solutions update from 7ed0c61

correct 2D Gaussian + add separable alternative answer

.github/workflows/generate_solutions_files.yml

@@ -0,0 +1,46 @@
+name: Generate Solutions Files
+
+on:
+  push:
+    branches:
+      - master
+    paths:
+      - source/exercises100.ktx
+
+jobs:
+  generate_files:
+    runs-on: ubuntu-22.04 # Python 3.7 is not supported on latest Ubuntu
+
+    permissions:
+      contents: write
+
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@v4
+
+      - name: Setup Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: '3.7'
+          cache: 'pip'
+
+      - name: Install dependencies
+        run: pip3 install -r requirements.txt
+
+      - name: Generate solutions files
+        run: python3 generators.py
+
+      - name: Set environment variables
+        run: echo "SHA_SHORT=$(git rev-parse --short $GITHUB_SHA)" >> $GITHUB_ENV
+
+      - name: Commit changes
+        uses: stefanzweifel/git-auto-commit-action@v5
+        with:
+          commit_message: "solutions update from ${{ env.SHA_SHORT }}"
+          file_pattern: >
+            100_Numpy_exercises.ipynb
+            100_Numpy_random.ipynb
+            100_Numpy_exercises.md
+            100_Numpy_exercises_with_hints.md
+            100_Numpy_exercises_with_hints_with_solutions.md
+            100_Numpy_exercises_with_solutions.md

100_Numpy_exercises.md

@@ -3,15 +3,12 @@
 
 # 100 numpy exercises
 
-This is a collection of exercises that have been collected in the numpy mailing list, on stack 
-overflow
+This is a collection of exercises that have been collected in the numpy mailing list, on stack overflow
 and in the numpy documentation. The goal of this collection is to offer a quick reference for both old
-and new 
-users but also to provide a set of exercises for those who teach.
+and new users but also to provide a set of exercises for those who teach.
 
 
-If you find an error or think you've a better way to
- solve some of them, feel
+If you find an error or think you've a better way to solve some of them, feel
 free to open an issue at <https://github.com/rougier/numpy-100>.
 File automatically generated. See the documentation to update questions/answers/hints programmatically.
 
@@ -128,7 +125,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 
 #### 41. How to sum a small array faster than np.sum? (★★☆)
 
-#### 42. Consider two random array A and B, check if they are equal (★★☆)
+#### 42. Consider two random arrays A and B, check if they are equal (★★☆)
 
 #### 43. Make an array immutable (read-only) (★★☆)
 
@@ -140,7 +137,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 
 #### 47. Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj)) (★★☆)
 
-#### 48. Print the minimum and maximum representable value for each numpy scalar type (★★☆)
+#### 48. Print the minimum and maximum representable values for each numpy scalar type (★★☆)
 
 #### 49. How to print all the values of an array? (★★☆)
 
@@ -150,7 +147,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 
 #### 52. Consider a random vector with shape (100,2) representing coordinates, find point by point distances (★★☆)
 
-#### 53. How to convert a float (32 bits) array into an integer (32 bits) in place?
+#### 53. How to convert a float (32 bits) array into an integer (32 bits) array in place?
 
 #### 54. How to read the following file? (★★☆)
 ```
@@ -191,7 +188,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 
 #### 70. Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3 consecutive zeros interleaved between each value? (★★★)
 
-#### 71. Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★)
+#### 71. Consider an array of dimension (5,5,3), how to multiply it by an array with dimensions (5,5)? (★★★)
 
 #### 72. How to swap two rows of an array? (★★★)
 
@@ -209,7 +206,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 
 #### 79. Consider 2 sets of points P0,P1 describing lines (2d) and a set of points P, how to compute distance from each point j (P[j]) to each line i (P0[i],P1[i])? (★★★)
 
-#### 80. Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
+#### 80. Consider an arbitrary array, write a function that extracts a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
 
 #### 81. Consider an array Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14], how to generate an array R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ..., [11,12,13,14]]? (★★★)
 
@@ -221,7 +218,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 
 #### 85. Create a 2D array subclass such that Z[i,j] == Z[j,i] (★★★)
 
-#### 86. Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)
+#### 86. Consider a set of p matrices with shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)
 
 #### 87. Consider a 16x16 array, how to get the block-sum (block size is 4x4)? (★★★)
 
@@ -229,7 +226,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 
 #### 89. How to get the n largest values of an array (★★★)
 
-#### 90. Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★)
+#### 90. Given an arbitrary number of vectors, build the cartesian product (every combination of every item) (★★★)
 
 #### 91. How to create a record array from a regular array? (★★★)
 

100_Numpy_exercises_with_hints.md

@@ -3,15 +3,12 @@
 
 # 100 numpy exercises
 
-This is a collection of exercises that have been collected in the numpy mailing list, on stack 
-overflow
+This is a collection of exercises that have been collected in the numpy mailing list, on stack overflow
 and in the numpy documentation. The goal of this collection is to offer a quick reference for both old
-and new 
-users but also to provide a set of exercises for those who teach.
+and new users but also to provide a set of exercises for those who teach.
 
 
-If you find an error or think you've a better way to
- solve some of them, feel
+If you find an error or think you've a better way to solve some of them, feel
 free to open an issue at <https://github.com/rougier/numpy-100>.
 File automatically generated. See the documentation to update questions/answers/hints programmatically.
 
@@ -128,7 +125,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 `hint: sort`
 #### 41. How to sum a small array faster than np.sum? (★★☆)
 `hint: np.add.reduce`
-#### 42. Consider two random array A and B, check if they are equal (★★☆)
+#### 42. Consider two random arrays A and B, check if they are equal (★★☆)
 `hint: np.allclose, np.array_equal`
 #### 43. Make an array immutable (read-only) (★★☆)
 `hint: flags.writeable`
@@ -140,7 +137,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 `hint: np.meshgrid`
 #### 47. Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj)) (★★☆)
 `hint: np.subtract.outer`
-#### 48. Print the minimum and maximum representable value for each numpy scalar type (★★☆)
+#### 48. Print the minimum and maximum representable values for each numpy scalar type (★★☆)
 `hint: np.iinfo, np.finfo, eps`
 #### 49. How to print all the values of an array? (★★☆)
 `hint: np.set_printoptions`
@@ -150,7 +147,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 `hint: dtype`
 #### 52. Consider a random vector with shape (100,2) representing coordinates, find point by point distances (★★☆)
 `hint: np.atleast_2d, T, np.sqrt`
-#### 53. How to convert a float (32 bits) array into an integer (32 bits) in place?
+#### 53. How to convert a float (32 bits) array into an integer (32 bits) array in place?
 `hint: view and [:] =`
 #### 54. How to read the following file? (★★☆)
 ```
@@ -191,7 +188,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 `hint: np.diag`
 #### 70. Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3 consecutive zeros interleaved between each value? (★★★)
 `hint: array[::4]`
-#### 71. Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★)
+#### 71. Consider an array of dimension (5,5,3), how to multiply it by an array with dimensions (5,5)? (★★★)
 `hint: array[:, :, None]`
 #### 72. How to swap two rows of an array? (★★★)
 `hint: array[[]] = array[[]]`
@@ -209,7 +206,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 `No hints provided...`
 #### 79. Consider 2 sets of points P0,P1 describing lines (2d) and a set of points P, how to compute distance from each point j (P[j]) to each line i (P0[i],P1[i])? (★★★)
 `No hints provided...`
-#### 80. Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
+#### 80. Consider an arbitrary array, write a function that extracts a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
 `hint: minimum maximum`
 #### 81. Consider an array Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14], how to generate an array R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ..., [11,12,13,14]]? (★★★)
 `hint: stride_tricks.as_strided, from numpy.lib.stride_tricks import sliding_window_view (np>=1.20.0)`
@@ -221,7 +218,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 `hint: stride_tricks.as_strided, from numpy.lib.stride_tricks import sliding_window_view (np>=1.20.0)`
 #### 85. Create a 2D array subclass such that Z[i,j] == Z[j,i] (★★★)
 `hint: class method`
-#### 86. Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)
+#### 86. Consider a set of p matrices with shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)
 `hint: np.tensordot`
 #### 87. Consider a 16x16 array, how to get the block-sum (block size is 4x4)? (★★★)
 `hint: np.add.reduceat, from numpy.lib.stride_tricks import sliding_window_view (np>=1.20.0)`
@@ -229,7 +226,7 @@ np.sqrt(-1) == np.emath.sqrt(-1)
 `No hints provided...`
 #### 89. How to get the n largest values of an array (★★★)
 `hint: np.argsort | np.argpartition`
-#### 90. Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★)
+#### 90. Given an arbitrary number of vectors, build the cartesian product (every combination of every item) (★★★)
 `hint: np.indices`
 #### 91. How to create a record array from a regular array? (★★★)
 `hint: np.core.records.fromarrays`

100_Numpy_exercises_with_hints_with_solutions.md

@@ -3,15 +3,12 @@
 
 # 100 numpy exercises
 
-This is a collection of exercises that have been collected in the numpy mailing list, on stack 
-overflow
+This is a collection of exercises that have been collected in the numpy mailing list, on stack overflow
 and in the numpy documentation. The goal of this collection is to offer a quick reference for both old
-and new 
-users but also to provide a set of exercises for those who teach.
+and new users but also to provide a set of exercises for those who teach.
 
 
-If you find an error or think you've a better way to
- solve some of them, feel
+If you find an error or think you've a better way to solve some of them, feel
 free to open an issue at <https://github.com/rougier/numpy-100>.
 File automatically generated. See the documentation to update questions/answers/hints programmatically.
 
@@ -41,6 +38,9 @@ print(Z)
 ```python
 Z = np.zeros((10,10))
 print("%d bytes" % (Z.size * Z.itemsize))
+
+# Simpler alternative
+print("%d bytes" % Z.nbytes)
 ```
 #### 5. How to get the documentation of the numpy add function from the command line? (★☆☆)
 `hint: np.info`
@@ -131,7 +131,7 @@ Z = np.ones((5,5))
 Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0)
 print(Z)
 
-# Using fancy indexing
+# Not a solution to this problem but good to know: using fancy indexing for in-place edit
 Z[:, [0, -1]] = 0
 Z[[0, -1], :] = 0
 print(Z)
@@ -205,7 +205,7 @@ color = np.dtype([("r", np.ubyte),
 `hint:`
 
 ```python
-Z = np.dot(np.ones((5,3)), np.ones((3,2)))
+Z = np.matmul(np.ones((5, 3)), np.ones((3, 2)))
 print(Z)
 
 # Alternative solution, in Python 3.5 and above
@@ -399,7 +399,7 @@ print(Z)
 Z = np.arange(10)
 np.add.reduce(Z)
 ```
-#### 42. Consider two random array A and B, check if they are equal (★★☆)
+#### 42. Consider two random arrays A and B, check if they are equal (★★☆)
 `hint: np.allclose, np.array_equal`
 
 ```python
@@ -461,7 +461,7 @@ Y = X + 0.5
 C = 1.0 / np.subtract.outer(X, Y)
 print(np.linalg.det(C))
 ```
-#### 48. Print the minimum and maximum representable value for each numpy scalar type (★★☆)
+#### 48. Print the minimum and maximum representable values for each numpy scalar type (★★☆)
 `hint: np.iinfo, np.finfo, eps`
 
 ```python
@@ -519,7 +519,7 @@ Z = np.random.random((10,2))
 D = scipy.spatial.distance.cdist(Z,Z)
 print(D)
 ```
-#### 53. How to convert a float (32 bits) array into an integer (32 bits) in place?
+#### 53. How to convert a float (32 bits) array into an integer (32 bits) array in place?
 `hint: view and [:] =`
 
 ```python
@@ -548,7 +548,7 @@ s = StringIO('''1, 2, 3, 4, 5
 
                  ,  , 9,10,11
 ''')
-Z = np.genfromtxt(s, delimiter=",", dtype=np.int)
+Z = np.genfromtxt(s, delimiter=",", dtype = int, filling_values = 0)
 print(Z)
 ```
 #### 55. What is the equivalent of enumerate for numpy arrays? (★★☆)
@@ -566,9 +566,17 @@ for index in np.ndindex(Z.shape):
 
 ```python
 X, Y = np.meshgrid(np.linspace(-1, 1, 10), np.linspace(-1, 1, 10))
-D = np.sqrt(X*X+Y*Y)
 sigma, mu = 1.0, 0.0
-G = np.exp(-( (D-mu)**2 / ( 2.0 * sigma**2 ) ) )
+G = np.exp(-((X - mu) ** 2 + (Y - mu) ** 2) / (2.0 * sigma**2))
+print(G)
+
+# Another solution using the fact that a 2D Gaussian is separable
+# Author: Nin17
+x = np.linspace(-1, 1, 10)
+y = np.linspace(-1, 1, 10)
+gx = np.exp(-((x - mu) ** 2 / (2.0 * sigma**2)))
+gy = np.exp(-((y - mu) ** 2 / (2.0 * sigma**2)))
+G = gy[:, None] * gx[None, :]
 print(G)
 ```
 #### 57. How to randomly place p elements in a 2D array? (★★☆)
@@ -615,8 +623,17 @@ print(Z[Z[:,1].argsort()])
 ```python
 # Author: Warren Weckesser
 
+# null : 0 
 Z = np.random.randint(0,3,(3,10))
 print((~Z.any(axis=0)).any())
+
+# null : np.nan
+Z=np.array([
+    [0,1,np.nan],
+    [1,2,np.nan],
+    [4,5,np.nan]
+])
+print(np.isnan(Z).all(axis=0))
 ```
 #### 61. Find the nearest value from a given value in an array (★★☆)
 `hint: np.abs, argmin, flat`
@@ -648,7 +665,7 @@ class NamedArray(np.ndarray):
         return obj
     def __array_finalize__(self, obj):
         if obj is None: return
-        self.info = getattr(obj, 'name', "no name")
+        self.name = getattr(obj, 'name', "no name")
 
 Z = NamedArray(np.arange(10), "range_10")
 print (Z.name)
@@ -766,7 +783,7 @@ Z0 = np.zeros(len(Z) + (len(Z)-1)*(nz))
 Z0[::nz+1] = Z
 print(Z0)
 ```
-#### 71. Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★)
+#### 71. Consider an array of dimension (5,5,3), how to multiply it by an array with dimensions (5,5)? (★★★)
 `hint: array[:, :, None]`
 
 ```python
@@ -864,7 +881,27 @@ np.negative(Z, out=Z)
 `No hints provided...`
 
 ```python
-def distance(P0, P1, p):
+P0 = np.random.uniform(-10,10,(10,2))
+P1 = np.random.uniform(-10,10,(10,2))
+p  = np.random.uniform(-10,10,( 1,2))
+
+def distance_faster(P0,P1,p):
+    #Author: Hemanth Pasupuleti
+    #Reference: https://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
+
+    v = P1- P0 
+    v[:,[0,1]] = v[:,[1,0]]
+    v[:,1]*=-1 
+    norm = np.linalg.norm(v,axis=1)   
+    r = P0 - p
+    d = np.abs(np.einsum("ij,ij->i",r,v)) / norm 
+
+    return d
+
+print(distance_faster(P0, P1, p))
+
+##--------------- OR ---------------##
+def distance_slower(P0, P1, p):
     T = P1 - P0
     L = (T**2).sum(axis=1)
     U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / L
@@ -872,10 +909,7 @@ def distance(P0, P1, p):
     D = P0 + U*T - p
     return np.sqrt((D**2).sum(axis=1))
 
-P0 = np.random.uniform(-10,10,(10,2))
-P1 = np.random.uniform(-10,10,(10,2))
-p  = np.random.uniform(-10,10,( 1,2))
-print(distance(P0, P1, p))
+print(distance_slower(P0, P1, p))
 ```
 #### 79. Consider 2 sets of points P0,P1 describing lines (2d) and a set of points P, how to compute distance from each point j (P[j]) to each line i (P0[i],P1[i])? (★★★)
 `No hints provided...`
@@ -888,8 +922,34 @@ P0 = np.random.uniform(-10, 10, (10,2))
 P1 = np.random.uniform(-10,10,(10,2))
 p = np.random.uniform(-10, 10, (10,2))
 print(np.array([distance(P0,P1,p_i) for p_i in p]))
+
+# Author: Yang Wu (Broadcasting)
+def distance_points_to_lines(p: np.ndarray, p_1: np.ndarray, p_2: np.ndarray) -> np.ndarray:
+    x_0, y_0 = p.T  # Shape -> (n points, )
+    x_1, y_1 = p_1.T  # Shape -> (n lines, )
+    x_2, y_2 = p_2.T  # Shape -> (n lines, )
+
+    # Displacement vector coordinates from p_1 -> p_2
+    dx = x_2 - x_1  # Shape -> (n lines, )
+    dy = y_2 - y_1  # Shape -> (n lines, )
+
+    # The 'cross product' term
+    cross_term = x_2 * y_1 - y_2 * x_1  # Shape -> (n lines, )
+
+    # Broadcast x_0, y_0 (n points, 1) and dx, dy, cross_term (1, n lines) -> (n points, n lines)
+    numerator = np.abs(
+        dy[np.newaxis, :] * x_0[:, np.newaxis]
+        - dx[np.newaxis, :] * y_0[:, np.newaxis]
+        + cross_term[np.newaxis, :]
+    )
+    denominator = np.sqrt(dx**2 + dy**2)  # Shape -> (n lines, )
+
+    # Shape (n points, n lines) / (1, n_lines) -> (n points, n lines)
+    return numerator / denominator[np.newaxis, :]
+
+distance_points_to_lines(p, P0, P1)
 ```
-#### 80. Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
+#### 80. Consider an arbitrary array, write a function that extracts a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
 `hint: minimum maximum`
 
 ```python
@@ -915,8 +975,8 @@ Z_start = (np.maximum(Z_start,0)).tolist()
 R_stop = np.maximum(R_start, (R_stop - np.maximum(Z_stop-Zs,0))).tolist()
 Z_stop = (np.minimum(Z_stop,Zs)).tolist()
 
-r = [slice(start,stop) for start,stop in zip(R_start,R_stop)]
-z = [slice(start,stop) for start,stop in zip(Z_start,Z_stop)]
+r = tuple([slice(start,stop) for start,stop in zip(R_start,R_stop)])
+z = tuple([slice(start,stop) for start,stop in zip(Z_start,Z_stop)])
 R[r] = Z[z]
 print(Z)
 print(R)
@@ -944,7 +1004,8 @@ print(sliding_window_view(Z, window_shape=4))
 
 Z = np.random.uniform(0,1,(10,10))
 U, S, V = np.linalg.svd(Z) # Singular Value Decomposition
-rank = np.sum(S > 1e-10)
+threshold = len(S) * S.max() * np.finfo(S.dtype).eps
+rank = np.sum(S > threshold)
 print(rank)
 
 # alternative solution:
@@ -998,7 +1059,7 @@ S = symetric(np.random.randint(0,10,(5,5)))
 S[2,3] = 42
 print(S)
 ```
-#### 86. Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)
+#### 86. Consider a set of p matrices with shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)
 `hint: np.tensordot`
 
 ```python
@@ -1037,11 +1098,8 @@ k = 4
 windows = np.lib.stride_tricks.sliding_window_view(Z, (k, k))
 S = windows[::k, ::k, ...].sum(axis=(-2, -1))
 
-# Author: Jeff Luo (@Jeff1999)
-
-Z = np.ones((16, 16))
-k = 4
-print(sliding_window_view(Z, window_shape=(k, k))[::k, ::k].sum(axis=(-2, -1)))
+# alternative solution (by @Gattocrucco)
+S = Z.reshape(4, 4, 4, 4).sum((1, 3))
 ```
 #### 88. How to implement the Game of Life using numpy arrays? (★★★)
 `No hints provided...`
@@ -1080,7 +1138,7 @@ print (Z[np.argsort(Z)[-n:]])
 # Fast
 print (Z[np.argpartition(-Z,n)[:n]])
 ```
-#### 90. Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★)
+#### 90. Given an arbitrary number of vectors, build the cartesian product (every combination of every item) (★★★)
 `hint: np.indices`
 
 ```python

100_Numpy_exercises_with_solutions.md

@@ -3,15 +3,12 @@
 
 # 100 numpy exercises
 
-This is a collection of exercises that have been collected in the numpy mailing list, on stack 
-overflow
+This is a collection of exercises that have been collected in the numpy mailing list, on stack overflow
 and in the numpy documentation. The goal of this collection is to offer a quick reference for both old
-and new 
-users but also to provide a set of exercises for those who teach.
+and new users but also to provide a set of exercises for those who teach.
 
 
-If you find an error or think you've a better way to
- solve some of them, feel
+If you find an error or think you've a better way to solve some of them, feel
 free to open an issue at <https://github.com/rougier/numpy-100>.
 File automatically generated. See the documentation to update questions/answers/hints programmatically.
 
@@ -41,6 +38,9 @@ print(Z)
 ```python
 Z = np.zeros((10,10))
 print("%d bytes" % (Z.size * Z.itemsize))
+
+# Simpler alternative
+print("%d bytes" % Z.nbytes)
 ```
 #### 5. How to get the documentation of the numpy add function from the command line? (★☆☆)
 
@@ -131,7 +131,7 @@ Z = np.ones((5,5))
 Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0)
 print(Z)
 
-# Using fancy indexing
+# Not a solution to this problem but good to know: using fancy indexing for in-place edit
 Z[:, [0, -1]] = 0
 Z[[0, -1], :] = 0
 print(Z)
@@ -205,7 +205,7 @@ color = np.dtype([("r", np.ubyte),
 
 
 ```python
-Z = np.dot(np.ones((5,3)), np.ones((3,2)))
+Z = np.matmul(np.ones((5, 3)), np.ones((3, 2)))
 print(Z)
 
 # Alternative solution, in Python 3.5 and above
@@ -399,7 +399,7 @@ print(Z)
 Z = np.arange(10)
 np.add.reduce(Z)
 ```
-#### 42. Consider two random array A and B, check if they are equal (★★☆)
+#### 42. Consider two random arrays A and B, check if they are equal (★★☆)
 
 
 ```python
@@ -461,7 +461,7 @@ Y = X + 0.5
 C = 1.0 / np.subtract.outer(X, Y)
 print(np.linalg.det(C))
 ```
-#### 48. Print the minimum and maximum representable value for each numpy scalar type (★★☆)
+#### 48. Print the minimum and maximum representable values for each numpy scalar type (★★☆)
 
 
 ```python
@@ -519,7 +519,7 @@ Z = np.random.random((10,2))
 D = scipy.spatial.distance.cdist(Z,Z)
 print(D)
 ```
-#### 53. How to convert a float (32 bits) array into an integer (32 bits) in place?
+#### 53. How to convert a float (32 bits) array into an integer (32 bits) array in place?
 
 
 ```python
@@ -548,7 +548,7 @@ s = StringIO('''1, 2, 3, 4, 5
 
                  ,  , 9,10,11
 ''')
-Z = np.genfromtxt(s, delimiter=",", dtype=np.int)
+Z = np.genfromtxt(s, delimiter=",", dtype = int, filling_values = 0)
 print(Z)
 ```
 #### 55. What is the equivalent of enumerate for numpy arrays? (★★☆)
@@ -566,9 +566,17 @@ for index in np.ndindex(Z.shape):
 
 ```python
 X, Y = np.meshgrid(np.linspace(-1, 1, 10), np.linspace(-1, 1, 10))
-D = np.sqrt(X*X+Y*Y)
 sigma, mu = 1.0, 0.0
-G = np.exp(-( (D-mu)**2 / ( 2.0 * sigma**2 ) ) )
+G = np.exp(-((X - mu) ** 2 + (Y - mu) ** 2) / (2.0 * sigma**2))
+print(G)
+
+# Another solution using the fact that a 2D Gaussian is separable
+# Author: Nin17
+x = np.linspace(-1, 1, 10)
+y = np.linspace(-1, 1, 10)
+gx = np.exp(-((x - mu) ** 2 / (2.0 * sigma**2)))
+gy = np.exp(-((y - mu) ** 2 / (2.0 * sigma**2)))
+G = gy[:, None] * gx[None, :]
 print(G)
 ```
 #### 57. How to randomly place p elements in a 2D array? (★★☆)
@@ -615,8 +623,17 @@ print(Z[Z[:,1].argsort()])
 ```python
 # Author: Warren Weckesser
 
+# null : 0 
 Z = np.random.randint(0,3,(3,10))
 print((~Z.any(axis=0)).any())
+
+# null : np.nan
+Z=np.array([
+    [0,1,np.nan],
+    [1,2,np.nan],
+    [4,5,np.nan]
+])
+print(np.isnan(Z).all(axis=0))
 ```
 #### 61. Find the nearest value from a given value in an array (★★☆)
 
@@ -648,7 +665,7 @@ class NamedArray(np.ndarray):
         return obj
     def __array_finalize__(self, obj):
         if obj is None: return
-        self.info = getattr(obj, 'name', "no name")
+        self.name = getattr(obj, 'name', "no name")
 
 Z = NamedArray(np.arange(10), "range_10")
 print (Z.name)
@@ -766,7 +783,7 @@ Z0 = np.zeros(len(Z) + (len(Z)-1)*(nz))
 Z0[::nz+1] = Z
 print(Z0)
 ```
-#### 71. Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★)
+#### 71. Consider an array of dimension (5,5,3), how to multiply it by an array with dimensions (5,5)? (★★★)
 
 
 ```python
@@ -864,7 +881,27 @@ np.negative(Z, out=Z)
 
 
 ```python
-def distance(P0, P1, p):
+P0 = np.random.uniform(-10,10,(10,2))
+P1 = np.random.uniform(-10,10,(10,2))
+p  = np.random.uniform(-10,10,( 1,2))
+
+def distance_faster(P0,P1,p):
+    #Author: Hemanth Pasupuleti
+    #Reference: https://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
+
+    v = P1- P0 
+    v[:,[0,1]] = v[:,[1,0]]
+    v[:,1]*=-1 
+    norm = np.linalg.norm(v,axis=1)   
+    r = P0 - p
+    d = np.abs(np.einsum("ij,ij->i",r,v)) / norm 
+
+    return d
+
+print(distance_faster(P0, P1, p))
+
+##--------------- OR ---------------##
+def distance_slower(P0, P1, p):
     T = P1 - P0
     L = (T**2).sum(axis=1)
     U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / L
@@ -872,10 +909,7 @@ def distance(P0, P1, p):
     D = P0 + U*T - p
     return np.sqrt((D**2).sum(axis=1))
 
-P0 = np.random.uniform(-10,10,(10,2))
-P1 = np.random.uniform(-10,10,(10,2))
-p  = np.random.uniform(-10,10,( 1,2))
-print(distance(P0, P1, p))
+print(distance_slower(P0, P1, p))
 ```
 #### 79. Consider 2 sets of points P0,P1 describing lines (2d) and a set of points P, how to compute distance from each point j (P[j]) to each line i (P0[i],P1[i])? (★★★)
 
@@ -888,8 +922,34 @@ P0 = np.random.uniform(-10, 10, (10,2))
 P1 = np.random.uniform(-10,10,(10,2))
 p = np.random.uniform(-10, 10, (10,2))
 print(np.array([distance(P0,P1,p_i) for p_i in p]))
+
+# Author: Yang Wu (Broadcasting)
+def distance_points_to_lines(p: np.ndarray, p_1: np.ndarray, p_2: np.ndarray) -> np.ndarray:
+    x_0, y_0 = p.T  # Shape -> (n points, )
+    x_1, y_1 = p_1.T  # Shape -> (n lines, )
+    x_2, y_2 = p_2.T  # Shape -> (n lines, )
+
+    # Displacement vector coordinates from p_1 -> p_2
+    dx = x_2 - x_1  # Shape -> (n lines, )
+    dy = y_2 - y_1  # Shape -> (n lines, )
+
+    # The 'cross product' term
+    cross_term = x_2 * y_1 - y_2 * x_1  # Shape -> (n lines, )
+
+    # Broadcast x_0, y_0 (n points, 1) and dx, dy, cross_term (1, n lines) -> (n points, n lines)
+    numerator = np.abs(
+        dy[np.newaxis, :] * x_0[:, np.newaxis]
+        - dx[np.newaxis, :] * y_0[:, np.newaxis]
+        + cross_term[np.newaxis, :]
+    )
+    denominator = np.sqrt(dx**2 + dy**2)  # Shape -> (n lines, )
+
+    # Shape (n points, n lines) / (1, n_lines) -> (n points, n lines)
+    return numerator / denominator[np.newaxis, :]
+
+distance_points_to_lines(p, P0, P1)
 ```
-#### 80. Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
+#### 80. Consider an arbitrary array, write a function that extracts a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
 
 
 ```python
@@ -915,8 +975,8 @@ Z_start = (np.maximum(Z_start,0)).tolist()
 R_stop = np.maximum(R_start, (R_stop - np.maximum(Z_stop-Zs,0))).tolist()
 Z_stop = (np.minimum(Z_stop,Zs)).tolist()
 
-r = [slice(start,stop) for start,stop in zip(R_start,R_stop)]
-z = [slice(start,stop) for start,stop in zip(Z_start,Z_stop)]
+r = tuple([slice(start,stop) for start,stop in zip(R_start,R_stop)])
+z = tuple([slice(start,stop) for start,stop in zip(Z_start,Z_stop)])
 R[r] = Z[z]
 print(Z)
 print(R)
@@ -944,7 +1004,8 @@ print(sliding_window_view(Z, window_shape=4))
 
 Z = np.random.uniform(0,1,(10,10))
 U, S, V = np.linalg.svd(Z) # Singular Value Decomposition
-rank = np.sum(S > 1e-10)
+threshold = len(S) * S.max() * np.finfo(S.dtype).eps
+rank = np.sum(S > threshold)
 print(rank)
 
 # alternative solution:
@@ -998,7 +1059,7 @@ S = symetric(np.random.randint(0,10,(5,5)))
 S[2,3] = 42
 print(S)
 ```
-#### 86. Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)
+#### 86. Consider a set of p matrices with shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)
 
 
 ```python
@@ -1037,11 +1098,8 @@ k = 4
 windows = np.lib.stride_tricks.sliding_window_view(Z, (k, k))
 S = windows[::k, ::k, ...].sum(axis=(-2, -1))
 
-# Author: Jeff Luo (@Jeff1999)
-
-Z = np.ones((16, 16))
-k = 4
-print(sliding_window_view(Z, window_shape=(k, k))[::k, ::k].sum(axis=(-2, -1)))
+# alternative solution (by @Gattocrucco)
+S = Z.reshape(4, 4, 4, 4).sum((1, 3))
 ```
 #### 88. How to implement the Game of Life using numpy arrays? (★★★)
 
@@ -1080,7 +1138,7 @@ print (Z[np.argsort(Z)[-n:]])
 # Fast
 print (Z[np.argpartition(-Z,n)[:n]])
 ```
-#### 90. Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★)
+#### 90. Given an arbitrary number of vectors, build the cartesian product (every combination of every item) (★★★)
 
 
 ```python

100_Numpy_random.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "a194d42e",
+   "id": "94b10be0",
    "metadata": {},
    "source": [
     "# 100 numpy exercises\n",
@@ -18,7 +18,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7fd49f7",
+   "id": "1d0b9900",
    "metadata": {},
    "source": [
     "File automatically generated. See the documentation to update questions/answers/hints programmatically."
@@ -26,17 +26,17 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b702d5a2",
+   "id": "21313ae9",
    "metadata": {},
    "source": [
-    "Run the `initialize.py` module, then call a random question with `pick()` an hint towards its solution with\n",
+    "Run the `initialise.py` module, then call a random question with `pick()` an hint towards its solution with\n",
     "`hint(n)` and the answer with `answer(n)`, where n is the number of the picked question."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "da60e1d0",
+   "id": "c4ad3a14",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -46,7 +46,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9fb544fe",
+   "id": "13bdf6d0",
    "metadata": {},
    "outputs": [],
    "source": [

README.md

@@ -19,5 +19,4 @@ This work is licensed under the MIT license.
 
 ### Variants in Other Languages
 
-#### Julia 
- - [100 Julia Exercises](https://github.com/RoyiAvital/Julia100Exercises).
+ - **Julia**: [100 Julia Exercises](https://github.com/RoyiAvital/Julia100Exercises).

generators.py

@@ -108,7 +108,7 @@ def create_markdown(destination_filename='100_Numpy_exercises', with_hints=False
 
     # Add questions (and hint or answers if required)
     for n in range(1, 101):
-        mdfile.new_header(title=f"{n}. {QHA[f'q{n}']}", level=4)
+        mdfile.new_header(title=f"{n}. {QHA[f'q{n}']}", level=4, add_table_of_contents="n")
         if with_hints:
             mdfile.write(f"`{QHA[f'h{n}']}`")
         if with_solutions:

requirements.txt

@@ -1,5 +1,3 @@
-numpy==1.17.4
-pandas==0.25.3
-jupyter==1.0.0
-jupyterthemes==0.20.0
-mdutils==1.0.0
+numpy
+mdutils
+nbformat

runtime.txt

@@ -0,0 +1 @@
+python-3.7.17

source/exercises100.ktx

@@ -37,6 +37,9 @@ hint: size, itemsize
 Z = np.zeros((10,10))
 print("%d bytes" % (Z.size * Z.itemsize))
 
+# Simpler alternative
+print("%d bytes" % Z.nbytes)
+
 < q5
 How to get the documentation of the numpy add function from the command line? (★☆☆)
 
@@ -162,7 +165,7 @@ Z = np.ones((5,5))
 Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0)
 print(Z)
 
-# Using fancy indexing
+# Not a solution to this problem but good to know: using fancy indexing for in-place edit
 Z[:, [0, -1]] = 0
 Z[[0, -1], :] = 0
 print(Z)
@@ -260,7 +263,7 @@ Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆)
 hint:
 
 < a24
-Z = np.dot(np.ones((5,3)), np.ones((3,2)))
+Z = np.matmul(np.ones((5, 3)), np.ones((3, 2)))
 print(Z)
 
 # Alternative solution, in Python 3.5 and above
@@ -506,7 +509,7 @@ Z = np.arange(10)
 np.add.reduce(Z)
 
 < q42
-Consider two random array A and B, check if they are equal (★★☆)
+Consider two random arrays A and B, check if they are equal (★★☆)
 
 < h42
 hint: np.allclose, np.array_equal
@@ -586,7 +589,7 @@ C = 1.0 / np.subtract.outer(X, Y)
 print(np.linalg.det(C))
 
 < q48
-Print the minimum and maximum representable value for each numpy scalar type (★★☆)
+Print the minimum and maximum representable values for each numpy scalar type (★★☆)
 
 < h48
 hint: np.iinfo, np.finfo, eps
@@ -659,7 +662,7 @@ D = scipy.spatial.distance.cdist(Z,Z)
 print(D)
 
 < q53
-How to convert a float (32 bits) array into an integer (32 bits) in place?
+How to convert a float (32 bits) array into an integer (32 bits) array in place?
 
 < h53
 hint: view and [:] =
@@ -693,7 +696,7 @@ s = StringIO('''1, 2, 3, 4, 5
 
                  ,  , 9,10,11
 ''')
-Z = np.genfromtxt(s, delimiter=",", dtype=np.int)
+Z = np.genfromtxt(s, delimiter=",", dtype = int, filling_values = 0)
 print(Z)
 
 < q55
@@ -717,9 +720,17 @@ hint: np.meshgrid, np.exp
 
 < a56
 X, Y = np.meshgrid(np.linspace(-1, 1, 10), np.linspace(-1, 1, 10))
-D = np.sqrt(X*X+Y*Y)
 sigma, mu = 1.0, 0.0
-G = np.exp(-( (D-mu)**2 / ( 2.0 * sigma**2 ) ) )
+G = np.exp(-((X - mu) ** 2 + (Y - mu) ** 2) / (2.0 * sigma**2))
+print(G)
+
+# Another solution using the fact that a 2D Gaussian is separable
+# Author: Nin17
+x = np.linspace(-1, 1, 10)
+y = np.linspace(-1, 1, 10)
+gx = np.exp(-((x - mu) ** 2 / (2.0 * sigma**2)))
+gy = np.exp(-((y - mu) ** 2 / (2.0 * sigma**2)))
+G = gy[:, None] * gx[None, :]
 print(G)
 
 < q57
@@ -969,7 +980,7 @@ Z0[::nz+1] = Z
 print(Z0)
 
 < q71
-Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★)
+Consider an array of dimension (5,5,3), how to multiply it by an array with dimensions (5,5)? (★★★)
 
 < h71
 hint: array[:, :, None]
@@ -1090,7 +1101,27 @@ Consider 2 sets of points P0,P1 describing lines (2d) and a point p, how to comp
 No hints provided...
 
 < a78
-def distance(P0, P1, p):
+P0 = np.random.uniform(-10,10,(10,2))
+P1 = np.random.uniform(-10,10,(10,2))
+p  = np.random.uniform(-10,10,( 1,2))
+
+def distance_faster(P0,P1,p):
+    #Author: Hemanth Pasupuleti
+    #Reference: https://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
+
+    v = P1- P0 
+    v[:,[0,1]] = v[:,[1,0]]
+    v[:,1]*=-1 
+    norm = np.linalg.norm(v,axis=1)   
+    r = P0 - p
+    d = np.abs(np.einsum("ij,ij->i",r,v)) / norm 
+
+    return d
+
+print(distance_faster(P0, P1, p))
+
+##--------------- OR ---------------##
+def distance_slower(P0, P1, p):
     T = P1 - P0
     L = (T**2).sum(axis=1)
     U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / L
@@ -1098,10 +1129,7 @@ def distance(P0, P1, p):
     D = P0 + U*T - p
     return np.sqrt((D**2).sum(axis=1))
 
-P0 = np.random.uniform(-10,10,(10,2))
-P1 = np.random.uniform(-10,10,(10,2))
-p  = np.random.uniform(-10,10,( 1,2))
-print(distance(P0, P1, p))
+print(distance_slower(P0, P1, p))
 
 < q79
 Consider 2 sets of points P0,P1 describing lines (2d) and a set of points P, how to compute distance from each point j (P[j]) to each line i (P0[i],P1[i])? (★★★)
@@ -1118,8 +1146,34 @@ P1 = np.random.uniform(-10,10,(10,2))
 p = np.random.uniform(-10, 10, (10,2))
 print(np.array([distance(P0,P1,p_i) for p_i in p]))
 
+# Author: Yang Wu (Broadcasting)
+def distance_points_to_lines(p: np.ndarray, p_1: np.ndarray, p_2: np.ndarray) -> np.ndarray:
+    x_0, y_0 = p.T  # Shape -> (n points, )
+    x_1, y_1 = p_1.T  # Shape -> (n lines, )
+    x_2, y_2 = p_2.T  # Shape -> (n lines, )
+
+    # Displacement vector coordinates from p_1 -> p_2
+    dx = x_2 - x_1  # Shape -> (n lines, )
+    dy = y_2 - y_1  # Shape -> (n lines, )
+
+    # The 'cross product' term
+    cross_term = x_2 * y_1 - y_2 * x_1  # Shape -> (n lines, )
+
+    # Broadcast x_0, y_0 (n points, 1) and dx, dy, cross_term (1, n lines) -> (n points, n lines)
+    numerator = np.abs(
+        dy[np.newaxis, :] * x_0[:, np.newaxis]
+        - dx[np.newaxis, :] * y_0[:, np.newaxis]
+        + cross_term[np.newaxis, :]
+    )
+    denominator = np.sqrt(dx**2 + dy**2)  # Shape -> (n lines, )
+
+    # Shape (n points, n lines) / (1, n_lines) -> (n points, n lines)
+    return numerator / denominator[np.newaxis, :]
+
+distance_points_to_lines(p, P0, P1)
+
 < q80
-Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
+Consider an arbitrary array, write a function that extracts a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)
 
 < h80
 hint: minimum maximum
@@ -1147,8 +1201,8 @@ Z_start = (np.maximum(Z_start,0)).tolist()
 R_stop = np.maximum(R_start, (R_stop - np.maximum(Z_stop-Zs,0))).tolist()
 Z_stop = (np.minimum(Z_stop,Zs)).tolist()
 
-r = [slice(start,stop) for start,stop in zip(R_start,R_stop)]
-z = [slice(start,stop) for start,stop in zip(Z_start,Z_stop)]
+r = tuple([slice(start,stop) for start,stop in zip(R_start,R_stop)])
+z = tuple([slice(start,stop) for start,stop in zip(Z_start,Z_stop)])
 R[r] = Z[z]
 print(Z)
 print(R)
@@ -1182,7 +1236,8 @@ hint: np.linalg.svd, np.linalg.matrix_rank
 
 Z = np.random.uniform(0,1,(10,10))
 U, S, V = np.linalg.svd(Z) # Singular Value Decomposition
-rank = np.sum(S > 1e-10)
+threshold = len(S) * S.max() * np.finfo(S.dtype).eps
+rank = np.sum(S > threshold)
 print(rank)
 
 # alternative solution:
@@ -1246,7 +1301,7 @@ S[2,3] = 42
 print(S)
 
 < q86
-Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)
+Consider a set of p matrices with shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)
 
 < h86
 hint: np.tensordot
@@ -1290,11 +1345,8 @@ k = 4
 windows = np.lib.stride_tricks.sliding_window_view(Z, (k, k))
 S = windows[::k, ::k, ...].sum(axis=(-2, -1))
 
-# Author: Jeff Luo (@Jeff1999)
-
-Z = np.ones((16, 16))
-k = 4
-print(sliding_window_view(Z, window_shape=(k, k))[::k, ::k].sum(axis=(-2, -1)))
+# alternative solution (by @Gattocrucco)
+S = Z.reshape(4, 4, 4, 4).sum((1, 3))
 
 < q88
 How to implement the Game of Life using numpy arrays? (★★★)
@@ -1340,7 +1392,7 @@ print (Z[np.argsort(Z)[-n:]])
 print (Z[np.argpartition(-Z,n)[:n]])
 
 < q90
-Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★)
+Given an arbitrary number of vectors, build the cartesian product (every combination of every item) (★★★)
 
 < h90
 hint: np.indices

source/headers.ktx

@@ -15,11 +15,11 @@ File automatically generated. See the documentation to update questions/answers/
 
 
 < jupyter_instruction
-Run the `initialize.py` module, then for each question you can query the
+Run the `initialise.py` module, then for each question you can query the
 answer or an hint with `hint(n)` or `answer(n)` for `n` question number.
 
 
 < jupyter_instruction_rand
-Run the `initialize.py` module, then call a random question with `pick()` an hint towards its solution with
+Run the `initialise.py` module, then call a random question with `pick()` an hint towards its solution with
 `hint(n)` and the answer with `answer(n)`, where n is the number of the picked question.