Homework 6

analytics.py

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+import math     # For all of the math used
+# import utils
+
+from utils import generate_rand_points
+# ------------------------------------------------------------------
+#
+# Joseph Cruz
+# analytics.py
+#
+# Stores the functions from point_pattern.py that perform analysis
+# on data.
+# ------------------------------------------------------------------
+
+# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+#
+# function mean_nearest_neighbors_randomPoints
+#
+# Determines the mean nearest neighbor of randomly generated points
+# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+
+
+def permutations(p = 99, n = 100):
+    list_means = []
+
+    for i in range(p):
+        # randPoints = utils.generate_rand_points(n)
+        rand_points = generate_rand_points(n)
+        newMean = average_nearest_neighbor_distance(rand_points)
+        list_means.append(newMean)
+
+    return list_means
+
+#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+#
+# function find_crit_points
+#
+# Finds the critical points (min and max) of a list
+#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+
+
+def find_crit_points(list_means):
+    entries = list_means
+    maxEntry = 0
+    minEntry = 2
+    for i in range(len(list_means)):
+        if entries[i] > maxEntry:
+            maxEntry = entries[i]
+        if entries[i] < minEntry:
+            minEntry = entries[i]
+
+    return minEntry,maxEntry
+
+#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+#
+# function crit_point_check
+#
+# Checks if the observed value is within the range of the min and max
+#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+
+
+def crit_point_check(minEntry, maxEntry, observed):
+    if observed < minEntry or observed > maxEntry:
+        return True
+    else:
+        return False
+
+
+def mean_center(points):
+    """
+    Given a set of points, compute the mean center
+
+    Parameters
+    ----------
+    points : list
+         A list of points in the form (x,y)
+
+    Returns
+    -------
+    x : float
+        Mean x coordinate
+
+    y : float
+        Mean y coordinate
+    """
+    x = 0
+    y = 0
+    numOfPoints = len(points)
+
+    for i in range(numOfPoints):
+        x = x + points[i][0]
+        y = y + points[i][1]
+
+    x = x/numOfPoints
+    y = y/numOfPoints
+
+    return x, y
+
+def average_nearest_neighbor_distance(points):
+    """
+    Given a set of points, compute the average nearest neighbor.
+
+    Parameters
+    ----------
+    points : list
+             A list of points in the form (x,y)
+
+    Returns
+    -------
+    mean_d : float
+             Average nearest neighbor distance
+
+    References
+    ----------
+    Clark and Evan (1954 Distance to Nearest Neighbor as a
+     Measure of Spatial Relationships in Populations. Ecology. 35(4)
+     p. 445-453.
+    """
+    mean_d = 0
+    total = 0
+    local_nn = 0
+    numOfPoints = len(points)
+
+    for i in range(numOfPoints):
+        local_nn = 0 #reset local_nn for the new point
+        for j in range(numOfPoints):
+            if i != j:
+                newDistance = euclidean_distance(points[i],points[j])
+                if local_nn == 0:
+                    local_nn = newDistance
+                elif newDistance < local_nn:
+                    local_nn = newDistance
+
+        total = total + local_nn
+
+    mean_d = total/numOfPoints
+
+
+    return mean_d
+
+
+def minimum_bounding_rectangle(points):
+    """
+    Given a set of points, compute the minimum bounding rectangle.
+
+    Parameters
+    ----------
+    points : list
+             A list of points in the form (x,y)
+
+    Returns
+    -------
+     : list
+       Corners of the MBR in the form [xmin, ymin, xmax, ymax]
+    """
+    mbr = [0,0,0,0]
+    numOfPoints = len(points)
+    for i in range(numOfPoints):
+        #Check for min and max x
+        if points[i][0] < mbr[0]:
+            mbr[0] = points[i][0]
+        if points[i][0] > mbr[2]:
+            mbr[2] = points[i][0]
+        #Check for min and max y
+        if points[i][1] < mbr[1]:
+            mbr[1] = points[i][1]
+        if points[i][1] > mbr[3]:
+            mbr[3] = points[i][1]
+
+    return mbr
+
+
+def mbr_area(mbr):
+    """
+    Compute the area of a minimum bounding rectangle
+    """
+    area = (mbr[2] - mbr[0])*(mbr[3] - mbr[1])
+
+    return area
+
+
+def expected_distance(area, n):
+    """
+    Compute the expected mean distance given
+    some study area.
+
+    This makes lots of assumptions and is not
+    necessarily how you would want to compute
+    this.  This is just an example of the full
+    analysis pipe, e.g. compute the mean distance
+    and the expected mean distance.
+
+    Parameters
+    ----------
+    area : float
+           The area of the study area
+
+    n : int
+        The number of points
+    """
+
+    expected = (1/2)*math.sqrt(area/n)
+    return expected
+
+def manhattan_distance(a, b):
+    """
+    Compute the Manhattan distance between two points
+
+    Parameters
+    ----------
+    a : tuple
+        A point in the form (x,y)
+
+    b : tuple
+        A point in the form (x,y)
+
+    Returns
+    -------
+    distance : float
+               The Manhattan distance between the two points
+    """
+    distance =  abs(a[0] - b[0]) + abs(a[1] - b[1])
+    return distance
+
+
+def euclidean_distance(a, b):
+    """
+    Compute the Euclidean distance between two points
+
+    Parameters
+    ----------
+    a : tuple
+        A point in the form (x,y)
+
+    b : tuple
+        A point in the form (x,y)
+
+    Returns
+    -------
+
+    distance : float
+               The Euclidean distance between the two points
+    """
+    distance = math.sqrt((a[0] - b[0])**2 + (a[1] - b[1])**2)
+    return distance
+
+def check_coincident(a, b):
+    """
+    Check whether two points are coincident
+    Parameters
+    ----------
+    a : tuple
+        A point in the form (x,y)
+
+    b : tuple
+        A point in the form (x,y)
+
+    Returns
+    -------
+    equal : bool
+            Whether the points are equal
+    """
+    return a == b
+
+
+def check_in(point, point_list):
+    """
+    Check whether point is in the point list
+
+    Parameters
+    ----------
+    point : tuple
+            In the form (x,y)
+
+    point_list : list
+                 in the form [point, point_1, point_2, ..., point_n]
+    """
+    return point in point_list
+