misc/numworks: add echelon script for numworks.

misc/numworks/README.md

@@ -0,0 +1,29 @@
+numworks
+========
+
+Various programs for my [numworks](https://numworks.com/) calculator.
+
+
+Echelon
+-------
+
+This is a tool to help explore transformations to convert a matrix to
+row echelon form.
+
+```python
+>>> from echelon import *
+>>> m = EMatrix([[1, 1, 1], [3, 2, 1], [2, 1, 2]], [15, 28, 23])
+>>> print(m)
+ 1  1  1  -> 15
+ 3  2  1  -> 28
+ 2  1  2  -> 23
+>>> m.add(-3, 0, 1)
+>>> m.add(-2, 0, 2)
+>>> m.scale(-1, 1)
+>>> m.add(1, 1, 2)
+>>> m.scale(1/2, 2)
+>>> print(m)
+ 1  1  1  -> 15
+ 0  1  2  -> 17
+ 0  0  1  ->  5
+```

misc/numworks/echelon.py

@@ -0,0 +1,89 @@
+class EMatrix:
+
+    def __init__(self, mat, sol):
+        self.mat = []
+        l = -1
+        for i in range(len(mat)):
+            tmp = []
+            if l == -1:
+                l = len(mat[i])
+            else:
+                assert(len(mat[i]) == l)
+            for j in range(len(mat[i])):
+                tmp.append(mat[i][j])
+            self.mat.append(tmp)
+
+        assert(len(sol) == l)
+        self.sol = []
+        for i in range(len(sol)):
+            self.sol.append(sol[i])
+
+    def copy(self):
+        mat = []
+        sol = []
+        for i in range(len(self.mat)):
+            tmp = []
+            for j in range(len(self.mat[i])):
+                tmp.append(self.mat[i][j])
+            mat.append(tmp)
+
+        for i in range(len(self.sol)):
+            sol.append(self.sol[i])
+
+        return EMatrix(mat, sol)
+
+    def add(self, k, r1, r2):
+        row1 = [v for v in self.mat[r1]]
+        row2 = self.mat[r2]
+
+        for i in range(len(row1)):
+            row1[i] = k * row1[i]
+            row2[i] += row1[i]
+
+        sol = self.sol[r1] * k
+
+        self.mat[r2] = row2
+        self.sol[r2] += sol
+
+    def sub(self, k, r1, r2):
+        row1 = [v for v in self.mat[r1]]
+        row2 = self.mat[r2]
+
+        for i in range(len(row1)):
+            row1[i] = k * row1[i]
+            row2[i] -= row1[i]
+
+        sol = self.sol[r1] * k
+
+        self.mat[r2] = row2
+        self.sol[r2] -= sol
+
+    def scale(self, k, r):
+        for i in range(len(self.mat[r])):
+            self.mat[r][i] *= k
+
+        self.sol[r] *= k
+
+    def __repr__(self):
+        return "{}x{} EMatrix".format(len(self.sol), len(self.mat))
+
+    def __str__(self):
+        m = 0
+        s = ''
+        for i in range(len(self.mat)):
+            for j in range(len(self.mat[i])):
+                m = max(m, len('{:g}'.format(self.mat[i][j])))
+
+        for i in range(len(self.sol)):
+            m = max(m, len('{:g}'.format(self.sol[i])))
+        
+        fmt = '{' + ':>{}g'.format(m) + '}'
+
+        for i in range(len(self.mat)):
+            for j in range(len(self.mat[i])):
+                s += fmt.format(self.mat[i][j])
+                s += ' '
+            
+            s += ' -> ' + fmt.format(self.sol[i]) + '\n'
+        
+        return s