Add LinearLayout inversion and live matrix visualization with basis calculation

src/core/LinearLayout.test.ts

@@ -33,6 +33,24 @@ describe('LinearLayout', () => {
     })
   })
 
+  describe('fromBitMatrix', () => {
+    it('should reconstruct a 1D identity layout', () => {
+      const matrix = [
+        [1, 0],
+        [0, 1],
+      ]
+      const layout = LinearLayout.fromBitMatrix(
+        matrix,
+        [{ name: 'in', size: 4 }],
+        [{ name: 'out', size: 4 }]
+      )
+
+      for (let i = 0; i < 4; i++) {
+        expect(layout.apply({ in: i }).out).toBe(i)
+      }
+    })
+  })
+
   describe('XOR linearity', () => {
     it('should satisfy L(a⊕b) = L(a)⊕L(b)', () => {
       const layout = LinearLayout.identity1D(8, 'in', 'out')
@@ -215,6 +233,36 @@ describe('LinearLayout', () => {
         }
       }
     })
+
+    it('should report non-invertible layouts', () => {
+      const nonSquare = new LinearLayout(
+        [
+          ['in', [[1, 0]]],
+        ],
+        [
+          ['out0', 4],
+          ['out1', 4],
+        ]
+      )
+
+      expect(nonSquare.isInvertible()).toBe(false)
+      expect(() => nonSquare.invert()).toThrowError()
+    })
+
+    it('should reject layouts where output bits are zero but inputs are not', () => {
+      const broadcast = LinearLayout.zeros1D(8, 'reg', 'zero')
+      expect(broadcast.isInvertible()).toBe(false)
+      expect(() => broadcast.invert()).toThrowError(/square and surjective/i)
+    })
+
+    it('should invert layouts whose input/output spaces collapse to a single value', () => {
+      const trivial = LinearLayout.identity1D(1, 'in', 'out')
+      expect(trivial.isInvertible()).toBe(true)
+      const inverted = trivial.invert()
+      expect(inverted.apply({ out: 0 }).in).toBe(0)
+      expect(inverted.getOutDimNames()).toEqual(['in'])
+      expect(inverted.getInDimNames()).toEqual(['out'])
+    })
   })
 
   describe('ensureNotSmallerThan', () => {