Final

Circuit_2.py

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+#
+# Two methods for solving a system of linear equations A * a = b, where a and b are vectors:
+# (1) Matrix A is square (N, N)
+# https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve.html
+#
+# (2) Matrix A is not square (N, M), where the number of rows (N conditions) exceeds the number of columns (M unknowns)
+# https://scipy.github.io/devdocs/reference/generated/scipy.linalg.lstsq.html#scipy.linalg.lstsq
+#
+# This algorithm computes the vector a such that the norm ||b - A * a|| is minimized.
+#
+# Dr. Dmitriy Makhnovskiy, City College Plymouth, England, 07.04.2024
+#
+
+from scipy.linalg import lstsq
+
+# Parameters used in the A matrix
+R1 = 4.0
+R2 = 7.0
+R3 = 9.0
+R4 = 5.0
+R5 = 20.0
+
+# A matrix
+A = [
+     [1.0, 1.0, -1.0, -1.0, 0.0],
+     [1.0, 0.0, -1.0, 0.0, -1.0],
+     [0.0, 1.0, 0.0, -1.0, 1.0],
+     [R1, 0.0, R3, 0.0, 0.0],
+     [0.0, R2, 0.0, R4, 0.0],
+     [-R1, R2, 0.0, 0.0, -R5],
+     [0.0, 0.0, -R3, R1, R5],
+     [R1, -R2, R3, -R4, 0.0],
+     ]
+
+# b vector (right part of the equation)
+b = [
+     [0.0],
+     [0.0],
+     [0.0],
+     [32],
+     [32],
+     [0.0],
+     [0.0],
+     [0.0],
+      ]
+
+# Minimization of the norm ||b - A * a|| --> 0
+a, res, rnk, s = lstsq(A, b)
+a = a.flatten()  # 2D a-array was converted to a 1D array
+a = [round(x, 3) for x in a]  # rounding to three significant figures after the dot
+
+print('I1 = ', a[0], 'A')
+print('I2 = ', a[1], 'A')
+print('I3 = ', a[2], 'A')
+print('I4 = ', a[3], 'A')
+print('I5 = ', a[4], 'A')
+print('Total current = ', a[0] + a[1], 'A')
+print('')
+print('V1 = ', a[0] * R1, 'V')
+print('V2 = ', a[1] * R2, 'V')
+print('V3 = ', a[2] * R3, 'V')
+print('V4 = ', a[3] * R4, 'V')
+print('V5 = ', a[4] * R5, 'V')