simple workflow to load EESSI, determine number of modules and run a python code

.github/workflows/test_python_uq.yaml

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+name: Minimal usage
+on: [push, pull_request]
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+    - uses: eessi/github-action-eessi@v3
+    - name: Test EESSI
+      run: |
+        module avail 2>&1 | wc -l
+      shell: bash
+    - name: Checkout repo
+      uses: actions/checkout@93ea575cb5d8a053eaa0ac8fa3b40d7e05a33cc8 # v3.1.0
+    - name: Run UQ example
+      run: |
+        module load MODULE1
+        which python
+        module load MODULE2
+        module load MODULE3
+        python uq-in-python.py
+      shell: bash

CI/SOLUTION_test_python_uq.yaml

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+name: Minimal usage
+on: [push, pull_request]
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+    - uses: eessi/github-action-eessi@v3
+    - name: Test EESSI
+      run: |
+        module avail 2>&1 | wc -l
+      shell: bash
+    - name: Checkout repo
+      uses: actions/checkout@93ea575cb5d8a053eaa0ac8fa3b40d7e05a33cc8 # v3.1.0
+    - name: Run UQ example
+      run: |
+        module load Python
+        which python
+        module load SciPy-bundle
+        module load matplotlib
+        python uq-in-python.py
+      shell: bash

uq-in-python.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+# ==========================================
+# Part 1: Integral of sin(pi * x)
+# ==========================================
+print("--- Part 1: Integral of sin(pi * x) ---")
+
+def f(x):
+    return np.sin(np.pi * x)
+
+M = 10000  # Number of samples
+approximate_integral = 0.0
+
+# Using a loop to match the original script's logic
+for i in range(M):
+    x = np.random.rand()  # Sample uniformly in [0, 1)
+    approximate_integral += f(x)
+
+approximate_integral /= M  # Average over samples
+print(f"Estimated integral of sin(pi * x) over [0, 1]: {approximate_integral}")
+print(f"Exact integral: {2 / np.pi}")
+print()
+
+
+# ==========================================
+# Part 2: Estimate value of Pi
+# ==========================================
+print("--- Part 2: Estimate value of Pi ---")
+
+def I(x, y):
+    return 1.0 if x**2 + y**2 <= 1 else 0.0
+
+M = 10000
+approximate_pi = 0.0
+
+for i in range(M):
+    # uniform(-1, 1) in numpy
+    x = np.random.uniform(-1, 1)
+    y = np.random.uniform(-1, 1)
+    approximate_pi += I(x, y)
+
+approximate_pi = (approximate_pi / M) * 4  # Scale by area
+print(f"Estimated value of pi: {approximate_pi}")
+print(f"Exact value of pi: {np.pi}")
+print()
+
+
+# ==========================================
+# Part 3: Convergence Analysis & Plotting
+# ==========================================
+print("--- Part 3: Convergence Analysis ---")
+
+# 2^(4:15) in Python equivalent
+M_values = 2 ** np.arange(4, 16)
+reruns = 10
+errors = np.zeros((len(M_values), reruns))
+
+for j, M in enumerate(M_values):
+    for r in range(reruns):
+        # Vectorized operation for better performance in Python
+        # (Replaces the inner loop 1:M)
+        x = np.random.uniform(-1, 1, M)
+        y = np.random.uniform(-1, 1, M)
+
+        # Count points inside the unit circle
+        # (x^2 + y^2 <= 1) creates a boolean array, sum() counts Trues
+        hits = np.sum(x**2 + y**2 <= 1)
+
+        current_approx_pi = (hits / M) * 4
+        errors[j, r] = abs(current_approx_pi - np.pi)
+
+# Calculate statistics along axis 1 (rows are M values, cols are reruns)
+mean_errors = np.mean(errors, axis=1)
+std_errors = np.std(errors, axis=1)
+
+# Theoretical Standard Deviation Calculation
+# Variance of Bernoulli trial p(1-p) where p = pi/4
+variance = (np.pi / 4) - (np.pi**2 / 16)
+theoretical_std = 4 * np.sqrt(variance / M_values)
+
+# Plotting
+plt.figure(figsize=(10, 6))
+
+# Log-Log plot with error bars
+plt.errorbar(M_values, mean_errors, yerr=std_errors, fmt='-o', 
+             label='Mean absolute error with std dev', capsize=5)
+
+# Plot theoretical standard deviation
+plt.plot(M_values, theoretical_std, linestyle='--', linewidth=2, 
+         label='Theoretical std dev', color='orange')
+
+plt.xscale('log', base=10)
+plt.yscale('log', base=10)
+plt.xlabel("Number of samples M")
+plt.ylabel("Absolute error")
+plt.title("Convergence of Monte Carlo estimate of pi")
+plt.legend(loc='upper right')
+plt.grid(True, which="both", ls="-", alpha=0.4)
+
+# Adjust Y limits similar to the Julia script
+plt.ylim(bottom=np.min(mean_errors) / 4, top=np.max(mean_errors) * 2)
+
+plt.show()