Add project related project

.gitignore

@@ -1,2 +1,5 @@
+.idea/
+target/
+__pycache__
 *.out
 *.o

pwr_project/src/matrix.py

@@ -0,0 +1,2 @@
+class Matrix:
+    

pwr_project/src/vector.py

@@ -0,0 +1,46 @@
+class Vector:
+    __data__ = []
+
+    def __init__(self, data):
+        if isinstance(data, list):
+            self.__data__ = data
+        elif isinstance(data, int):
+            self.__init__([0] * data)
+        else:
+            raise ValueError("data must be a list or an integer for dimension")
+
+    def get_data(self):
+        return self.__data__
+
+    def get_dimension(self):
+        return len(self.__data__)
+
+    def __iter__(self):
+        return iter(self.__data__)
+
+    def __eq__(self, other):
+        return self.__data__ == other.__data__
+
+    def __str__(self):
+        return f"{self.__data__}"
+
+    def __add__(self, other):
+        if self.get_dimension() != other.get_dimension():
+            raise ValueError("The vectors to be added must have the same dimension")
+
+        data = []
+        for (i, j) in zip(self, other):
+            data.append(i + j)
+
+        return Vector(data)
+
+    def __mul__(self, other):
+        if isinstance(other, Vector):
+            ...
+        elif isinstance(other, int) or isinstance(other, float):
+            ...
+        else:
+            raise ValueError("A vector can only be multiplied with an vector (dot product) or a scalar")
+
+    def __rmul__(self, other):
+        return self * other

pwr_project/test/test_vector.py

@@ -0,0 +1,47 @@
+from unittest import TestCase
+
+from vector import Vector
+
+
+class TestVector(TestCase):
+    def test_should_create_vector_dim_5(self):
+        dim = 5
+        vector = Vector(dim)
+
+        actual = vector.get_dimension()
+        expected = dim
+
+        self.assertEqual(expected, actual)
+
+    def test_should_create_zero_vector(self):
+        dim = 5
+        vector = Vector(dim)
+
+        actual = vector.get_data()
+        expected = [0, 0, 0, 0, 0]
+
+        self.assertEqual(expected, actual)
+
+    def test_should_create_vector(self):
+        data = list(range(5))
+        vector = Vector(data)
+
+        actual = vector.get_data()
+        expected = [0, 1, 2, 3, 4]
+
+        self.assertEqual(expected, actual)
+
+    def test_should_add_vectors(self):
+        v1 = Vector([1, 2])
+        v2 = Vector([3, 4])
+
+        expected = Vector([4, 6])
+        actual = v1 + v2
+
+        self.assertEqual(expected, actual)
+
+    def test_should_raise_error_while_adding_vectors(self):
+        v1 = Vector(1)
+        v2 = Vector(2)
+
+        self.assertRaises(ValueError, lambda: v1 + v2)

uebung_03/exercise_02/exercise_02a.py

@@ -0,0 +1,11 @@
+from mpi4py import MPI
+
+comm = MPI.COMM_WORLD
+rank = comm.Get_rank()
+
+if rank == 0:
+    data = "Hello, from process 0!"
+    comm.send(data, dest=1)
+elif rank == 1:
+    received_data = comm.recv(source=0)
+    print(f"Process 1 received: {received_data}")

uebung_03/exercise_02/exercise_02b.py

@@ -0,0 +1,23 @@
+from mpi4py import MPI
+
+comm = MPI.COMM_WORLD
+rank = comm.Get_rank()
+size = comm.Get_size()
+
+send_data = f"Hello, from process {rank}!"
+print(f"I am rank {rank}. I send to process {(rank+1)}")
+print(f"I am rank {rank}. I receive from process {(rank-1)}")
+
+if rank == size-1:
+    comm.send(send_data, dest=(0))
+else:
+    comm.send(send_data, dest=(rank + 1))
+
+recv_data = ""
+
+if rank == 0:
+    recv_data= comm.recv(source=(size - 1))
+else:
+    recv_data= comm.recv(source=(rank - 1))
+
+print(f"I am rank {rank}. I have received: {recv_data}")

uebung_03/exercise_03/exercise_03a.py

@@ -0,0 +1,37 @@
+from mpi4py import MPI
+import numpy as np
+import math
+
+comm = MPI.COMM_WORLD
+rank = comm.Get_rank()
+size = comm.Get_size()
+
+chunk = 0
+
+if rank == 0:
+    N = 100000
+    x = np.random.uniform(0,1,(N,1))
+
+    chunksize = math.floor(N / size)
+    for i in range(1,size):
+        from_index = 0 + chunksize * i
+        to_index = (chunksize * (i + 1)) - 1
+        chunk = x[from_index:to_index]
+        comm.send(chunk, dest = i)
+else:
+    chunk = comm.recv(source = 0)
+
+chunk_sum = 0.0
+for i in range(len(chunk)):
+    chunk_sum += chunk[i] * chunk[i]
+
+if rank != 0:
+    comm.send(chunk_sum, dest = 0) 
+
+if rank == 0:
+    sum = chunk_sum 
+
+    for i in range(1,size):
+        sum += comm.recv(source = i)
+
+    print(f"The squared euclidian norm of x is {sum[0]:.2f}.")

uebung_03/exercise_03/exercise_03b.py

@@ -0,0 +1,33 @@
+from mpi4py import MPI
+import numpy as np
+import math
+
+comm = MPI.COMM_WORLD
+rank = comm.Get_rank()
+size = comm.Get_size()
+
+chunk = 0
+
+if rank == 0:
+    N = 100000
+    x = np.random.uniform(0,1,(N,1))
+
+    chunksize = math.floor(N / size)
+    for i in range(1,size):
+        from_index = 0 + chunksize * i
+        to_index = (chunksize * (i + 1)) - 1
+        chunk = x[from_index:to_index]
+        comm.send(chunk, dest = i)
+else:
+    chunk = comm.recv(source = 0)
+
+chunk_sum = 0.0
+for i in range(len(chunk)):
+    chunk_sum += chunk[i] * chunk[i]
+
+comm.Barrier()
+
+sum = comm.reduce(chunk_sum, op = MPI.SUM, root = 0)
+
+if rank == 0:
+    print(f"The squared euclidian norm of x is {sum[0]:.2f}.")

uebung_03/exercise_04/exercise_04.py

@@ -0,0 +1,41 @@
+from mpi4py import MPI
+import numpy as np
+import math
+import sys
+
+def dot_product(a, x):
+    result = 0
+    for i in range(len(a)):
+        result += a[i] * x[i]
+    return result
+
+def row(i):
+    row = []
+    for j in range(1, n+1):
+        row.append(i / j)
+    return row
+
+comm = MPI.COMM_WORLD
+rank = comm.Get_rank()
+size = comm.Get_size()
+
+n = int(sys.argv[1])
+
+x = list(range(1, n+1))
+
+# each rank should compute almost the same amount of matrix.row * x
+# for this split the list [1,...,n+1] in sublists containing the rownumbers every rank has to compute
+# if n is a multiple of size all ranks have the same amount to compute, if not, the first (n % size) ranks compute each one more
+chunks = np.array_split(list(range(1,n+1)), size) 
+
+chunk = chunks[rank]
+sub_b = []
+for i in chunk:
+    sub_b.append(dot_product(row(i), x)) # every rank computes its delegated rows times x
+
+comm.barrier()
+
+b = comm.gather(sub_b)
+
+if rank == 0:
+    b = np.concatenate(b).tolist() # b is a list of lists, np.concatenate 'flattens' the list of lists into an np.ndarray and tolist() to get an python list

uebung_03/exercise_04/exercise_04_visualization.py

@@ -0,0 +1,30 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import timeit
+
+nthreads = [1, 2, 4, 8, 16]
+sizes = [100, 400, 1600, 6400, 12800, 25600, 51200]
+
+thread_timings = [] 
+for t in nthreads:
+    print(f"Measure timing for {t} thread(s)")
+    size_timings = []
+    for s in sizes:
+        print(f"--- Measure timing for size {s}")
+        command = f"subprocess.run(\"mpirun --use-hwthread-cpus -n {t} python3 exercise_04.py {s}\", shell = True)"
+        size_timings.append(timeit.timeit(command, setup = "import subprocess", number = 1) * 1000)
+    thread_timings.append(size_timings)
+
+plt.plot(sizes, thread_timings[0], "green", label=f"{nthreads[0]}")
+plt.plot(sizes, thread_timings[1], "blue", label=f"{nthreads[1]}")
+plt.plot(sizes, thread_timings[2], "purple", label=f"{nthreads[2]}")
+plt.plot(sizes, thread_timings[3], "red", label=f"{nthreads[3]}")
+plt.plot(sizes, thread_timings[4], "orange", label=f"{nthreads[4]}")
+
+plt.title("Matrix-Vector-Multiplication time/threads comparison")
+plt.xlabel("Sizes")
+plt.ylabel("Time (ms)")
+plt.loglog()
+plt.legend(title = "# of Threads")
+
+plt.show()  

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@@ -0,0 +1,495 @@
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uebung_04/exercise_06/Cargo.toml

@@ -0,0 +1,9 @@
+[package]
+name = "exercise_06"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+mpi = "0.7.0"

uebung_04/exercise_06/src/main.rs

@@ -0,0 +1,76 @@
+use std::f64::consts::PI;
+use mpi::collective::SystemOperation;
+use mpi::traits::*;
+
+fn main() {
+    let universe = mpi::initialize().unwrap();
+    let world = universe.world();
+
+    let size = world.size();
+    let rank = world.rank();
+
+    let support_points = 100;
+    let a = 0.0;
+    let b = 1.0;
+    let N = (b - a) / size as f64;
+
+    let f = |x: f64| 1.0 / (1.0 + x.powi(2)) as f64; // function
+    let n = (support_points / size) as u32; // fewer ranks should also use an appropriate amount of support points; the support points are distributed among the ranks
+    let partial_integral = trapezoidal_rule(f, a + rank as f64 * N, a + (rank + 1) as f64 * N, n);
+    println!("Rank {}: Partial integral is {} on [{},{}]", rank, partial_integral, (a + rank as f64 * N), (a + (rank + 1) as f64 * N));
+
+    world.barrier();
+
+    let mut integral = 0.0;
+
+    world.all_reduce_into(&partial_integral, &mut integral, SystemOperation::sum());
+
+    if rank == 0 {
+        println!("The approximated integral is {}", integral);
+        println!("The error is |{:.7} - {:.7}| = {}", (PI / 4.0), integral, (integral - (PI / 4.0)).abs());
+    }
+}
+
+fn trapezoidal_rule(f: fn(f64) -> f64, a: f64, b: f64, n: u32) -> f64 {
+    let h = (b - a) / n as f64;
+    let mut result = 0.5 * (f(a) + f(b));
+
+    for i in 1..n {
+        let x_i = a + i as f64 * h;
+        result += f(x_i);
+    }
+
+    h * result
+}
+
+#[cfg(test)]
+mod tests {
+    use std::f64::consts::PI;
+    use crate::trapezoidal_rule;
+
+    #[test]
+    fn should_return_0_trapezoid_rule() {
+        let expected = 0.0;
+        let actual = trapezoidal_rule(|_x| 0.0, 0.0, 10.0, 1);
+
+        assert_eq!(expected, actual, "Integral is {} but should be {}", actual, expected);
+    }
+
+    #[test]
+    fn should_return_1_trapezoid_rule() {
+        let expected = 1.0;
+        let actual = trapezoidal_rule(|_x| 1.0, 0.0, 1.0, 1);
+
+        assert_eq!(expected, actual, "Integral is {} but should be {}", actual, expected);
+    }
+
+    #[test]
+    fn should_return_pi_trapezoid_rule() {
+        let expected = PI / 4.0;
+        let actual = trapezoidal_rule(|x| 1.0 / (1.0 + x.powi(2)), 0.0, 1.0, 10);
+
+        let tolerance = 1e-3;
+
+        assert!((expected - actual).abs() < tolerance, "Integral is {} but should be {}", actual, expected);
+    }
+}

uebung_05/exercise_01/exercise_01.py

@@ -0,0 +1,20 @@
+class Ball:
+    __diameter__ = 0.0
+    
+    ## Methods
+    # Constructor
+    def __init__(self, diameter = 1.0):
+        self.__diameter__ = diameter
+        pass
+        
+    # a simple method
+    def introduction(self):
+        print(f"My diameter is {self.__diameter__:.3f}.")
+        pass
+        
+# main code
+a = Ball()
+b = Ball(2.0)
+
+a.introduction()
+b.introduction()

uebung_05/exercise_02/exercise_02.py

@@ -0,0 +1,51 @@
+import numpy as np
+
+class Ball:
+    __diameter__ = 0.0
+    
+    ## Methods
+    # Constructor
+    def __init__(self, diameter = 1.0):
+        self.__diameter__ = diameter
+        pass
+        
+    # a simple method
+    def introduction(self):
+        print(f"My diameter is {self.__diameter__:.3f}.")
+        pass
+
+    # Getter
+    def get_diameter(self):
+        return self.__diameter__
+
+    # overload __add_ (+)
+    def __add__(self, other):
+        d1 = self.get_diameter()
+
+        if(isinstance(other, Ball)):
+            d2 = other.get_diameter()
+            combined_volume = 1/6 * np.pi * (d1**3 + d2**3)
+        elif(isinstance(other, int) or isinstance(other, float)):
+            combined_volume = 1/6 * np.pi*d1**3 + other
+        else:
+            raise ValueError("Invalid summand.")
+        d_combined = np.power(6 * combined_volume / np.pi, 1/3)
+        return Ball(d_combined)
+        
+    # overload __radd__ (number + Ball)
+    def __radd__(self, other):
+        return self + other
+
+# main code
+a = Ball()
+b = Ball(2.0)
+
+c = a + b
+
+d = a + 5
+e = 5 + a
+
+a.introduction()
+b.introduction()
+c.introduction()
+d.introduction()

uebung_05/exercise_03/exercise_03.py

@@ -0,0 +1,74 @@
+import math
+import matplotlib.pyplot as plt
+
+class Point:
+    __x__ = 0.0
+    __y__ = 0.0
+
+    def __init__(self, x = 0.0, y = 0.0):
+        self.__x__ = x
+        self.__y__ = y
+
+    def __str__(self):
+        return f"({self.__x__:.3f},{self.__y__:.3f})"
+
+    def __neg__(self):
+        return Point(-self.__x__, -self.__y__)
+
+    def __add__(self, other):
+        if isinstance(other, Point):
+            return Point(self.__x__ + other.__x__, self.__y__ + other.__y__)
+        elif isinstance(other, int) or isinstance(other, float):
+            return Point(self.__x__ + other, self.__y__ + other)
+        else:
+            raise ValueError("Operand must be Point, int or float.")
+
+    def __radd__(self, other):
+        return self + other
+
+    def __sub__(self, other):
+        return self + (-other)
+
+    def __rsub__(self, other):
+        return self - other
+
+    def __mul__(self, other):
+        if isinstance(other, Point):
+            return Point(self.__x__ * other.__x__, self.__x__ * other.__y__)
+        elif isinstance(other, int) or isinstance(other, float):
+            return Point(self.__x__ * other, self.__x__ * other)
+        else:
+            raise ValueError("Operand must be Point, int or float.")
+
+    def __rmul__(self, other):
+        return self * other
+
+    def rot(self, degree):
+        x =  math.cos(degree) * self.__x__ + math.sin(degree) * self.__y__
+        y =  -math.sin(degree) * self.__x__ + math.cos(degree) * self.__y__
+        return Point(x, y)
+
+    def get_x(self):
+        return self.__x__
+
+    def get_y(self):
+        return self.__y__
+
+p1 = Point()
+p2 = Point(1, 1)
+p3 = Point (3, 2)
+p4 = 2 * p2 + p3 - 1
+p5 = p4.rot(math.pi / 2)
+
+plt.plot(p1.get_x(), p1.get_y(), "orange", marker = "o", label = p1)
+plt.plot(p2.get_x(), p2.get_y(), "green", marker = "o", label = p2)
+plt.plot(p3.get_x(), p3.get_y(), "yellow", marker = "o", label = p3)
+plt.plot(p4.get_x(), p4.get_y(), "purple", marker = "o", label = 2 * p2 + p3 - 1)
+plt.plot(p5.get_x(), p5.get_y(), "purple", marker = "o", label = f"{p4} rotated 90°")
+
+plt.title("Points")
+plt.xlabel("x")
+plt.ylabel("y")
+plt.legend()
+
+plt.show()