Fixed division by zero in QR decomposition. Issue #1058 (#1473)

tensorflow/tfjs#1058
The sign() function returns 0 on 0, which causes a division by zero in the QR decomposition function qr() if there is a zero on the diagonal.

BUG

src/io/passthrough_test.ts

@@ -115,8 +115,8 @@ describeWithFlags('Passthrough Saver', BROWSER_ENVS, () => {
 
 describeWithFlags('Passthrough Loader', BROWSER_ENVS, () => {
   it('load topology and weights: legacy signature', async () => {
-    const passthroughHandler = tf.io.fromMemory(
-        modelTopology1, weightSpecs1, weightData1);
+    const passthroughHandler =
+        tf.io.fromMemory(modelTopology1, weightSpecs1, weightData1);
     const modelArtifacts = await passthroughHandler.load();
     expect(modelArtifacts.modelTopology).toEqual(modelTopology1);
     expect(modelArtifacts.weightSpecs).toEqual(weightSpecs1);
@@ -147,9 +147,8 @@ describeWithFlags('Passthrough Loader', BROWSER_ENVS, () => {
   });
 
   it('load model topology only', async () => {
-    const passthroughHandler = tf.io.fromMemory({
-      modelTopology: modelTopology1
-    });
+    const passthroughHandler =
+        tf.io.fromMemory({modelTopology: modelTopology1});
     const modelArtifacts = await passthroughHandler.load();
     expect(modelArtifacts.modelTopology).toEqual(modelTopology1);
     expect(modelArtifacts.weightSpecs).toEqual(undefined);

src/jasmine_util.ts

@@ -40,8 +40,8 @@ export const SYNC_BACKEND_ENVS: Constraints = {
 };
 
 export const HAS_WORKER = {
-  predicate: () => typeof(Worker) !== 'undefined'
-      && typeof(Blob) !== 'undefined' && typeof(URL) !== 'undefined'
+  predicate: () => typeof (Worker) !== 'undefined' &&
+      typeof (Blob) !== 'undefined' && typeof (URL) !== 'undefined'
 };
 
 export const HAS_NODE_WORKER = {
@@ -52,7 +52,7 @@ export const HAS_NODE_WORKER = {
     } catch {
       hasWorker = false;
     }
-    return typeof(process) !== 'undefined' && hasWorker;
+    return typeof (process) !== 'undefined' && hasWorker;
   }
 };
 

src/ops/concat_test.ts

@@ -88,7 +88,7 @@ describeWithFlags('concat1d', ALL_ENVS, () => {
     expectArraysClose(await result.data(), expected);
   });
 
-  it('concat complex input', async() => {
+  it('concat complex input', async () => {
     // [1+1j, 2+2j]
     const c1 = tf.complex([1, 2], [1, 2]);
     // [3+3j, 4+4j]
@@ -234,7 +234,7 @@ describeWithFlags('concat2d', ALL_ENVS, () => {
     expectArraysEqual(await res2.data(), []);
   });
 
-  it('concat complex input axis=0', async() => {
+  it('concat complex input axis=0', async () => {
     // [[1+1j, 2+2j], [3+3j, 4+4j]]
     const c1 = tf.complex([[1, 2], [3, 4]], [[1, 2], [3, 4]]);
     // [[5+5j, 6+6j], [7+7j, 8+8j]]
@@ -247,7 +247,7 @@ describeWithFlags('concat2d', ALL_ENVS, () => {
     expectArraysClose(await result.data(), expected);
   });
 
-  it('concat complex input axis=1', async() => {
+  it('concat complex input axis=1', async () => {
     // [[1+1j, 2+2j], [3+3j, 4+4j]]
     const c1 = tf.complex([[1, 2], [3, 4]], [[1, 2], [3, 4]]);
     // [[5+5j, 6+6j], [7+7j, 8+8j]]
@@ -500,50 +500,56 @@ describeWithFlags('concat3d', ALL_ENVS, () => {
     expectArraysClose(await values.data(), [1, 2, 3, 4, 5, 6]);
   });
 
-  it('concat complex input axis=0', async() => {
+  it('concat complex input axis=0', async () => {
     // [[[1+1j, 2+2j], [3+3j, 4+4j], [5+5j, 6+6j]]]
-    const c1 = tf.complex(
-      [[[1, 2], [3, 4], [5, 6]]], [[[1, 2], [3, 4], [5, 6]]]);
+    const c1 =
+        tf.complex([[[1, 2], [3, 4], [5, 6]]], [[[1, 2], [3, 4], [5, 6]]]);
     // [[[7+7j, 8+8j], [9+9j, 10+10j], [11+11j, 12+12j]]]
     const c2 = tf.complex(
-      [[[7, 8], [9, 10], [11, 12]]], [[[7, 8], [9, 10], [11, 12]]]);
+        [[[7, 8], [9, 10], [11, 12]]], [[[7, 8], [9, 10], [11, 12]]]);
 
     const axis = 0;
     const result = tf.concat([c1, c2], axis);
-    const expected = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6,
-      7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12];
+    const expected = [
+      1, 1, 2, 2, 3, 3, 4,  4,  5,  5,  6,  6,
+      7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12
+    ];
     expect(result.dtype).toEqual('complex64');
     expectArraysClose(await result.data(), expected);
   });
 
-  it('concat complex input axis=1', async() => {
+  it('concat complex input axis=1', async () => {
     // [[[1+1j, 2+2j], [3+3j, 4+4j], [5+5j, 6+6j]]]
-    const c1 = tf.complex(
-      [[[1, 2], [3, 4], [5, 6]]], [[[1, 2], [3, 4], [5, 6]]]);
+    const c1 =
+        tf.complex([[[1, 2], [3, 4], [5, 6]]], [[[1, 2], [3, 4], [5, 6]]]);
     // [[[7+7j, 8+8j], [9+9j, 10+10j], [11+11j, 12+12j]]]
     const c2 = tf.complex(
-      [[[7, 8], [9, 10], [11, 12]]], [[[7, 8], [9, 10], [11, 12]]]);
+        [[[7, 8], [9, 10], [11, 12]]], [[[7, 8], [9, 10], [11, 12]]]);
 
     const axis = 1;
     const result = tf.concat([c1, c2], axis);
-    const expected = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6,
-      7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12];
+    const expected = [
+      1, 1, 2, 2, 3, 3, 4,  4,  5,  5,  6,  6,
+      7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12
+    ];
     expect(result.dtype).toEqual('complex64');
     expectArraysClose(await result.data(), expected);
   });
 
-  it('concat complex input axis=1', async() => {
+  it('concat complex input axis=1', async () => {
     // [[[1+1j, 2+2j], [3+3j, 4+4j], [5+5j, 6+6j]]]
-    const c1 = tf.complex(
-      [[[1, 2], [3, 4], [5, 6]]], [[[1, 2], [3, 4], [5, 6]]]);
+    const c1 =
+        tf.complex([[[1, 2], [3, 4], [5, 6]]], [[[1, 2], [3, 4], [5, 6]]]);
     // [[[7+7j, 8+8j], [9+9j, 10+10j], [11+11j, 12+12j]]]
     const c2 = tf.complex(
-      [[[7, 8], [9, 10], [11, 12]]], [[[7, 8], [9, 10], [11, 12]]]);
+        [[[7, 8], [9, 10], [11, 12]]], [[[7, 8], [9, 10], [11, 12]]]);
 
     const axis = 2;
     const result = tf.concat([c1, c2], axis);
-    const expected = [1, 1, 2, 2, 7, 7, 8, 8, 3, 3, 4, 4,
-      9, 9, 10, 10, 5, 5, 6, 6, 11, 11, 12, 12];
+    const expected = [
+      1, 1, 2,  2,  7, 7, 8, 8, 3,  3,  4,  4,
+      9, 9, 10, 10, 5, 5, 6, 6, 11, 11, 12, 12
+    ];
     expect(result.dtype).toEqual('complex64');
     expectArraysClose(await result.data(), expected);
   });

src/ops/linalg_ops.ts

@@ -215,7 +215,10 @@ function qr2d(x: Tensor2D, fullMatrices = false): [Tensor2D, Tensor2D] {
         const rjEnd1 = r.slice([j, j], [m - j, 1]);
         const normX = rjEnd1.norm();
         const rjj = r.slice([j, j], [1, 1]);
-        const s = rjj.sign().neg() as Tensor2D;
+
+        // The sign() function returns 0 on 0, which causes division by zero.
+        const s = tensor2d([[-1]]).where(rjj.greater(0), tensor2d([[1]]));
+
         const u1 = rjj.sub(s.mul(normX)) as Tensor2D;
         const wPre = rjEnd1.div(u1);
         if (wPre.shape[0] === 1) {

src/ops/linalg_ops_test.ts

@@ -140,6 +140,17 @@ describeWithFlags('qr', ALL_ENVS, () => {
         [[-8.3066, 8.3066, -2.4077], [0, 4.5826, -2.1822], [0, 0, 7.6447]]);
   });
 
+  it('3x3, zero on diagonal', async () => {
+    const x = tensor2d([[0, 2, 2], [1, 1, 1], [0, 1, 2]], [3, 3]);
+    const [q, r] = tf.linalg.qr(x);
+    expectArraysClose(await q.data(), [
+      [0., -0.89442719, 0.4472136], [1., 0., 0.], [0., -0.4472136, -0.89442719]
+    ]);
+    expectArraysClose(
+        await r.data(),
+        [[1., 1., 1.], [0., -2.23606798, -2.68328157], [0., 0., -0.89442719]]);
+  });
+
   it('3x2, fullMatrices = default false', async () => {
     const x = tensor2d([[1, 2], [3, -3], [-2, 1]], [3, 2]);
     const [q, r] = tf.linalg.qr(x);