65685425],
       [4.24264069, 5.65685425, 7.07106781]])



In [31]:

    
oriens_d = orients_d(fx, fy)



In [32]:

    
oriens_d









    Out[32]:





array([[135., 135., 135.],
       [135., 135., 135.],
       [135., 135., 135.]])



In [33]:

    
magn_grad_along_flowlines(
        fld_x=fx,
        fld_y=fy,
        cell_size_x=1,
        cell_size_y=1)









    Out[33]:





array([[2., 2., 2.],
       [2., 2., 2.],
       [2., 2., 2.]])

Cell (0,0) vs. cell (1,1):

sqrt(2) vs. 3 sqrt(2)

dist = sqrt(2)

gradient = (3sqrt(2) - sqrt(2))/sqrt(2) = 2

Result is correct.



In [34]:

    
magn_grad_along_flowlines(
        fld_x=fx,
        fld_y=fy,
        cell_size_x=10,
        cell_size_y=10)









    Out[34]:





array([[0.2, 0.2, 0.2],
       [0.2, 0.2, 0.2],
       [0.2, 0.2, 0.2]])

Result is correct.