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| /**
| * @license
| * Copyright 2017 Google LLC. All Rights Reserved.
| * Licensed under the Apache License, Version 2.0 (the "License");
| * you may not use this file except in compliance with the License.
| * You may obtain a copy of the License at
| *
| * http://www.apache.org/licenses/LICENSE-2.0
| *
| * Unless required by applicable law or agreed to in writing, software
| * distributed under the License is distributed on an "AS IS" BASIS,
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
| * See the License for the specific language governing permissions and
| * limitations under the License.
| * =============================================================================
| */
| // Empirically determined minimal shared dimension in matmul before we forward
| // to a.mul(b).sum() in order to take advantage of GPU parallelism. See
| // https://github.com/tensorflow/tfjs-core/pull/1379 for benchmarks.
| // Copied from webgl backend.
| // TODO(yassogba, annyuan) copy tests over to webgl backend that want to
| // explicitly test this threshold.
| export const MATMUL_SHARED_DIM_THRESHOLD = 1000;
| import * as tf from '../index';
| import { ALL_ENVS, describeWithFlags } from '../jasmine_util';
| import { expectArraysClose, expectArraysEqual } from '../test_util';
| describeWithFlags('matmul', ALL_ENVS, () => {
| it('A x B', async () => {
| const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
| const b = tf.tensor2d([0, 1, -3, 2, 2, 1], [3, 2]);
| const c = tf.matMul(a, b);
| expect(c.shape).toEqual([2, 2]);
| expectArraysClose(await c.data(), [0, 8, -3, 20]);
| });
| it('[8,4]x[4,8]', async () => {
| const a = tf.tensor2d([
| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
| 17, 18, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8
| ], [8, 4]);
| const b = tf.tensor2d([
| 0, 1, -3, 2, 1, -1, 0, 5, 6, 7, 8, 0, -2, -2, 1, 9,
| 11, 10, 0, 1, -3, 2, 1, -1, 1, 2, 3, 4, 5, 6, 7, 8
| ], [4, 8]);
| const c = tf.matMul(a, b);
| const cData = await c.data();
| expect(c.shape).toEqual([8, 8]);
| expectArraysClose(cData, [
| 49, 53, 25, 21, 8, 25, 33, 52, 121, 133, 57, 49, 12,
| 45, 69, 136, 193, 213, 89, 77, 16, 65, 105, 220, 265, 293,
| 121, 105, 20, 85, 141, 304, 337, 373, 153, 133, 24, 105, 177,
| 388, 409, 453, 185, 161, 28, 125, 213, 472, 49, 53, 25, 21,
| 8, 25, 33, 52, 121, 133, 57, 49, 12, 45, 69, 136
| ]);
| });
| it('broadcast with unequal batch dims', async () => {
| const a = tf.tensor3d([
| 2, 1, 3, 2, 1, 1, 1, 5, 6, 7, 8, 1,
| 2, 2, 1, 9, 11, 10, 1, 1, 3, 2, 1, 1
| ], [4, 3, 2]);
| const b = tf.tensor3d([1, 0.5], [1, 2, 1]);
| const c = tf.matMul(a, b);
| expect(c.shape).toEqual([4, 3, 1]);
| expectArraysClose(await c.data(), [2.5, 4, 1.5, 3.5, 9.5, 8.5, 3, 5.5, 16, 1.5, 4, 1.5]);
| });
| it('broadcast with unequal ranks', async () => {
| const a = tf.tensor5d([
| 2, 1, 3, 2, 1, 1, 1, 5, 6, 7, 8, 1,
| 2, 2, 1, 9, 11, 10, 1, 1, 3, 2, 1, 1
| ], [1, 2, 2, 3, 2]);
| const b = tf.tensor2d([1, 0.5], [2, 1]);
| const c = tf.matMul(a, b);
| expect(c.shape).toEqual([1, 2, 2, 3, 1]);
| expectArraysClose(await c.data(), [2.5, 4, 1.5, 3.5, 9.5, 8.5, 3, 5.5, 16, 1.5, 4, 1.5]);
| });
| it('matmul followed by mul', async () => {
| const a = tf.tensor2d([1, 2, 3, 4], [2, 2]);
| const b = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
| const c = tf.matMul(a, b);
| const f = tf.tensor2d([0, 1, 0.5, 0, 0.25, 2], [2, 3]);
| const d = tf.mul(c, f);
| const dData = await d.data();
| expect(d.shape).toEqual([2, 3]);
| expectArraysClose(dData, [0, 12, 7.5, 0, 6.5, 66]);
| });
| it('upcasts when dtypes dont match', async () => {
| const a = [1, 2, 3, 4, 5, 6];
| const b = [0, 1, -3, 2, 2, 1];
| let c = tf.matMul(tf.tensor(a, [2, 3], 'float32'), tf.tensor(b, [3, 2], 'int32'));
| expect(c.shape).toEqual([2, 2]);
| expect(c.dtype).toBe('float32');
| expectArraysClose(await c.data(), [0, 8, -3, 20]);
| c = tf.matMul(tf.tensor(a, [2, 3], 'int32'), tf.tensor(b, [3, 2], 'bool'));
| expect(c.shape).toEqual([2, 2]);
| expect(c.dtype).toBe('int32');
| expectArraysClose(await c.data(), [5, 6, 11, 15]);
| });
| it('A x B^t', async () => {
| const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
| const b = tf.tensor2d([1, 0, 2, 4, 3, 0], [2, 3]);
| const transposeA = false;
| const transposeB = true;
| const c = tf.matMul(a, b, transposeA, transposeB);
| const expected = [7, 10, 16, 31];
| expectArraysClose(await c.data(), expected);
| });
| it('A^t x B', async () => {
| const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
| const b = tf.tensor2d([1, 0, 2, 4, 3, 0], [2, 3]);
| const transposeA = true;
| const transposeB = false;
| const c = tf.matMul(a, b, transposeA, transposeB);
| const expected = [17, 12, 2, 22, 15, 4, 27, 18, 6];
| expectArraysClose(await c.data(), expected);
| });
| it('A^t x B^t', async () => {
| const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [3, 2]);
| const b = tf.tensor2d([1, 0, 2, 4, 3, 0], [2, 3]);
| const transposeA = true;
| const transposeB = true;
| const c = tf.matMul(a, b, transposeA, transposeB);
| const expected = [11, 13, 14, 20];
| expectArraysClose(await c.data(), expected);
| });
| it('A x B^t shapes do not match', () => {
| const a = tf.zeros([2, 3]);
| const b = tf.zeros([3, 2]);
| const f = () => {
| const transposeA = false;
| const transposeB = true;
| tf.matMul(a, b, transposeA, transposeB);
| };
| expect(f).toThrowError();
| });
| it('A^t x B shapes do not match', () => {
| const a = tf.zeros([2, 3]);
| const b = tf.zeros([3, 2]);
| const f = () => {
| const transposeA = true;
| const transposeB = false;
| tf.matMul(a, b, transposeA, transposeB);
| };
| expect(f).toThrowError();
| });
| it('A^t x B^t shapes do not match', () => {
| const a = tf.zeros([3, 2]);
| const b = tf.zeros([3, 2]);
| const f = () => {
| const transposeA = true;
| const transposeB = true;
| tf.matMul(a, b, transposeA, transposeB);
| };
| expect(f).toThrowError();
| });
| it('matmul throws when inner dimensions dont match', () => {
| const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
| const b = tf.tensor2d([0, 1, -3, 2, 2, 1, 2, 2], [4, 2]);
| expect(() => tf.matMul(a, b)).toThrowError();
| });
| it('matmul throws when passed non matrices', () => {
| // tslint:disable-next-line:no-any
| const a = tf.tensor3d([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [2, 3, 2]);
| const b = tf.tensor2d([0, 1, -3, 2, 2, 1, 2, 2], [4, 2]);
| expect(() => tf.matMul(a, b)).toThrowError();
| expect(() => tf.matMul(b, a)).toThrowError();
| });
| it('matmul throws when passed a vector', () => {
| // tslint:disable-next-line:no-any
| const v = tf.tensor1d([2, 3]);
| const matrix = tf.tensor2d([1, 2, 3, 4], [2, 2]);
| expect(() => tf.matMul(matrix, v)).toThrowError();
| });
| it('Vector times matrix', async () => {
| const v = tf.tensor1d([2, 3]);
| const matrix = tf.tensor2d([1, 2, 3, 4], [2, 2]);
| const result = tf.dot(v, matrix);
| const expected = [11, 16];
| expectArraysClose(await result.data(), expected);
| });
| it('Vector times matrix with implicit reshape', async () => {
| const v = tf.tensor1d([2, 3]);
| const matrix = tf.tensor2d([1, 2, 3, 4], [2, 2]);
| const result = tf.dot(v, matrix);
| const expected = [11, 16];
| expectArraysClose(await result.data(), expected);
| });
| it('Matrix times vector', async () => {
| const matrix = tf.tensor2d([1, 2, 3, 4], [2, 2]);
| const v = tf.tensor1d([2, 3]);
| const result = tf.dot(matrix, v);
| const expected = [8, 18];
| expectArraysClose(await result.data(), expected);
| });
| it('batched matmul with the matrices being vectors', async () => {
| const batch = 3;
| const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;
| const values = new Float32Array(batch * sharedDim);
| values[10] = 2;
| const a = tf.tensor(values, [batch, 1, sharedDim]);
| const b = tf.tensor(values, [batch, sharedDim, 1]);
| const result = tf.matMul(a, b);
| expect(result.shape).toEqual([batch, 1, 1]);
| expectArraysClose(await result.data(), [4, 0, 0]);
| });
| it('batched matmul called twice so memory of output is reused', async () => {
| const batch = 3;
| const n = 2;
| const vals = new Float32Array(batch * n * n);
| vals[0] = 2;
| vals[4] = 3;
| vals[8] = 4;
| const a = tf.tensor(vals, [batch, n, n]);
| const b = tf.tensor(vals, [batch, n, n]);
| const result = tf.matMul(a, b);
| expect(result.shape).toEqual([batch, n, n]);
| expectArraysClose(await result.data(), [4, 0, 0, 0, 9, 0, 0, 0, 16, 0, 0, 0]);
| // Dispose the first output, so memory of the second output (which has the
| // same shape), could be reused.
| result.dispose();
| const vals2 = new Float32Array(batch * n * n);
| vals2[3] = 2;
| vals2[7] = 3;
| vals2[11] = 4;
| const a2 = tf.tensor(vals2, [batch, n, n]);
| const b2 = tf.tensor(vals2, [batch, n, n]);
| const result2 = tf.matMul(a2, b2);
| expect(result2.shape).toEqual([batch, n, n]);
| expectArraysClose(await result2.data(), [0, 0, 0, 4, 0, 0, 0, 9, 0, 0, 0, 16]);
| });
| it('batched matmul with the matrices being vectors transposedA', async () => {
| const batch = 3;
| const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;
| const values = new Float32Array(batch * sharedDim);
| values[10] = 2;
| const a = tf.tensor(values, [batch, sharedDim, 1]);
| const b = tf.tensor(values, [batch, sharedDim, 1]);
| const transposeA = true;
| const transposeB = false;
| const result = tf.matMul(a, b, transposeA, transposeB);
| expect(result.shape).toEqual([batch, 1, 1]);
| expectArraysClose(await result.data(), [4, 0, 0]);
| });
| it('batched matmul with the matrices being vectors transposedB', async () => {
| const batch = 3;
| const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;
| const values = new Float32Array(batch * sharedDim);
| values[10] = 2;
| const a = tf.tensor(values, [batch, 1, sharedDim]);
| const b = tf.tensor(values, [batch, 1, sharedDim]);
| const transposeA = false;
| const transposeB = true;
| const result = tf.matMul(a, b, transposeA, transposeB);
| expect(result.shape).toEqual([batch, 1, 1]);
| expectArraysClose(await result.data(), [4, 0, 0]);
| });
| it('batched matmul with matrix x vector', async () => {
| const batch = 3;
| const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;
| const values = new Float32Array(batch * sharedDim);
| values[10] = 2;
| const a = tf.ones([batch, 2, sharedDim]);
| const b = tf.tensor(values, [batch, sharedDim, 1]);
| const result = tf.matMul(a, b);
| expect(result.shape).toEqual([batch, 2, 1]);
| expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);
| });
| it('batched matmul with matrix x vector transposedA', async () => {
| const batch = 3;
| const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;
| const values = new Float32Array(batch * sharedDim);
| values[10] = 2;
| const a = tf.ones([batch, sharedDim, 2]);
| const b = tf.tensor(values, [batch, sharedDim, 1]);
| const transposeA = true;
| const transposeB = false;
| const result = tf.matMul(a, b, transposeA, transposeB);
| expect(result.shape).toEqual([batch, 2, 1]);
| expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);
| });
| it('batched matmul with matrix x vector transposedB', async () => {
| const batch = 3;
| const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;
| const values = new Float32Array(batch * sharedDim);
| values[10] = 2;
| const a = tf.ones([batch, 2, sharedDim]);
| const b = tf.tensor(values, [batch, 1, sharedDim]);
| const transposeA = false;
| const transposeB = true;
| const result = tf.matMul(a, b, transposeA, transposeB);
| expect(result.shape).toEqual([batch, 2, 1]);
| expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);
| });
| it('batched matmul with vector x matrix', async () => {
| const batch = 3;
| const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;
| const values = new Float32Array(batch * sharedDim);
| values[10] = 2;
| const a = tf.tensor(values, [batch, 1, sharedDim]);
| const b = tf.ones([batch, sharedDim, 2]);
| const result = tf.matMul(a, b);
| expect(result.shape).toEqual([batch, 1, 2]);
| expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);
| });
| it('batched matmul with vector x matrix transposedA', async () => {
| const batch = 3;
| const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;
| const values = new Float32Array(batch * sharedDim);
| values[10] = 2;
| const a = tf.tensor(values, [batch, sharedDim, 1]);
| const b = tf.ones([batch, sharedDim, 2]);
| const transposeA = true;
| const transposeB = false;
| const result = tf.matMul(a, b, transposeA, transposeB);
| expect(result.shape).toEqual([batch, 1, 2]);
| expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);
| });
| it('batched matmul with vector x matrix transposedB', async () => {
| const batch = 3;
| const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;
| const values = new Float32Array(batch * sharedDim);
| values[10] = 2;
| const a = tf.tensor(values, [batch, 1, sharedDim]);
| const b = tf.ones([batch, 2, sharedDim]);
| const transposeA = false;
| const transposeB = true;
| const result = tf.matMul(a, b, transposeA, transposeB);
| expect(result.shape).toEqual([batch, 1, 2]);
| expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);
| });
| it('Matrix * vector propagates NaNs', async () => {
| const matrix = tf.tensor2d([1, 2, 3, 4], [2, 2]);
| const v = tf.tensor1d([2, NaN]);
| const result = tf.dot(matrix, v);
| const expected = [NaN, NaN];
| expectArraysClose(await result.data(), expected);
| });
| it('matrix times vector throws when not passed a matrix', () => {
| const v = tf.tensor1d([2, 3]);
| // tslint:disable-next-line:no-any
| const matrix = tf.tensor3d([1, 2, 3, 4, 5, 6, 7, 8], [2, 2, 2]);
| expect(() => tf.dot(matrix, v)).toThrowError();
| });
| it('Dot product', async () => {
| const v1 = tf.tensor1d([2, 3]);
| const v2 = tf.tensor1d([2, 1]);
| const result = tf.dot(v1, v2);
| expectArraysClose(await result.data(), [7]);
| });
| it('Dot product propagates NaNs', async () => {
| const v1 = tf.tensor1d([2, NaN]);
| const v2 = tf.tensor1d([2, 1]);
| const result = tf.dot(v1, v2);
| expectArraysEqual(await result.data(), [NaN]);
| });
| it('Dot product throws when vectors are different size', () => {
| const v1 = tf.tensor1d([2, 3, 3]);
| const v2 = tf.tensor1d([2, 1]);
| expect(() => tf.dot(v1, v2)).toThrowError();
| expect(() => tf.dot(v2, v1)).toThrowError();
| });
| it('Outer product', async () => {
| const v1 = tf.tensor1d([2, 3]);
| const v2 = tf.tensor1d([2, 1]);
| const result = tf.outerProduct(v1, v2);
| const expected = [4, 2, 6, 3];
| expect(result.shape).toEqual([2, 2]);
| expectArraysClose(await result.data(), expected);
| });
| it('outer product accepts a tensor-like object', async () => {
| const v1 = [2, 3];
| const v2 = [2, 1];
| const result = tf.outerProduct(v1, v2);
| const expected = [4, 2, 6, 3];
| expect(result.shape).toEqual([2, 2]);
| expectArraysClose(await result.data(), expected);
| });
| it('gradients: A * B', async () => {
| const aT = tf.tensor2d([1, 2, 3, 10, 20, 30], [2, 3]);
| const bT = tf.tensor2d([2, 3, 4, 1, 2, 3], [3, 2]);
| const dyT = tf.tensor2d([1, 10, 20, 30], [2, 2]);
| const transposeA = false;
| const transposeB = false;
| const grads = tf.grads((a, b) => tf.matMul(a, b, transposeA, transposeB));
| const [da, db] = grads([aT, bT], dyT);
| // da = dy * bT
| expect(da.shape).toEqual(aT.shape);
| const a = await aT.buffer();
| const dy = await dyT.buffer();
| const b = await bT.buffer();
| expectArraysClose(await da.data(), [
| dy.get(0, 0) * b.get(0, 0) + dy.get(0, 1) * b.get(0, 1),
| dy.get(0, 0) * b.get(1, 0) + dy.get(0, 1) * b.get(1, 1),
| dy.get(0, 0) * b.get(2, 0) + dy.get(0, 1) * b.get(2, 1),
| dy.get(1, 0) * b.get(0, 0) + dy.get(1, 1) * b.get(0, 1),
| dy.get(1, 0) * b.get(1, 0) + dy.get(1, 1) * b.get(1, 1),
| dy.get(1, 0) * b.get(2, 0) + dy.get(1, 1) * b.get(2, 1)
| ], 1e-1);
| // db = aT * dy
| expect(db.shape).toEqual(b.shape);
| expectArraysClose(await db.data(), [
| a.get(0, 0) * dy.get(0, 0) + a.get(1, 0) * dy.get(1, 0),
| a.get(0, 0) * dy.get(0, 1) + a.get(1, 0) * dy.get(1, 1),
| a.get(0, 1) * dy.get(0, 0) + a.get(1, 1) * dy.get(1, 0),
| a.get(0, 1) * dy.get(0, 1) + a.get(1, 1) * dy.get(1, 1),
| a.get(0, 2) * dy.get(0, 0) + a.get(1, 2) * dy.get(1, 0),
| a.get(0, 2) * dy.get(0, 1) + a.get(1, 2) * dy.get(1, 1)
| ]);
| });
| it('gradient with clones', () => {
| const a = tf.tensor2d([1, 2, 3, 10, 20, 30], [2, 3]);
| const b = tf.tensor2d([2, 3, 4, 1, 2, 3], [3, 2]);
| const grads = tf.grads((a, b) => tf.matMul(a.clone(), b.clone()).clone());
| const [da, db] = grads([a, b]);
| expect(da.shape).toEqual(a.shape);
| expect(db.shape).toEqual(b.shape);
| });
| it('gradients: a * bT', async () => {
| const aT = tf.tensor2d([1, 2, 3, 10, 20, 30], [3, 2]);
| const bT = tf.tensor2d([2, 3, 4, 1, 2, 3], [3, 2]);
| const dyT = tf.tensor2d([1, 10, 20, 30, 40, 50, 60, 70, 80], [3, 3]);
| const transposeA = false;
| const transposeB = true;
| const grads = tf.grads((a, b) => tf.matMul(a, b, transposeA, transposeB));
| const [da, db] = grads([aT, bT], dyT);
| // da = dy * b
| expect(da.shape).toEqual(aT.shape);
| const a = await aT.buffer();
| const dy = await dyT.buffer();
| const b = await bT.buffer();
| expectArraysClose(await da.data(), [
| dy.get(0, 0) * b.get(0, 0) + dy.get(0, 1) * b.get(1, 0) +
| dy.get(0, 2) * b.get(2, 0),
| dy.get(0, 0) * b.get(0, 1) + dy.get(0, 1) * b.get(1, 1) +
| dy.get(0, 2) * b.get(2, 1),
| dy.get(1, 0) * b.get(0, 0) + dy.get(1, 1) * b.get(1, 0) +
| dy.get(1, 2) * b.get(2, 0),
| dy.get(1, 0) * b.get(0, 1) + dy.get(1, 1) * b.get(1, 1) +
| dy.get(1, 2) * b.get(2, 1),
| dy.get(2, 0) * b.get(0, 0) + dy.get(2, 1) * b.get(1, 0) +
| dy.get(2, 2) * b.get(2, 0),
| dy.get(2, 0) * b.get(0, 1) + dy.get(2, 1) * b.get(1, 1) +
| dy.get(2, 2) * b.get(2, 1)
| ]);
| // db = dyT * a
| expect(db.shape).toEqual(b.shape);
| expectArraysClose(await db.data(), [
| dy.get(0, 0) * a.get(0, 0) + dy.get(1, 0) * a.get(1, 0) +
| dy.get(2, 0) * a.get(2, 0),
| dy.get(0, 0) * a.get(0, 1) + dy.get(1, 0) * a.get(1, 1) +
| dy.get(2, 0) * a.get(2, 1),
| dy.get(0, 1) * a.get(0, 0) + dy.get(1, 1) * a.get(1, 0) +
| dy.get(2, 1) * a.get(2, 0),
| dy.get(0, 1) * a.get(0, 1) + dy.get(1, 1) * a.get(1, 1) +
| dy.get(2, 1) * a.get(2, 1),
| dy.get(0, 2) * a.get(0, 0) + dy.get(1, 2) * a.get(1, 0) +
| dy.get(2, 2) * a.get(2, 0),
| dy.get(0, 2) * a.get(0, 1) + dy.get(1, 2) * a.get(1, 1) +
| dy.get(2, 2) * a.get(2, 1)
| ]);
| });
| it('gradients: aT * b', async () => {
| const aT = tf.tensor2d([1, 2, 3, 10, 20, 30], [3, 2]);
| const bT = tf.tensor2d([2, 3, 4, 1, 2, 3], [3, 2]);
| const dyT = tf.tensor2d([1, 10, 20, 30], [2, 2]);
| const transposeA = true;
| const transposeB = false;
| const grads = tf.grads((a, b) => tf.matMul(a, b, transposeA, transposeB));
| const [da, db] = grads([aT, bT], dyT);
| // da = b * dyT
| expect(da.shape).toEqual(aT.shape);
| const a = await aT.buffer();
| const dy = await dyT.buffer();
| const b = await bT.buffer();
| expectArraysClose(await da.data(), [
| dy.get(0, 0) * b.get(0, 0) + dy.get(0, 1) * b.get(0, 1),
| dy.get(1, 0) * b.get(0, 0) + dy.get(1, 1) * b.get(0, 1),
| dy.get(0, 0) * b.get(1, 0) + dy.get(0, 1) * b.get(1, 1),
| dy.get(1, 0) * b.get(1, 0) + dy.get(1, 1) * b.get(1, 1),
| dy.get(0, 0) * b.get(2, 0) + dy.get(0, 1) * b.get(2, 1),
| dy.get(1, 0) * b.get(2, 0) + dy.get(1, 1) * b.get(2, 1)
| ]);
| // db = a * dy
| expect(db.shape).toEqual(b.shape);
| expectArraysClose(await db.data(), [
| dy.get(0, 0) * a.get(0, 0) + dy.get(1, 0) * a.get(0, 1),
| dy.get(0, 1) * a.get(0, 0) + dy.get(1, 1) * a.get(0, 1),
| dy.get(0, 0) * a.get(1, 0) + dy.get(1, 0) * a.get(1, 1),
| dy.get(0, 1) * a.get(1, 0) + dy.get(1, 1) * a.get(1, 1),
| dy.get(0, 0) * a.get(2, 0) + dy.get(1, 0) * a.get(2, 1),
| dy.get(0, 1) * a.get(2, 0) + dy.get(1, 1) * a.get(2, 1)
| ]);
| });
| it('gradients: aT * bT', async () => {
| const aT = tf.tensor2d([1, 2, 3, 10, 20, 30], [3, 2]);
| const bT = tf.tensor2d([2, 3, 4, 1, 2, 3], [2, 3]);
| const dyT = tf.tensor2d([1, 10, 20, 30], [2, 2]);
| const transposeA = true;
| const transposeB = true;
| const grads = tf.grads((a, b) => tf.matMul(a, b, transposeA, transposeB));
| const [da, db] = grads([aT, bT], dyT);
| // da = bT * dyT
| expect(da.shape).toEqual(aT.shape);
| const a = await aT.buffer();
| const dy = await dyT.buffer();
| const b = await bT.buffer();
| expectArraysClose(await da.data(), [
| dy.get(0, 0) * b.get(0, 0) + dy.get(0, 1) * b.get(1, 0),
| dy.get(1, 0) * b.get(0, 0) + dy.get(1, 1) * b.get(1, 0),
| dy.get(0, 0) * b.get(0, 1) + dy.get(0, 1) * b.get(1, 1),
| dy.get(1, 0) * b.get(0, 1) + dy.get(1, 1) * b.get(1, 1),
| dy.get(0, 0) * b.get(0, 2) + dy.get(0, 1) * b.get(1, 2),
| dy.get(1, 0) * b.get(0, 2) + dy.get(1, 1) * b.get(1, 2)
| ]);
| // db = dyT * aT
| expect(db.shape).toEqual(b.shape);
| expectArraysClose(await db.data(), [
| dy.get(0, 0) * a.get(0, 0) + dy.get(1, 0) * a.get(0, 1),
| dy.get(0, 0) * a.get(1, 0) + dy.get(1, 0) * a.get(1, 1),
| dy.get(0, 0) * a.get(2, 0) + dy.get(1, 0) * a.get(2, 1),
| dy.get(0, 1) * a.get(0, 0) + dy.get(1, 1) * a.get(0, 1),
| dy.get(0, 1) * a.get(1, 0) + dy.get(1, 1) * a.get(1, 1),
| dy.get(0, 1) * a.get(2, 0) + dy.get(1, 1) * a.get(2, 1)
| ]);
| });
| it('throws when passed a as a non-tensor', () => {
| expect(() => tf.matMul({}, tf.tensor2d([2], [1, 1])))
| .toThrowError(/Argument 'a' passed to 'matMul' must be a Tensor/);
| });
| it('throws when passed b as a non-tensor', () => {
| expect(() => tf.matMul(tf.tensor2d([2], [1, 1]), {}))
| .toThrowError(/Argument 'b' passed to 'matMul' must be a Tensor/);
| });
| it('accepts a tensor-like object', async () => {
| const a = [[1, 2, 3], [4, 5, 6]]; // 2x3
| const b = [[0, 1], [-3, 2], [2, 1]]; // 3x2
| const c = tf.matMul(a, b);
| expect(c.shape).toEqual([2, 2]);
| expectArraysClose(await c.data(), [0, 8, -3, 20]);
| });
| it('accepts a tensor-like object chained', async () => {
| const a = tf.tensor2d([[1, 2, 3], [4, 5, 6]], [2, 3]); // 2x3
| const b = [[0, 1], [-3, 2], [2, 1]]; // 3x2
| const c = a.matMul(b);
| expect(c.shape).toEqual([2, 2]);
| expectArraysClose(await c.data(), [0, 8, -3, 20]);
| });
| it('a * b where a has zero in its shape', async () => {
| const a = tf.tensor2d([], [0, 3]);
| const b = tf.tensor2d([1, 2, 3, 4, 5, 6], [3, 2]);
| const c = tf.matMul(a, b);
| expect(c.shape).toEqual([0, 2]);
| expect(c.rank).toBe(2);
| expect(c.size).toBe(0);
| expectArraysClose(await c.data(), []);
| });
| it('(a * b) * c where a has zero in its shape, so a*b does also', async () => {
| const a = tf.tensor2d([], [0, 3]);
| const b = tf.tensor2d([1, 2, 3, 4, 5, 6], [3, 2]);
| const ab = tf.matMul(a, b);
| expect(ab.shape).toEqual([0, 2]);
| expectArraysClose(await ab.data(), []);
| const c = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
| const res = tf.matMul(ab, c);
| expect(res.shape).toEqual([0, 3]);
| expectArraysClose(await res.data(), []);
| });
| it('throws error for string tensor', () => {
| expect(() => tf.matMul([['a']], [['b']]))
| .toThrowError(/Argument 'a' passed to 'matMul' must be numeric tensor/);
| });
| });
| describeWithFlags('matmulBatch', ALL_ENVS, () => {
| it('A x B', async () => {
| const a = tf.tensor3d([
| -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3, 7, -2, 5,
| -6, 3, 8, 7, -8, 1, 4, -4, 6, 4, -4, -9, -5, 2, -2
| ], [5, 2, 3]);
| const b = tf.tensor3d([
| -8, -4, -1, 0, -7, 0, 3, 3, 6, 2, -1, 8, -4, 9, -6,
| 5, 8, 9, -9, 7, 0, -1, -1, -10, -7, 3, 4, 6, 3, -4
| ], [5, 3, 2]);
| const c = tf.matMul(a, b);
| expect(c.shape).toEqual([5, 2, 2]);
| expectArraysClose(await c.data(), [
| 87, 20, -6, -32, -24, -50, -36, -5, 24, 98,
| 70, 33, -64, 47, -42, -28, -71, 24, 37, 5
| ]);
| });
| it('A x B in 4D', async () => {
| const a = tf.tensor4d([
| -2, 3, 5, -5, 3, 9, -3, -5, 1, 1, -9, 9, -6, 6, -8,
| -7, -1, 3, 9, -7, -7, 2, 10, -6, -8, -6, 9, -6, 4, -1,
| 9, -6, 10, 8, -9, 5, -8, -7, 0, 2, -5, -1, -9, -4, 3,
| -2, 6, -4, 7, 1, -5, -4, 9, -8, -6, -8, 4, -1, 4, 3,
| -7, 8, -7, 5, -3, -2, -4, 9, 2, -1, 1, -10, -3, 5, -4,
| 6, -8, -8, 9, -3, -5, 10, 3, -3, -3, 9, 3, -3, 2, -8,
| 10, 1, 9, -2, -2, -3, -4, 6, -10, -1, 8, -8, 7, 3, -2,
| 3, 6, -2, -2, -4, 1, -5, -4, 0, 5, 1, 9, -8, -2, -1
| ], [4, 5, 2, 3]);
| const b = tf.tensor4d([
| -4, -3, -2, -6, 6, -1, -4, -1, 7, -4, 8, -9, -9, 0, -1,
| -4, -6, -7, -3, -4, -7, 6, -8, 1, -2, 1, -1, -3, 8, -5,
| 9, -2, 5, 9, -2, 2, -5, -5, -8, -1, -2, -3, -2, -10, 6,
| -3, 0, 1, 6, 7, 1, 2, -4, -5, 2, -5, -7, 9, 3, -6,
| 6, 4, -4, 6, 10, -3, -2, 8, 10, -8, 10, -1, -9, -7, -8,
| -3, 1, 1, -2, -9, -7, -6, -1, 0, 7, -9, -7, -5, 0, -4,
| -4, -7, 2, 4, 6, 6, -4, -6, -8, 3, -8, -9, 6, 9, -4,
| 1, -1, 0, 8, 9, 0, -5, 3, -1, 5, 0, -10, 7, -2, 6
| ], [4, 5, 3, 2]);
| const transposeA = false;
| const transposeB = false;
| const c = tf.matMul(a, b, transposeA, transposeB);
| expectArraysClose(await c.data(), [
| 32, -17, 68, -12, -15, 14, 5, -46, 96, 32, 46, -17, 78, -85,
| -28, 46, 94, -35, 0, -13, 31, -52, 17, -87, 96, 47, 32, -2,
| -6, 105, 40, -2, 63, 76, 17, 30, 56, -66, -21, 23, -144, 41,
| 22, 8, 118, -106, -88, -6, -17, 2, 2, -26, 8, -63, -38, -108,
| -84, -30, -35, 49, 16, -12, -14, -12, 48, 132, 4, 102, 32, 66,
| -4, 33, -13, 1, -40, -25, -3, 61, -18, -20
| ]);
| });
| it('A x B^t', async () => {
| const a = tf.tensor3d([
| -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3, 7, -2, 5,
| -6, 3, 8, 7, -8, 1, 4, -4, 6, 4, -4, -9, -5, 2, -2
| ], [5, 2, 3]);
| const b = tf.tensor3d([
| -8, -4, -1, 0, -7, 0, 3, 3, 6, 2, -1, 8, -4, 9, -6,
| 5, 8, 9, -9, 7, 0, -1, -1, -10, -7, 3, 4, 6, 3, -4
| ], [5, 2, 3]);
| const transposeA = false;
| const transposeB = true;
| const c = tf.matMul(a, b, transposeA, transposeB);
| expect(c.shape).toEqual([5, 2, 2]);
| expectArraysClose(await c.data(), [
| 66, 35, -48, 14, -45, -33, -12, 7, -76, 64,
| 3, 66, -119, -9, -64, -60, -76, 48, 33, -16
| ]);
| });
| it('A^t x B', async () => {
| const a = tf.tensor3d([
| -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3, 7, -2, 5,
| -6, 3, 8, 7, -8, 1, 4, -4, 6, 4, -4, -9, -5, 2, -2
| ], [5, 2, 3]);
| const b = tf.tensor3d([
| -8, -4, -1, 0, -7, 0, 3, 3, 6, 2, -1, 8, -4, 9, -6,
| 5, 8, 9, -9, 7, 0, -1, -1, -10, -7, 3, 4, 6, 3, -4
| ], [5, 2, 3]);
| const transposeA = true;
| const transposeB = false;
| const c = tf.matMul(a, b, transposeA, transposeB);
| expectArraysClose(await c.data(), [
| 40, -36, 5, 40, 34, 5, 48, 80, 6, -6, 21, -48, -23, -20, -50,
| -12, -21, -12, -58, 15, -96, 23, 6, 39, 20, 109, 42, -67, 45, -40,
| 76, -52, 40, -15, 1, -60, -58, -3, 36, 40, -6, -24, 51, -33, -28
| ]);
| });
| it('A^t x B in 4D', async () => {
| const a = tf.tensor4d([
| -2, 3, 5, -5, 3, 9, -3, -5, 1, 1, -9, 9, -6, 6, -8,
| -7, -1, 3, 9, -7, -7, 2, 10, -6, -8, -6, 9, -6, 4, -1,
| 9, -6, 10, 8, -9, 5, -8, -7, 0, 2, -5, -1, -9, -4, 3,
| -2, 6, -4, 7, 1, -5, -4, 9, -8, -6, -8, 4, -1, 4, 3,
| -7, 8, -7, 5, -3, -2, -4, 9, 2, -1, 1, -10, -3, 5, -4,
| 6, -8, -8, 9, -3, -5, 10, 3, -3, -3, 9, 3, -3, 2, -8,
| 10, 1, 9, -2, -2, -3, -4, 6, -10, -1, 8, -8, 7, 3, -2,
| 3, 6, -2, -2, -4, 1, -5, -4, 0, 5, 1, 9, -8, -2, -1
| ], [4, 5, 2, 3]);
| const b = tf.tensor4d([
| -4, -3, -2, -6, 6, -1, -4, -1, 7, -4, 8, -9, -9, 0, -1,
| -4, -6, -7, -3, -4, -7, 6, -8, 1, -2, 1, -1, -3, 8, -5,
| 9, -2, 5, 9, -2, 2, -5, -5, -8, -1, -2, -3, -2, -10, 6,
| -3, 0, 1, 6, 7, 1, 2, -4, -5, 2, -5, -7, 9, 3, -6,
| 6, 4, -4, 6, 10, -3, -2, 8, 10, -8, 10, -1, -9, -7, -8,
| -3, 1, 1, -2, -9, -7, -6, -1, 0, 7, -9, -7, -5, 0, -4,
| -4, -7, 2, 4, 6, 6, -4, -6, -8, 3, -8, -9, 6, 9, -4,
| 1, -1, 0, 8, 9, 0, -5, 3, -1, 5, 0, -10, 7, -2, 6
| ], [4, 5, 2, 3]);
| const transposeA = true;
| const transposeB = false;
| const c = tf.matMul(a, b, transposeA, transposeB);
| expectArraysClose(await c.data(), [
| 38, -24, 9, -30, 9, -9, -74, 39, -19, 8, 11, -30, 56, -67,
| 46, -40, 71, -74, 82, 42, 55, -50, 6, 1, 60, -18, -13, -15,
| -52, -61, 81, -52, 59, -15, 76, 43, 34, -56, 38, 0, 26, -14,
| -15, 1, -4, 153, -34, 61, -135, 30, -48, 135, -30, 60, 38, 36,
| 58, 40, 45, 71, 1, 2, 3, 24, 90, -56, -10, 40, -18, 6,
| -30, 14, 34, 65, 27, 24, -29, -44, -46, -3, 35, -21, 27, 48,
| 20, 52, 32, 35, -11, -46, -12, 22, 13, 30, 2, -23, -54, -48,
| 34, 16, -42, -39, -26, 82, 89, 76, -84, 30, 9, 27, 30, -21,
| -43, -48, 60, 20, 24, -78, -91, -63, -12, 24, 21, 28, 48, 35,
| -6, 27, 33, 53, -81, -71, 61, -27, 11, -48, -82, 8, -12, -19,
| -10, -48, -81, 0, 13, 32, 41, 0, -100, -120, 16, 124, 152, 45,
| 60, -28, 24, 21, -12, -14, -16, 8, 9, -33, 5, -12, -48, 4,
| 8, 9, 0, -31, 16, -98, -9, 4, -22, 38, 2, -96
| ]);
| });
| it('A^t x B^t', async () => {
| const a = tf.tensor3d([
| -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3, 7, -2, 5,
| -6, 3, 8, 7, -8, 1, 4, -4, 6, 4, -4, -9, -5, 2, -2
| ], [5, 3, 2]);
| const b = tf.tensor3d([
| -8, -4, -1, 0, -7, 0, 3, 3, 6, 2, -1, 8, -4, 9, -6,
| 5, 8, 9, -9, 7, 0, -1, -1, -10, -7, 3, 4, 6, 3, -4
| ], [5, 2, 3]);
| const transposeA = true;
| const transposeB = true;
| const c = tf.matMul(a, b, transposeA, transposeB);
| expectArraysClose(await c.data(), [
| 66, 42, 16, -56, -12, 6, -30, 19, -1, 102,
| -94, 14, -56, 32, 100, -56, -47, -11, 5, -31
| ]);
| });
| it('A has more batch dimensions than B', async () => {
| const a = tf.tensor4d([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [2, 2, 2, 2]);
| const b = tf.tensor3d([1, 2, 3, 4], [2, 2, 1]);
| const c = tf.matMul(a, b);
| expectArraysClose(await c.data(), [5, 11, 39, 53, 29, 35, 95, 109]);
| });
| it('batch dimensions do not match', () => {
| const a = tf.tensor3d([
| -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3,
| 7, -2, 5, -6, 3, 8, 7, -8, 1, 4, -4, 6
| ], [4, 3, 2]);
| const b = tf.tensor3d([
| -8, -4, -1, 0, -7, 0, 3, 3, 6, 2, -1, 8, -4, 9, -6,
| 5, 8, 9, -9, 7, 0, -1, -1, -10, -7, 3, 4, 6, 3, -4
| ], [5, 2, 3]);
| const f = () => {
| tf.matMul(a, b, false, false);
| };
| expect(f).toThrowError();
| });
| it('gradients: A x B', async () => {
| const a = tf.tensor3d([
| -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3, 7, -2, 5,
| -6, 3, 8, 7, -8, 1, 4, -4, 6, 4, -4, -9, -5, 2, -2
| ], [5, 2, 3]);
| const b = tf.tensor3d([
| -8, -4, -1, 0, -7, 0, 3, 3, 6, 2, -1, 8, -4, 9, -6,
| 5, 8, 9, -9, 7, 0, -1, -1, -10, -7, 3, 4, 6, 3, -4
| ], [5, 3, 2]);
| const dy = tf.tensor3d([8, 2, -3, -2, -8, 4, 5, 7, 4, -4, -4, 5, 8, 10, 1, 0, 6, 6, -4, 7], [5, 2, 2]);
| const grads = tf.grads((a, b) => tf.matMul(a, b, false, false));
| const [da, db] = grads([a, b], dy);
| // da = dy * bT
| expect(da.shape).toEqual(a.shape);
| expectArraysClose(await da.data(), [
| -72, -8, -56, 32, 3, 21, -12, -40, 40, 36, 44, 51, -52, -44, -4,
| 61, 49, 13, -2, -10, -108, -9, 0, -1, -24, 60, -6, 49, 26, -40
| ]);
| // db = aT * dy
| expect(db.shape).toEqual(b.shape);
| expectArraysClose(await db.data(), [
| -64, -26, -34, -6, -24, 4, -77, -47, 51, -35, 63, -3, 52, -58, -20,
| 23, -12, 20, 60, 70, -68, -80, 14, 10, 44, -11, -32, -10, -46, -68
| ]);
| });
| it('4d gradients: A x B', async () => {
| const a = tf.tensor4d([
| -2, 3, 5, -5, 3, 9, -3, -5, 1, 1, -9, 9, -6, 6, -8,
| -7, -1, 3, 9, -7, -7, 2, 10, -6, -8, -6, 9, -6, 4, -1,
| 9, -6, 10, 8, -9, 5, -8, -7, 0, 2, -5, -1, -9, -4, 3,
| -2, 6, -4, 7, 1, -5, -4, 9, -8, -6, -8, 4, -1, 4, 3,
| -7, 8, -7, 5, -3, -2, -4, 9, 2, -1, 1, -10, -3, 5, -4,
| 6, -8, -8, 9, -3, -5, 10, 3, -3, -3, 9, 3, -3, 2, -8,
| 10, 1, 9, -2, -2, -3, -4, 6, -10, -1, 8, -8, 7, 3, -2,
| 3, 6, -2, -2, -4, 1, -5, -4, 0, 5, 1, 9, -8, -2, -1
| ], [4, 5, 2, 3]);
| const b = tf.tensor4d([
| -4, -3, -2, -6, 6, -1, -4, -1, 7, -4, 8, -9, -9, 0, -1,
| -4, -6, -7, -3, -4, -7, 6, -8, 1, -2, 1, -1, -3, 8, -5,
| 9, -2, 5, 9, -2, 2, -5, -5, -8, -1, -2, -3, -2, -10, 6,
| -3, 0, 1, 6, 7, 1, 2, -4, -5, 2, -5, -7, 9, 3, -6,
| 6, 4, -4, 6, 10, -3, -2, 8, 10, -8, 10, -1, -9, -7, -8,
| -3, 1, 1, -2, -9, -7, -6, -1, 0, 7, -9, -7, -5, 0, -4,
| -4, -7, 2, 4, 6, 6, -4, -6, -8, 3, -8, -9, 6, 9, -4,
| 1, -1, 0, 8, 9, 0, -5, 3, -1, 5, 0, -10, 7, -2, 6
| ], [4, 5, 3, 2]);
| const dy = tf.tensor4d([
| 8, -7, 0, -9, -5, -5, 0, 3, 7, -4, 6, -8, -8, 0, -1, -8,
| -9, -7, -4, -9, 2, 3, 5, 8, -5, -7, 3, -10, -5, -9, -5, 1,
| 7, 1, -9, -10, 8, 5, 0, 8, -6, 4, 0, -5, 8, -7, -2, 1,
| -8, 9, 9, -7, 1, 7, -2, 5, -2, 9, 1, -5, 7, 5, -7, -6,
| 6, 7, -8, 7, 4, -5, 4, -5, 3, -4, -5, 4, -6, 3, -8, 10
| ], [4, 5, 2, 2]);
| const grads = tf.grads((a, b) => tf.matMul(a, b, false, false));
| const [da, db] = grads([a, b], dy);
| // da = dy * bT
| expect(da.shape).toEqual(a.shape);
| expectArraysClose(await da.data(), [
| -11, 26, 55, 27, 54, 9, 25, -15, 5, -3, -12, -27, -63, 9,
| -14, -54, 26, 20, 24, 56, 64, 35, -41, 0, 11, 30, -37, -1,
| 31, 13, 12, 37, 2, 29, 97, 6, 60, 47, 31, 35, -14, 24,
| 100, -3, -9, 0, -33, 1, 49, 9, -33, -124, -29, 86, -9, -11,
| -6, -40, 72, -48, -20, 48, -72, -20, -30, 15, -72, 136, 87, 12,
| -28, -21, 9, 37, 1, -32, -51, 2, -65, -49, -1, -41, -16, 2,
| -95, -31, -36, 52, 18, 20, -63, 34, 72, 70, -38, -78, -66, -27,
| -111, -10, 85, 1, -21, -21, -4, -21, -21, -4, -12, 20, 13, -4,
| -20, -19, -30, 81, 30, -40, 150, 76
| ]);
| // db = aT * dy
| expect(db.shape).toEqual(b.shape);
| expectArraysClose(await db.data(), [
| -16, 59, 24, -48, 40, -116, 15, 18, 25, -2, -5, 22, -84, 80,
| 36, -16, -38, 8, -74, -16, 46, -80, 62, 48, 96, 110, 38, 6,
| -77, -54, 58, 91, -57, -90, 45, 70, 46, 36, 20, 99, -3, 10,
| 55, 79, -10, 42, 5, -31, 85, 47, -74, -89, 37, 75, -48, -38,
| -64, -8, 32, 44, 42, -53, -48, 47, 42, -18, -30, 27, 70, -62,
| 36, -24, 78, -69, -112, 101, -40, 20, -11, 113, -9, -6, 1, -50,
| 3, -12, -16, 71, -14, 67, 84, 62, 21, 17, 84, 63, -16, -35,
| -28, 98, 4, -126, 40, -50, 36, -45, -16, 20, 19, -12, 8, 0,
| 3, -4, 34, -65, 10, -17, -46, 17
| ]);
| });
| it('gradients: A x B^t', async () => {
| const a = tf.tensor3d([
| -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3, 7, -2, 5,
| -6, 3, 8, 7, -8, 1, 4, -4, 6, 4, -4, -9, -5, 2, -2
| ], [5, 3, 2]);
| const b = tf.tensor3d([
| -8, -4, -1, 0, -7, 0, 3, 3, 6, 2, -1, 8, -4, 9, -6,
| 5, 8, 9, -9, 7, 0, -1, -1, -10, -7, 3, 4, 6, 3, -4
| ], [5, 3, 2]);
| const dy = tf.tensor3d([
| -0, 7, 5, 0, -9, 5, -7, 6, -5, -3, -2, -2, -4, 10, -3,
| 5, -1, 3, -2, -9, 4, -5, 7, 9, -10, -8, -8, -5, -0, -1,
| 3, 3, 4, 9, -7, 6, -2, -9, 5, 1, -5, -3, -1, 9, 4
| ], [5, 3, 3]);
| const grads = tf.grads((a, b) => tf.matMul(a, b, false, true));
| const [da, db] = grads([a, b], dy);
| expect(da.shape).toEqual(a.shape);
| expectArraysClose(await da.data(), [
| -42, 0, -26, 0, 85, 28, -19, -29, 51, -16, 6, 37, 94, -27, 50,
| 71, 24, -202, 46, -25, -31, -22, -87, 10, -7, -80, -36, -15, 55, 35
| ]);
| expect(db.shape).toEqual(b.shape);
| expectArraysClose(await db.data(), [
| 14, 56, 7, -155, -45, 55, 7, 72, -67, -79, 7, 50, -69, -46, -52,
| -88, 49, -126, -68, 106, 31, -30, -27, 60, -19, 5, 27, 43, 55, -13
| ]);
| });
| it('4d gradients: A x B^t', async () => {
| const a = tf.tensor4d([
| -2, 3, 5, -5, 3, 9, -3, -5, 1, 1, -9, 9, -6, 6, -8,
| -7, -1, 3, 9, -7, -7, 2, 10, -6, -8, -6, 9, -6, 4, -1,
| 9, -6, 10, 8, -9, 5, -8, -7, 0, 2, -5, -1, -9, -4, 3,
| -2, 6, -4, 7, 1, -5, -4, 9, -8, -6, -8, 4, -1, 4, 3,
| -7, 8, -7, 5, -3, -2, -4, 9, 2, -1, 1, -10, -3, 5, -4,
| 6, -8, -8, 9, -3, -5, 10, 3, -3, -3, 9, 3, -3, 2, -8,
| 10, 1, 9, -2, -2, -3, -4, 6, -10, -1, 8, -8, 7, 3, -2,
| 3, 6, -2, -2, -4, 1, -5, -4, 0, 5, 1, 9, -8, -2, -1
| ], [4, 5, 3, 2]);
| const b = tf.tensor4d([
| -4, -3, -2, -6, 6, -1, -4, -1, 7, -4, 8, -9, -9, 0, -1,
| -4, -6, -7, -3, -4, -7, 6, -8, 1, -2, 1, -1, -3, 8, -5,
| 9, -2, 5, 9, -2, 2, -5, -5, -8, -1, -2, -3, -2, -10, 6,
| -3, 0, 1, 6, 7, 1, 2, -4, -5, 2, -5, -7, 9, 3, -6,
| 6, 4, -4, 6, 10, -3, -2, 8, 10, -8, 10, -1, -9, -7, -8,
| -3, 1, 1, -2, -9, -7, -6, -1, 0, 7, -9, -7, -5, 0, -4,
| -4, -7, 2, 4, 6, 6, -4, -6, -8, 3, -8, -9, 6, 9, -4,
| 1, -1, 0, 8, 9, 0, -5, 3, -1, 5, 0, -10, 7, -2, 6
| ], [4, 5, 3, 2]);
| const dy = tf.tensor4d([
| 5, -1, -5, -4, -1, 9, 1, -2, 10, 7, -1, 6, -8, 8, -3,
| 9, -4, 2, -4, -8, 8, 4, 8, -10, -8, -8, 6, 6, -5, 9,
| -1, -7, -5, -3, -3, 2, -6, 5, 8, -9, 5, -8, -3, 8, 6,
| 2, 8, 5, 9, 7, 6, 2, -3, 10, 7, 7, -3, 4, -3, -6,
| -8, -8, 9, 0, -8, -3, -2, -2, 8, 2, 3, -6, 3, 6, -3,
| 7, 7, -9, -3, 8, 7, 7, -1, -6, 5, 2, -1, -1, 1, 5,
| 0, -4, 3, -4, -10, 1, -2, -8, -9, -6, 4, 4, -7, -1, -1,
| -9, 7, 1, -1, 8, 0, -2, -7, 5, 7, 8, 9, -3, -8, -6,
| -7, -8, -1, 8, -4, 7, 5, -9, 9, 3, 0, -10, 7, -9, 4,
| -7, 5, -2, -2, 3, 3, -6, 2, 0, 8, -5, -10, 3, -7, 0,
| -6, 2, 3, -1, 3, 3, -10, 1, 3, -7, -1, 8, -2, -1, -1,
| -3, -9, 7, 4, -6, 3, 0, -7, -4, -5, -8, -6, 10, -6, 4
| ], [4, 5, 3, 3]);
| const grads = tf.grads((a, b) => tf.matMul(a, b, false, true));
| const [da, db] = grads([a, b], dy);
| expect(da.shape).toEqual(a.shape);
| expectArraysClose(await da.data(), [
| -48, -4, 72, 9, 60, -1, 13, -57, 64, 3, -48, -11, -4, -24,
| 16, 38, 44, -10, -55, -45, 92, -43, 14, -4, 71, -61, -51, 16,
| 46, -57, 48, 78, 104, 57, -17, -11, -85, -33, 16, 1, 86, 21,
| -48, 21, -8, 34, 14, -35, 36, 48, 85, 108, -38, -40, 3, -8,
| -7, -1, 6, -16, 46, -33, 26, -79, -70, -29, 92, -84, -6, -47,
| 98, -129, -55, -17, 79, 40, -118, -64, 68, 75, 71, 111, 5, -48,
| 98, -36, 21, 13, 112, -34, 26, 57, 32, 44, 28, 50, 88, 27,
| 44, -39, -16, 15, -21, -6, -67, -89, -46, -64, -19, -12, -3, 11,
| 41, 63, 78, -73, 67, -92, 102, -18
| ]);
| expect(db.shape).toEqual(b.shape);
| expectArraysClose(await db.data(), [
| -27, 44, -9, -16, 85, 30, -110, 38, 47, -23, -39, -15, 0, -76,
| -8, -128, 26, 136, 31, -26, -26, 39, 136, -85, -45, 93, 37, -68,
| -112, -6, 90, 70, 169, -7, 15, 68, -16, -33, -16, -47, -21, 0,
| 6, -4, 84, 24, 15, 20, -41, -1, 79, -86, 87, -23, -26, -64,
| 18, 9, 52, 64, 34, -16, 122, -66, -1, 47, 1, 43, -11, -33,
| -17, 27, -45, -73, -60, -66, -92, -42, 32, -85, -44, -44, -28, -13,
| 8, -20, 9, -9, -49, 79, -76, 15, 73, -7, 7, -8, -110, 93,
| 106, -39, 64, -84, -29, -19, 13, 14, 63, 2, -15, 23, 17, 49,
| -3, -31, -65, 30, -95, 63, -82, 40
| ]);
| });
| it('gradients: A^t x B', async () => {
| const a = tf.tensor3d([
| -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3, 7, -2, 5,
| -6, 3, 8, 7, -8, 1, 4, -4, 6, 4, -4, -9, -5, 2, -2
| ], [5, 3, 2]);
| const b = tf.tensor3d([
| -8, -4, -1, 0, -7, 0, 3, 3, 6, 2, -1, 8, -4, 9, -6,
| 5, 8, 9, -9, 7, 0, -1, -1, -10, -7, 3, 4, 6, 3, -4
| ], [5, 3, 2]);
| const dy = tf.tensor3d([8, 2, -3, -2, -8, 4, 5, 7, 4, -4, -4, 5, 8, 10, 1, 0, 6, 6, -4, 7], [5, 2, 2]);
| const grads = tf.grads((a, b) => tf.matMul(a, b, true, false));
| const [da, db] = grads([a, b], dy);
| expect(da.shape).toEqual(a.shape);
| expectArraysClose(await da.data(), [
| -72, 32, -8, 3, -56, 21, -12, 36, -40, 44, 40, 51, -52, 61, -44,
| 49, -4, 13, -2, -9, -10, 0, -108, -1, -24, 49, 60, 26, -6, -40
| ]);
| expect(db.shape).toEqual(b.shape);
| expectArraysClose(await db.data(), [
| -25, 0, -72, -28, 8, 12, -67, -33, 3, -87, 23, 17, 36, -38, 44,
| -50, -20, 28, 48, 70, 12, 10, -26, -40, 40, -4, -34, -89, 20, -2
| ]);
| });
| it('gradients: A^t x B^t', async () => {
| const a = tf.tensor3d([
| -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3, 7, -2, 5,
| -6, 3, 8, 7, -8, 1, 4, -4, 6, 4, -4, -9, -5, 2, -2
| ], [5, 3, 2]);
| const b = tf.tensor3d([
| -8, -4, -1, 0, -7, 0, 3, 3, 6, 2, -1, 8, -4, 9, -6,
| 5, 8, 9, -9, 7, 0, -1, -1, -10, -7, 3, 4, 6, 3, -4
| ], [5, 2, 3]);
| const dy = tf.tensor3d([8, 2, -3, -2, -8, 4, 5, 7, 4, -4, -4, 5, 8, 10, 1, 0, 6, 6, -4, 7], [5, 2, 2]);
| const grads = tf.grads((a, b) => tf.matMul(a, b, true, true));
| const [da, db] = grads([a, b], dy);
| expect(da.shape).toEqual(a.shape);
| expectArraysClose(await da.data(), [
| -64, 24, -46, 26, -8, 3, -16, 29, -28, 8, -16, 86, -36, 41, 4,
| 4, -60, 69, -82, -9, 46, 7, -100, 0, -6, 70, 36, 9, 0, -44
| ]);
| expect(db.shape).toEqual(b.shape);
| expectArraysClose(await db.data(), [
| -25, -72, 8, 0, -28, 12, -67, 3, 23, -33, -87, 17, 36, 44, -20,
| -38, -50, 28, 48, 12, -26, 70, 10, -40, 40, -34, 20, -4, -89, -2
| ]);
| });
| });
| describeWithFlags('dot', ALL_ENVS, () => {
| let a;
| let b;
| let c;
| let d;
| let e;
| let f;
| beforeEach(() => {
| a = tf.tensor1d([1, 2]);
| b = tf.tensor2d([[1, 2], [3, 4]]);
| c = tf.tensor2d([[1, 2, 3], [4, 5, 6]]);
| d = tf.tensor3d([1, 2], [1, 1, 2]);
| e = tf.scalar(1);
| f = tf.tensor3d([1, 2, 1, 2], [2, 1, 2]);
| });
| it('vector-vector', async () => {
| const aa = tf.dot(a, a);
| expectArraysClose(await aa.data(), [5]);
| expect(aa.shape).toEqual([]);
| });
| it('vector-matrix', async () => {
| const ab = tf.dot(a, b);
| const ac = tf.dot(a, c);
| expect(ab.shape).toEqual([2]);
| expect(ac.shape).toEqual([3]);
| expectArraysClose(await ab.data(), [7, 10]);
| expectArraysClose(await ac.data(), [9, 12, 15]);
| });
| it('matrix-vector', async () => {
| const ba = b.dot(a);
| expect(ba.shape).toEqual([2]);
| expectArraysClose(await ba.data(), [5, 11]);
| });
| it('matrix-matrix', async () => {
| const bb = tf.dot(b, b);
| const bc = tf.dot(b, c);
| expect(bb.shape).toEqual([2, 2]);
| expect(bc.shape).toEqual([2, 3]);
| expectArraysClose(await bb.data(), [7, 10, 15, 22]);
| expectArraysClose(await bc.data(), [9, 12, 15, 19, 26, 33]);
| });
| it('matmul A x B asymmetric', async () => {
| const a = tf.tensor2d([1, 2, 3, 4], [2, 2]);
| const b = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
| const c = tf.matMul(a, b);
| const cData = await c.data();
| expect(c.shape).toEqual([2, 3]);
| expectArraysClose(cData, [9, 12, 15, 19, 26, 33]);
| });
| it('broadcast batch shape', async () => {
| const a = tf.tensor3d([1, 2, 3, 4], [1, 2, 2]);
| const b = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
| const c = tf.matMul(a, b);
| const cData = await c.data();
| expect(c.shape).toEqual([1, 2, 3]);
| expectArraysClose(cData, [9, 12, 15, 19, 26, 33]);
| });
| it('throws error on incompatible dimensions', () => {
| expect(() => tf.dot(c, f)).toThrowError();
| });
| it('throws error when inputs are not rank 1 or 2', () => {
| expect(() => tf.dot(a, d)).toThrowError();
| expect(() => tf.dot(a, e)).toThrowError();
| });
| it('accepts a tensor-like object', async () => {
| const a = [1, 2, 3];
| const res = tf.dot(a, a);
| expectArraysClose(await res.data(), [14]);
| expect(res.shape).toEqual([]);
| });
| it('throws error for string tensors', () => {
| expect(() => tf.dot('a', 'b'))
| .toThrowError(/Argument 't1' passed to 'dot' must be numeric tensor/);
| });
| it('ensure no memory leak', async () => {
| const numTensorsBefore = tf.memory().numTensors;
| const numDataIdBefore = tf.engine().backend.numDataIds();
| const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
| const b = tf.tensor2d([0, 1, -3, 2, 2, 1], [3, 2]);
| const c = tf.matMul(a, b);
| expect(c.shape).toEqual([2, 2]);
| expectArraysClose(await c.data(), [0, 8, -3, 20]);
| a.dispose();
| b.dispose();
| c.dispose();
| const numTensorsAfter = tf.memory().numTensors;
| const numDataIdAfter = tf.engine().backend.numDataIds();
| expect(numTensorsAfter).toBe(numTensorsBefore);
| expect(numDataIdAfter).toBe(numDataIdBefore);
| });
| });
| //# 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* @license\n * Copyright 2017 Google LLC. All Rights Reserved.\n * Licensed under the Apache License, Version 2.0 (the \"License\");\n * you may not use this file except in compliance with the License.\n * You may obtain a copy of the License at\n *\n * http://www.apache.org/licenses/LICENSE-2.0\n *\n * Unless required by applicable law or agreed to in writing, software\n * distributed under the License is distributed on an \"AS IS\" BASIS,\n * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n * See the License for the specific language governing permissions and\n * limitations under the License.\n * =============================================================================\n */\n\n// Empirically determined minimal shared dimension in matmul before we forward\n// to a.mul(b).sum() in order to take advantage of GPU parallelism. See\n// https://github.com/tensorflow/tfjs-core/pull/1379 for benchmarks.\n// Copied from webgl backend.\n// TODO(yassogba, annyuan) copy tests over to webgl backend that want to\n// explicitly test this threshold.\nexport const MATMUL_SHARED_DIM_THRESHOLD = 1000;\n\nimport * as tf from '../index';\nimport {ALL_ENVS, describeWithFlags} from '../jasmine_util';\nimport {expectArraysClose, expectArraysEqual} from '../test_util';\nimport {Rank} from '../types';\n\ndescribeWithFlags('matmul', ALL_ENVS, () => {\n  it('A x B', async () => {\n    const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);\n    const b = tf.tensor2d([0, 1, -3, 2, 2, 1], [3, 2]);\n\n    const c = tf.matMul(a, b);\n\n    expect(c.shape).toEqual([2, 2]);\n    expectArraysClose(await c.data(), [0, 8, -3, 20]);\n  });\n\n  it('[8,4]x[4,8]', async () => {\n    const a = tf.tensor2d(\n        [\n          1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n          17, 18, 19, 20, 21, 22, 23, 24, 1, 2,  3,  4,  5,  6,  7,  8\n        ],\n        [8, 4]);\n    const b = tf.tensor2d(\n        [\n          0,  1,  -3, 2, 1,  -1, 0, 5,  6, 7, 8, 0, -2, -2, 1, 9,\n          11, 10, 0,  1, -3, 2,  1, -1, 1, 2, 3, 4, 5,  6,  7, 8\n        ],\n        [4, 8]);\n\n    const c = tf.matMul(a, b);\n    const cData = await c.data();\n\n    expect(c.shape).toEqual([8, 8]);\n    expectArraysClose(cData, [\n      49,  53,  25,  21,  8,   25,  33,  52,  121, 133, 57,  49,  12,\n      45,  69,  136, 193, 213, 89,  77,  16,  65,  105, 220, 265, 293,\n      121, 105, 20,  85,  141, 304, 337, 373, 153, 133, 24,  105, 177,\n      388, 409, 453, 185, 161, 28,  125, 213, 472, 49,  53,  25,  21,\n      8,   25,  33,  52,  121, 133, 57,  49,  12,  45,  69,  136\n    ]);\n  });\n\n  it('broadcast with unequal batch dims', async () => {\n    const a = tf.tensor3d(\n        [\n          2, 1, 3, 2, 1,  1,  1, 5, 6, 7, 8, 1,\n          2, 2, 1, 9, 11, 10, 1, 1, 3, 2, 1, 1\n        ],\n        [4, 3, 2]);\n    const b = tf.tensor3d([1, 0.5], [1, 2, 1]);\n    const c = tf.matMul(a, b);\n    expect(c.shape).toEqual([4, 3, 1]);\n    expectArraysClose(\n        await c.data(), [2.5, 4, 1.5, 3.5, 9.5, 8.5, 3, 5.5, 16, 1.5, 4, 1.5]);\n  });\n\n  it('broadcast with unequal ranks', async () => {\n    const a = tf.tensor5d(\n        [\n          2, 1, 3, 2, 1,  1,  1, 5, 6, 7, 8, 1,\n          2, 2, 1, 9, 11, 10, 1, 1, 3, 2, 1, 1\n        ],\n        [1, 2, 2, 3, 2]);\n    const b = tf.tensor2d([1, 0.5], [2, 1]);\n    const c = tf.matMul(a, b);\n    expect(c.shape).toEqual([1, 2, 2, 3, 1]);\n    expectArraysClose(\n        await c.data(), [2.5, 4, 1.5, 3.5, 9.5, 8.5, 3, 5.5, 16, 1.5, 4, 1.5]);\n  });\n\n  it('matmul followed by mul', async () => {\n    const a = tf.tensor2d([1, 2, 3, 4], [2, 2]);\n    const b = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);\n\n    const c = tf.matMul(a, b);\n\n    const f = tf.tensor2d([0, 1, 0.5, 0, 0.25, 2], [2, 3]);\n    const d = tf.mul(c, f);\n\n    const dData = await d.data();\n\n    expect(d.shape).toEqual([2, 3]);\n    expectArraysClose(dData, [0, 12, 7.5, 0, 6.5, 66]);\n  });\n\n  it('upcasts when dtypes dont match', async () => {\n    const a = [1, 2, 3, 4, 5, 6];\n    const b = [0, 1, -3, 2, 2, 1];\n\n    let c = tf.matMul(\n        tf.tensor(a, [2, 3], 'float32'), tf.tensor(b, [3, 2], 'int32'));\n\n    expect(c.shape).toEqual([2, 2]);\n    expect(c.dtype).toBe('float32');\n    expectArraysClose(await c.data(), [0, 8, -3, 20]);\n\n    c = tf.matMul(tf.tensor(a, [2, 3], 'int32'), tf.tensor(b, [3, 2], 'bool'));\n\n    expect(c.shape).toEqual([2, 2]);\n    expect(c.dtype).toBe('int32');\n    expectArraysClose(await c.data(), [5, 6, 11, 15]);\n  });\n\n  it('A x B^t', async () => {\n    const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);\n    const b = tf.tensor2d([1, 0, 2, 4, 3, 0], [2, 3]);\n\n    const transposeA = false;\n    const transposeB = true;\n    const c = tf.matMul(a, b, transposeA, transposeB);\n\n    const expected = [7, 10, 16, 31];\n    expectArraysClose(await c.data(), expected);\n  });\n\n  it('A^t x B', async () => {\n    const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);\n    const b = tf.tensor2d([1, 0, 2, 4, 3, 0], [2, 3]);\n\n    const transposeA = true;\n    const transposeB = false;\n    const c = tf.matMul(a, b, transposeA, transposeB);\n\n    const expected = [17, 12, 2, 22, 15, 4, 27, 18, 6];\n    expectArraysClose(await c.data(), expected);\n  });\n\n  it('A^t x B^t', async () => {\n    const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [3, 2]);\n    const b = tf.tensor2d([1, 0, 2, 4, 3, 0], [2, 3]);\n\n    const transposeA = true;\n    const transposeB = true;\n    const c = tf.matMul(a, b, transposeA, transposeB);\n\n    const expected = [11, 13, 14, 20];\n    expectArraysClose(await c.data(), expected);\n  });\n\n  it('A x B^t shapes do not match', () => {\n    const a = tf.zeros<Rank.R2>([2, 3]);\n    const b = tf.zeros<Rank.R2>([3, 2]);\n\n    const f = () => {\n      const transposeA = false;\n      const transposeB = true;\n      tf.matMul(a, b, transposeA, transposeB);\n    };\n    expect(f).toThrowError();\n  });\n\n  it('A^t x B shapes do not match', () => {\n    const a = tf.zeros<Rank.R2>([2, 3]);\n    const b = tf.zeros<Rank.R2>([3, 2]);\n\n    const f = () => {\n      const transposeA = true;\n      const transposeB = false;\n      tf.matMul(a, b, transposeA, transposeB);\n    };\n    expect(f).toThrowError();\n  });\n\n  it('A^t x B^t shapes do not match', () => {\n    const a = tf.zeros<Rank.R2>([3, 2]);\n    const b = tf.zeros<Rank.R2>([3, 2]);\n\n    const f = () => {\n      const transposeA = true;\n      const transposeB = true;\n      tf.matMul(a, b, transposeA, transposeB);\n    };\n    expect(f).toThrowError();\n  });\n\n  it('matmul throws when inner dimensions dont match', () => {\n    const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);\n    const b = tf.tensor2d([0, 1, -3, 2, 2, 1, 2, 2], [4, 2]);\n\n    expect(() => tf.matMul(a, b)).toThrowError();\n  });\n\n  it('matmul throws when passed non matrices', () => {\n    // tslint:disable-next-line:no-any\n    const a: any =\n        tf.tensor3d([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [2, 3, 2]);\n    const b = tf.tensor2d([0, 1, -3, 2, 2, 1, 2, 2], [4, 2]);\n\n    expect(() => tf.matMul(a, b)).toThrowError();\n    expect(() => tf.matMul(b, a)).toThrowError();\n  });\n\n  it('matmul throws when passed a vector', () => {\n    // tslint:disable-next-line:no-any\n    const v: any = tf.tensor1d([2, 3]);\n    const matrix = tf.tensor2d([1, 2, 3, 4], [2, 2]);\n\n    expect(() => tf.matMul(matrix, v)).toThrowError();\n  });\n\n  it('Vector times matrix', async () => {\n    const v = tf.tensor1d([2, 3]);\n    const matrix = tf.tensor2d([1, 2, 3, 4], [2, 2]);\n    const result = tf.dot(v, matrix);\n\n    const expected = [11, 16];\n    expectArraysClose(await result.data(), expected);\n  });\n\n  it('Vector times matrix with implicit reshape', async () => {\n    const v = tf.tensor1d([2, 3]);\n\n    const matrix = tf.tensor2d([1, 2, 3, 4], [2, 2]);\n    const result = tf.dot(v, matrix);\n\n    const expected = [11, 16];\n    expectArraysClose(await result.data(), expected);\n  });\n\n  it('Matrix times vector', async () => {\n    const matrix = tf.tensor2d([1, 2, 3, 4], [2, 2]);\n    const v = tf.tensor1d([2, 3]);\n    const result = tf.dot(matrix, v);\n\n    const expected = [8, 18];\n    expectArraysClose(await result.data(), expected);\n  });\n\n  it('batched matmul with the matrices being vectors', async () => {\n    const batch = 3;\n    const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;\n    const values = new Float32Array(batch * sharedDim);\n    values[10] = 2;\n\n    const a = tf.tensor(values, [batch, 1, sharedDim]);\n    const b = tf.tensor(values, [batch, sharedDim, 1]);\n    const result = tf.matMul(a, b);\n    expect(result.shape).toEqual([batch, 1, 1]);\n    expectArraysClose(await result.data(), [4, 0, 0]);\n  });\n\n  it('batched matmul called twice so memory of output is reused', async () => {\n    const batch = 3;\n    const n = 2;\n    const vals = new Float32Array(batch * n * n);\n    vals[0] = 2;\n    vals[4] = 3;\n    vals[8] = 4;\n\n    const a = tf.tensor(vals, [batch, n, n]);\n    const b = tf.tensor(vals, [batch, n, n]);\n    const result = tf.matMul(a, b);\n    expect(result.shape).toEqual([batch, n, n]);\n    expectArraysClose(\n        await result.data(), [4, 0, 0, 0, 9, 0, 0, 0, 16, 0, 0, 0]);\n    // Dispose the first output, so memory of the second output (which has the\n    // same shape), could be reused.\n    result.dispose();\n\n    const vals2 = new Float32Array(batch * n * n);\n    vals2[3] = 2;\n    vals2[7] = 3;\n    vals2[11] = 4;\n    const a2 = tf.tensor(vals2, [batch, n, n]);\n    const b2 = tf.tensor(vals2, [batch, n, n]);\n    const result2 = tf.matMul(a2, b2);\n    expect(result2.shape).toEqual([batch, n, n]);\n    expectArraysClose(\n        await result2.data(), [0, 0, 0, 4, 0, 0, 0, 9, 0, 0, 0, 16]);\n  });\n\n  it('batched matmul with the matrices being vectors transposedA', async () => {\n    const batch = 3;\n    const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;\n    const values = new Float32Array(batch * sharedDim);\n    values[10] = 2;\n\n    const a = tf.tensor(values, [batch, sharedDim, 1]);\n    const b = tf.tensor(values, [batch, sharedDim, 1]);\n    const transposeA = true;\n    const transposeB = false;\n    const result = tf.matMul(a, b, transposeA, transposeB);\n    expect(result.shape).toEqual([batch, 1, 1]);\n    expectArraysClose(await result.data(), [4, 0, 0]);\n  });\n\n  it('batched matmul with the matrices being vectors transposedB', async () => {\n    const batch = 3;\n    const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;\n    const values = new Float32Array(batch * sharedDim);\n    values[10] = 2;\n\n    const a = tf.tensor(values, [batch, 1, sharedDim]);\n    const b = tf.tensor(values, [batch, 1, sharedDim]);\n    const transposeA = false;\n    const transposeB = true;\n    const result = tf.matMul(a, b, transposeA, transposeB);\n    expect(result.shape).toEqual([batch, 1, 1]);\n    expectArraysClose(await result.data(), [4, 0, 0]);\n  });\n\n  it('batched matmul with matrix x vector', async () => {\n    const batch = 3;\n    const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;\n    const values = new Float32Array(batch * sharedDim);\n    values[10] = 2;\n\n    const a = tf.ones([batch, 2, sharedDim]);\n    const b = tf.tensor(values, [batch, sharedDim, 1]);\n    const result = tf.matMul(a, b);\n    expect(result.shape).toEqual([batch, 2, 1]);\n    expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);\n  });\n\n  it('batched matmul with matrix x vector transposedA', async () => {\n    const batch = 3;\n    const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;\n    const values = new Float32Array(batch * sharedDim);\n    values[10] = 2;\n\n    const a = tf.ones([batch, sharedDim, 2]);\n    const b = tf.tensor(values, [batch, sharedDim, 1]);\n    const transposeA = true;\n    const transposeB = false;\n    const result = tf.matMul(a, b, transposeA, transposeB);\n    expect(result.shape).toEqual([batch, 2, 1]);\n    expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);\n  });\n\n  it('batched matmul with matrix x vector transposedB', async () => {\n    const batch = 3;\n    const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;\n    const values = new Float32Array(batch * sharedDim);\n    values[10] = 2;\n\n    const a = tf.ones([batch, 2, sharedDim]);\n    const b = tf.tensor(values, [batch, 1, sharedDim]);\n    const transposeA = false;\n    const transposeB = true;\n    const result = tf.matMul(a, b, transposeA, transposeB);\n    expect(result.shape).toEqual([batch, 2, 1]);\n    expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);\n  });\n\n  it('batched matmul with vector x matrix', async () => {\n    const batch = 3;\n    const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;\n    const values = new Float32Array(batch * sharedDim);\n    values[10] = 2;\n\n    const a = tf.tensor(values, [batch, 1, sharedDim]);\n    const b = tf.ones([batch, sharedDim, 2]);\n    const result = tf.matMul(a, b);\n    expect(result.shape).toEqual([batch, 1, 2]);\n    expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);\n  });\n\n  it('batched matmul with vector x matrix transposedA', async () => {\n    const batch = 3;\n    const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;\n    const values = new Float32Array(batch * sharedDim);\n    values[10] = 2;\n\n    const a = tf.tensor(values, [batch, sharedDim, 1]);\n    const b = tf.ones([batch, sharedDim, 2]);\n    const transposeA = true;\n    const transposeB = false;\n    const result = tf.matMul(a, b, transposeA, transposeB);\n    expect(result.shape).toEqual([batch, 1, 2]);\n    expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);\n  });\n\n  it('batched matmul with vector x matrix transposedB', async () => {\n    const batch = 3;\n    const sharedDim = MATMUL_SHARED_DIM_THRESHOLD + 1;\n    const values = new Float32Array(batch * sharedDim);\n    values[10] = 2;\n\n    const a = tf.tensor(values, [batch, 1, sharedDim]);\n    const b = tf.ones([batch, 2, sharedDim]);\n    const transposeA = false;\n    const transposeB = true;\n    const result = tf.matMul(a, b, transposeA, transposeB);\n    expect(result.shape).toEqual([batch, 1, 2]);\n    expectArraysClose(await result.data(), [2, 2, 0, 0, 0, 0]);\n  });\n\n  it('Matrix * vector propagates NaNs', async () => {\n    const matrix = tf.tensor2d([1, 2, 3, 4], [2, 2]);\n    const v = tf.tensor1d([2, NaN]);\n    const result = tf.dot(matrix, v);\n\n    const expected = [NaN, NaN];\n    expectArraysClose(await result.data(), expected);\n  });\n\n  it('matrix times vector throws when not passed a matrix', () => {\n    const v = tf.tensor1d([2, 3]);\n\n    // tslint:disable-next-line:no-any\n    const matrix: any = tf.tensor3d([1, 2, 3, 4, 5, 6, 7, 8], [2, 2, 2]);\n\n    expect(() => tf.dot(matrix, v)).toThrowError();\n  });\n\n  it('Dot product', async () => {\n    const v1 = tf.tensor1d([2, 3]);\n    const v2 = tf.tensor1d([2, 1]);\n    const result = tf.dot(v1, v2);\n\n    expectArraysClose(await result.data(), [7]);\n  });\n\n  it('Dot product propagates NaNs', async () => {\n    const v1 = tf.tensor1d([2, NaN]);\n    const v2 = tf.tensor1d([2, 1]);\n    const result = tf.dot(v1, v2);\n    expectArraysEqual(await result.data(), [NaN]);\n  });\n\n  it('Dot product throws when vectors are different size', () => {\n    const v1 = tf.tensor1d([2, 3, 3]);\n    const v2 = tf.tensor1d([2, 1]);\n\n    expect(() => tf.dot(v1, v2)).toThrowError();\n    expect(() => tf.dot(v2, v1)).toThrowError();\n  });\n\n  it('Outer product', async () => {\n    const v1 = tf.tensor1d([2, 3]);\n    const v2 = tf.tensor1d([2, 1]);\n    const result = tf.outerProduct(v1, v2);\n\n    const expected = [4, 2, 6, 3];\n    expect(result.shape).toEqual([2, 2]);\n    expectArraysClose(await result.data(), expected);\n  });\n\n  it('outer product accepts a tensor-like object', async () => {\n    const v1 = [2, 3];\n    const v2 = [2, 1];\n    const result = tf.outerProduct(v1, v2);\n    const expected = [4, 2, 6, 3];\n    expect(result.shape).toEqual([2, 2]);\n    expectArraysClose(await result.data(), expected);\n  });\n\n  it('gradients: A * B', async () => {\n    const aT = tf.tensor2d([1, 2, 3, 10, 20, 30], [2, 3]);\n    const bT = tf.tensor2d([2, 3, 4, 1, 2, 3], [3, 2]);\n    const dyT = tf.tensor2d([1, 10, 20, 30], [2, 2]);\n\n    const transposeA = false;\n    const transposeB = false;\n    const grads = tf.grads(\n\n        (a: tf.Tensor2D, b: tf.Tensor2D) =>\n            tf.matMul(a, b, transposeA, transposeB));\n    const [da, db] = grads([aT, bT], dyT);\n\n    // da = dy * bT\n    expect(da.shape).toEqual(aT.shape);\n\n    const a = await aT.buffer();\n    const dy = await dyT.buffer();\n    const b = await bT.buffer();\n    expectArraysClose(\n        await da.data(),\n        [\n          dy.get(0, 0) * b.get(0, 0) + dy.get(0, 1) * b.get(0, 1),\n          dy.get(0, 0) * b.get(1, 0) + dy.get(0, 1) * b.get(1, 1),\n          dy.get(0, 0) * b.get(2, 0) + dy.get(0, 1) * b.get(2, 1),\n          dy.get(1, 0) * b.get(0, 0) + dy.get(1, 1) * b.get(0, 1),\n          dy.get(1, 0) * b.get(1, 0) + dy.get(1, 1) * b.get(1, 1),\n          dy.get(1, 0) * b.get(2, 0) + dy.get(1, 1) * b.get(2, 1)\n        ],\n        1e-1);\n\n    // db = aT * dy\n    expect(db.shape).toEqual(b.shape);\n    expectArraysClose(await db.data(), [\n      a.get(0, 0) * dy.get(0, 0) + a.get(1, 0) * dy.get(1, 0),\n      a.get(0, 0) * dy.get(0, 1) + a.get(1, 0) * dy.get(1, 1),\n      a.get(0, 1) * dy.get(0, 0) + a.get(1, 1) * dy.get(1, 0),\n      a.get(0, 1) * dy.get(0, 1) + a.get(1, 1) * dy.get(1, 1),\n      a.get(0, 2) * dy.get(0, 0) + a.get(1, 2) * dy.get(1, 0),\n      a.get(0, 2) * dy.get(0, 1) + a.get(1, 2) * dy.get(1, 1)\n    ]);\n  });\n\n  it('gradient with clones', () => {\n    const a = tf.tensor2d([1, 2, 3, 10, 20, 30], [2, 3]);\n    const b = tf.tensor2d([2, 3, 4, 1, 2, 3], [3, 2]);\n\n    const grads = tf.grads(\n        (a: tf.Tensor2D, b: tf.Tensor2D) =>\n            tf.matMul(a.clone(), b.clone()).clone());\n    const [da, db] = grads([a, b]);\n\n    expect(da.shape).toEqual(a.shape);\n    expect(db.shape).toEqual(b.shape);\n  });\n\n  it('gradients: a * bT', async () => {\n    const aT = tf.tensor2d([1, 2, 3, 10, 20, 30], [3, 2]);\n    const bT = tf.tensor2d([2, 3, 4, 1, 2, 3], [3, 2]);\n    const dyT = tf.tensor2d([1, 10, 20, 30, 40, 50, 60, 70, 80], [3, 3]);\n\n    const transposeA = false;\n    const transposeB = true;\n    const grads = tf.grads(\n\n        (a: tf.Tensor2D, b: tf.Tensor2D) =>\n            tf.matMul(a, b, transposeA, transposeB));\n    const [da, db] = grads([aT, bT], dyT);\n\n    // da = dy * b\n    expect(da.shape).toEqual(aT.shape);\n    const a = await aT.buffer();\n    const dy = await dyT.buffer();\n    const b = await bT.buffer();\n    expectArraysClose(await da.data(), [\n      dy.get(0, 0) * b.get(0, 0) + dy.get(0, 1) * b.get(1, 0) +\n          dy.get(0, 2) * b.get(2, 0),\n      dy.get(0, 0) * b.get(0, 1) + dy.get(0, 1) * b.get(1, 1) +\n          dy.get(0, 2) * b.get(2, 1),\n      dy.get(1, 0) * b.get(0, 0) + dy.get(1, 1) * b.get(1, 0) +\n          dy.get(1, 2) * b.get(2, 0),\n      dy.get(1, 0) * b.get(0, 1) + dy.get(1, 1) * b.get(1, 1) +\n          dy.get(1, 2) * b.get(2, 1),\n      dy.get(2, 0) * b.get(0, 0) + dy.get(2, 1) * b.get(1, 0) +\n          dy.get(2, 2) * b.get(2, 0),\n      dy.get(2, 0) * b.get(0, 1) + dy.get(2, 1) * b.get(1, 1) +\n          dy.get(2, 2) * b.get(2, 1)\n    ]);\n\n    // db = dyT * a\n    expect(db.shape).toEqual(b.shape);\n    expectArraysClose(await db.data(), [\n      dy.get(0, 0) * a.get(0, 0) + dy.get(1, 0) * a.get(1, 0) +\n          dy.get(2, 0) * a.get(2, 0),\n      dy.get(0, 0) * a.get(0, 1) + dy.get(1, 0) * a.get(1, 1) +\n          dy.get(2, 0) * a.get(2, 1),\n      dy.get(0, 1) * a.get(0, 0) + dy.get(1, 1) * a.get(1, 0) +\n          dy.get(2, 1) * a.get(2, 0),\n      dy.get(0, 1) * a.get(0, 1) + dy.get(1, 1) * a.get(1, 1) +\n          dy.get(2, 1) * a.get(2, 1),\n      dy.get(0, 2) * a.get(0, 0) + dy.get(1, 2) * a.get(1, 0) +\n          dy.get(2, 2) * a.get(2, 0),\n      dy.get(0, 2) * a.get(0, 1) + dy.get(1, 2) * a.get(1, 1) +\n          dy.get(2, 2) * a.get(2, 1)\n    ]);\n  });\n\n  it('gradients: aT * b', async () => {\n    const aT = tf.tensor2d([1, 2, 3, 10, 20, 30], [3, 2]);\n    const bT = tf.tensor2d([2, 3, 4, 1, 2, 3], [3, 2]);\n    const dyT = tf.tensor2d([1, 10, 20, 30], [2, 2]);\n\n    const transposeA = true;\n    const transposeB = false;\n    const grads = tf.grads(\n\n        (a: tf.Tensor2D, b: tf.Tensor2D) =>\n            tf.matMul(a, b, transposeA, transposeB));\n    const [da, db] = grads([aT, bT], dyT);\n\n    // da = b * dyT\n    expect(da.shape).toEqual(aT.shape);\n    const a = await aT.buffer();\n    const dy = await dyT.buffer();\n    const b = await bT.buffer();\n    expectArraysClose(await da.data(), [\n      dy.get(0, 0) * b.get(0, 0) + dy.get(0, 1) * b.get(0, 1),\n      dy.get(1, 0) * b.get(0, 0) + dy.get(1, 1) * b.get(0, 1),\n      dy.get(0, 0) * b.get(1, 0) + dy.get(0, 1) * b.get(1, 1),\n      dy.get(1, 0) * b.get(1, 0) + dy.get(1, 1) * b.get(1, 1),\n      dy.get(0, 0) * b.get(2, 0) + dy.get(0, 1) * b.get(2, 1),\n      dy.get(1, 0) * b.get(2, 0) + dy.get(1, 1) * b.get(2, 1)\n    ]);\n\n    // db = a * dy\n    expect(db.shape).toEqual(b.shape);\n    expectArraysClose(await db.data(), [\n      dy.get(0, 0) * a.get(0, 0) + dy.get(1, 0) * a.get(0, 1),\n      dy.get(0, 1) * a.get(0, 0) + dy.get(1, 1) * a.get(0, 1),\n      dy.get(0, 0) * a.get(1, 0) + dy.get(1, 0) * a.get(1, 1),\n      dy.get(0, 1) * a.get(1, 0) + dy.get(1, 1) * a.get(1, 1),\n      dy.get(0, 0) * a.get(2, 0) + dy.get(1, 0) * a.get(2, 1),\n      dy.get(0, 1) * a.get(2, 0) + dy.get(1, 1) * a.get(2, 1)\n    ]);\n  });\n\n  it('gradients: aT * bT', async () => {\n    const aT = tf.tensor2d([1, 2, 3, 10, 20, 30], [3, 2]);\n    const bT = tf.tensor2d([2, 3, 4, 1, 2, 3], [2, 3]);\n    const dyT = tf.tensor2d([1, 10, 20, 30], [2, 2]);\n\n    const transposeA = true;\n    const transposeB = true;\n    const grads = tf.grads(\n\n        (a: tf.Tensor2D, b: tf.Tensor2D) =>\n            tf.matMul(a, b, transposeA, transposeB));\n    const [da, db] = grads([aT, bT], dyT);\n\n    // da = bT * dyT\n    expect(da.shape).toEqual(aT.shape);\n    const a = await aT.buffer();\n    const dy = await dyT.buffer();\n    const b = await bT.buffer();\n    expectArraysClose(await da.data(), [\n      dy.get(0, 0) * b.get(0, 0) + dy.get(0, 1) * b.get(1, 0),\n      dy.get(1, 0) * b.get(0, 0) + dy.get(1, 1) * b.get(1, 0),\n      dy.get(0, 0) * b.get(0, 1) + dy.get(0, 1) * b.get(1, 1),\n      dy.get(1, 0) * b.get(0, 1) + dy.get(1, 1) * b.get(1, 1),\n      dy.get(0, 0) * b.get(0, 2) + dy.get(0, 1) * b.get(1, 2),\n      dy.get(1, 0) * b.get(0, 2) + dy.get(1, 1) * b.get(1, 2)\n    ]);\n\n    // db = dyT * aT\n    expect(db.shape).toEqual(b.shape);\n    expectArraysClose(await db.data(), [\n      dy.get(0, 0) * a.get(0, 0) + dy.get(1, 0) * a.get(0, 1),\n      dy.get(0, 0) * a.get(1, 0) + dy.get(1, 0) * a.get(1, 1),\n      dy.get(0, 0) * a.get(2, 0) + dy.get(1, 0) * a.get(2, 1),\n      dy.get(0, 1) * a.get(0, 0) + dy.get(1, 1) * a.get(0, 1),\n      dy.get(0, 1) * a.get(1, 0) + dy.get(1, 1) * a.get(1, 1),\n      dy.get(0, 1) * a.get(2, 0) + dy.get(1, 1) * a.get(2, 1)\n    ]);\n  });\n\n  it('throws when passed a as a non-tensor', () => {\n    expect(() => tf.matMul({} as tf.Tensor2D, tf.tensor2d([2], [1, 1])))\n        .toThrowError(/Argument 'a' passed to 'matMul' must be a Tensor/);\n  });\n  it('throws when passed b as a non-tensor', () => {\n    expect(() => tf.matMul(tf.tensor2d([2], [1, 1]), {} as tf.Tensor2D))\n        .toThrowError(/Argument 'b' passed to 'matMul' must be a Tensor/);\n  });\n\n  it('accepts a tensor-like object', async () => {\n    const a = [[1, 2, 3], [4, 5, 6]];     // 2x3\n    const b = [[0, 1], [-3, 2], [2, 1]];  // 3x2\n    const c = tf.matMul(a, b);\n\n    expect(c.shape).toEqual([2, 2]);\n    expectArraysClose(await c.data(), [0, 8, -3, 20]);\n  });\n\n  it('accepts a tensor-like object chained', async () => {\n    const a = tf.tensor2d([[1, 2, 3], [4, 5, 6]], [2, 3]);  // 2x3\n    const b = [[0, 1], [-3, 2], [2, 1]];                    // 3x2\n    const c = a.matMul(b);\n\n    expect(c.shape).toEqual([2, 2]);\n    expectArraysClose(await c.data(), [0, 8, -3, 20]);\n  });\n\n  it('a * b where a has zero in its shape', async () => {\n    const a = tf.tensor2d([], [0, 3]);\n    const b = tf.tensor2d([1, 2, 3, 4, 5, 6], [3, 2]);\n    const c = tf.matMul(a, b);\n    expect(c.shape).toEqual([0, 2]);\n    expect(c.rank).toBe(2);\n    expect(c.size).toBe(0);\n    expectArraysClose(await c.data(), []);\n  });\n\n  it('(a * b) * c where a has zero in its shape, so a*b does also',\n     async () => {\n       const a = tf.tensor2d([], [0, 3]);\n       const b = tf.tensor2d([1, 2, 3, 4, 5, 6], [3, 2]);\n       const ab = tf.matMul(a, b);\n       expect(ab.shape).toEqual([0, 2]);\n       expectArraysClose(await ab.data(), []);\n       const c = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);\n       const res = tf.matMul(ab, c);\n       expect(res.shape).toEqual([0, 3]);\n       expectArraysClose(await res.data(), []);\n     });\n\n  it('throws error for string tensor', () => {\n    expect(() => tf.matMul([['a']], [['b']]))\n        .toThrowError(/Argument 'a' passed to 'matMul' must be numeric tensor/);\n  });\n});\n\ndescribeWithFlags('matmulBatch', ALL_ENVS, () => {\n  it('A x B', async () => {\n    const a = tf.tensor3d(\n        [\n          -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3,  7,  -2, 5,\n          -6, 3,  8,  7, -8, 1,  4, -4, 6,  4,  -4, -9, -5, 2,  -2\n        ],\n        [5, 2, 3]);\n    const b = tf.tensor3d(\n        [\n          -8, -4, -1, 0,  -7, 0, 3,  3,  6,   2,  -1, 8, -4, 9, -6,\n          5,  8,  9,  -9, 7,  0, -1, -1, -10, -7, 3,  4, 6,  3, -4\n        ],\n        [5, 3, 2]);\n\n    const c = tf.matMul(a, b);\n    expect(c.shape).toEqual([5, 2, 2]);\n    expectArraysClose(await c.data(), [\n      87, 20, -6,  -32, -24, -50, -36, -5, 24, 98,\n      70, 33, -64, 47,  -42, -28, -71, 24, 37, 5\n    ]);\n  });\n\n  it('A x B in 4D', async () => {\n    const a = tf.tensor4d(\n        [\n          -2, 3,  5,  -5, 3,  9,  -3, -5, 1,   1,  -9, 9,   -6, 6,  -8,\n          -7, -1, 3,  9,  -7, -7, 2,  10, -6,  -8, -6, 9,   -6, 4,  -1,\n          9,  -6, 10, 8,  -9, 5,  -8, -7, 0,   2,  -5, -1,  -9, -4, 3,\n          -2, 6,  -4, 7,  1,  -5, -4, 9,  -8,  -6, -8, 4,   -1, 4,  3,\n          -7, 8,  -7, 5,  -3, -2, -4, 9,  2,   -1, 1,  -10, -3, 5,  -4,\n          6,  -8, -8, 9,  -3, -5, 10, 3,  -3,  -3, 9,  3,   -3, 2,  -8,\n          10, 1,  9,  -2, -2, -3, -4, 6,  -10, -1, 8,  -8,  7,  3,  -2,\n          3,  6,  -2, -2, -4, 1,  -5, -4, 0,   5,  1,  9,   -8, -2, -1\n        ],\n        [4, 5, 2, 3]);\n    const b = tf.tensor4d(\n        [\n          -4, -3, -2, -6, 6,  -1, -4, -1, 7,  -4, 8,  -9,  -9, 0,   -1,\n          -4, -6, -7, -3, -4, -7, 6,  -8, 1,  -2, 1,  -1,  -3, 8,   -5,\n          9,  -2, 5,  9,  -2, 2,  -5, -5, -8, -1, -2, -3,  -2, -10, 6,\n          -3, 0,  1,  6,  7,  1,  2,  -4, -5, 2,  -5, -7,  9,  3,   -6,\n          6,  4,  -4, 6,  10, -3, -2, 8,  10, -8, 10, -1,  -9, -7,  -8,\n          -3, 1,  1,  -2, -9, -7, -6, -1, 0,  7,  -9, -7,  -5, 0,   -4,\n          -4, -7, 2,  4,  6,  6,  -4, -6, -8, 3,  -8, -9,  6,  9,   -4,\n          1,  -1, 0,  8,  9,  0,  -5, 3,  -1, 5,  0,  -10, 7,  -2,  6\n        ],\n        [4, 5, 3, 2]);\n\n    const transposeA = false;\n    const transposeB = false;\n    const c = tf.matMul(a, b, transposeA, transposeB);\n\n    expectArraysClose(await c.data(), [\n      32,  -17, 68,  -12,  -15, 14,  5,   -46, 96,  32,  46,  -17, 78,   -85,\n      -28, 46,  94,  -35,  0,   -13, 31,  -52, 17,  -87, 96,  47,  32,   -2,\n      -6,  105, 40,  -2,   63,  76,  17,  30,  56,  -66, -21, 23,  -144, 41,\n      22,  8,   118, -106, -88, -6,  -17, 2,   2,   -26, 8,   -63, -38,  -108,\n      -84, -30, -35, 49,   16,  -12, -14, -12, 48,  132, 4,   102, 32,   66,\n      -4,  33,  -13, 1,    -40, -25, -3,  61,  -18, -20\n    ]);\n  });\n\n  it('A x B^t', async () => {\n    const a = tf.tensor3d(\n        [\n          -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3,  7,  -2, 5,\n          -6, 3,  8,  7, -8, 1,  4, -4, 6,  4,  -4, -9, -5, 2,  -2\n        ],\n        [5, 2, 3]);\n    const b = tf.tensor3d(\n        [\n          -8, -4, -1, 0,  -7, 0, 3,  3,  6,   2,  -1, 8, -4, 9, -6,\n          5,  8,  9,  -9, 7,  0, -1, -1, -10, -7, 3,  4, 6,  3, -4\n        ],\n        [5, 2, 3]);\n\n    const transposeA = false;\n    const transposeB = true;\n    const c = tf.matMul(a, b, transposeA, transposeB);\n    expect(c.shape).toEqual([5, 2, 2]);\n    expectArraysClose(await c.data(), [\n      66, 35, -48,  14, -45, -33, -12, 7,  -76, 64,\n      3,  66, -119, -9, -64, -60, -76, 48, 33,  -16\n    ]);\n  });\n\n  it('A^t x B', async () => {\n    const a = tf.tensor3d(\n        [\n          -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3,  7,  -2, 5,\n          -6, 3,  8,  7, -8, 1,  4, -4, 6,  4,  -4, -9, -5, 2,  -2\n        ],\n        [5, 2, 3]);\n    const b = tf.tensor3d(\n        [\n          -8, -4, -1, 0,  -7, 0, 3,  3,  6,   2,  -1, 8, -4, 9, -6,\n          5,  8,  9,  -9, 7,  0, -1, -1, -10, -7, 3,  4, 6,  3, -4\n        ],\n        [5, 2, 3]);\n\n    const transposeA = true;\n    const transposeB = false;\n    const c = tf.matMul(a, b, transposeA, transposeB);\n\n    expectArraysClose(await c.data(), [\n      40,  -36, 5,   40,  34, 5,   48,  80, 6,  -6, 21,  -48, -23, -20, -50,\n      -12, -21, -12, -58, 15, -96, 23,  6,  39, 20, 109, 42,  -67, 45,  -40,\n      76,  -52, 40,  -15, 1,  -60, -58, -3, 36, 40, -6,  -24, 51,  -33, -28\n    ]);\n  });\n\n  it('A^t x B in 4D', async () => {\n    const a = tf.tensor4d(\n        [\n          -2, 3,  5,  -5, 3,  9,  -3, -5, 1,   1,  -9, 9,   -6, 6,  -8,\n          -7, -1, 3,  9,  -7, -7, 2,  10, -6,  -8, -6, 9,   -6, 4,  -1,\n          9,  -6, 10, 8,  -9, 5,  -8, -7, 0,   2,  -5, -1,  -9, -4, 3,\n          -2, 6,  -4, 7,  1,  -5, -4, 9,  -8,  -6, -8, 4,   -1, 4,  3,\n          -7, 8,  -7, 5,  -3, -2, -4, 9,  2,   -1, 1,  -10, -3, 5,  -4,\n          6,  -8, -8, 9,  -3, -5, 10, 3,  -3,  -3, 9,  3,   -3, 2,  -8,\n          10, 1,  9,  -2, -2, -3, -4, 6,  -10, -1, 8,  -8,  7,  3,  -2,\n          3,  6,  -2, -2, -4, 1,  -5, -4, 0,   5,  1,  9,   -8, -2, -1\n        ],\n        [4, 5, 2, 3]);\n    const b = tf.tensor4d(\n        [\n          -4, -3, -2, -6, 6,  -1, -4, -1, 7,  -4, 8,  -9,  -9, 0,   -1,\n          -4, -6, -7, -3, -4, -7, 6,  -8, 1,  -2, 1,  -1,  -3, 8,   -5,\n          9,  -2, 5,  9,  -2, 2,  -5, -5, -8, -1, -2, -3,  -2, -10, 6,\n          -3, 0,  1,  6,  7,  1,  2,  -4, -5, 2,  -5, -7,  9,  3,   -6,\n          6,  4,  -4, 6,  10, -3, -2, 8,  10, -8, 10, -1,  -9, -7,  -8,\n          -3, 1,  1,  -2, -9, -7, -6, -1, 0,  7,  -9, -7,  -5, 0,   -4,\n          -4, -7, 2,  4,  6,  6,  -4, -6, -8, 3,  -8, -9,  6,  9,   -4,\n          1,  -1, 0,  8,  9,  0,  -5, 3,  -1, 5,  0,  -10, 7,  -2,  6\n        ],\n        [4, 5, 2, 3]);\n\n    const transposeA = true;\n    const transposeB = false;\n    const c = tf.matMul(a, b, transposeA, transposeB);\n\n    expectArraysClose(await c.data(), [\n      38,  -24, 9,   -30, 9,   -9,  -74,  39,  -19,  8,    11,  -30, 56,  -67,\n      46,  -40, 71,  -74, 82,  42,  55,   -50, 6,    1,    60,  -18, -13, -15,\n      -52, -61, 81,  -52, 59,  -15, 76,   43,  34,   -56,  38,  0,   26,  -14,\n      -15, 1,   -4,  153, -34, 61,  -135, 30,  -48,  135,  -30, 60,  38,  36,\n      58,  40,  45,  71,  1,   2,   3,    24,  90,   -56,  -10, 40,  -18, 6,\n      -30, 14,  34,  65,  27,  24,  -29,  -44, -46,  -3,   35,  -21, 27,  48,\n      20,  52,  32,  35,  -11, -46, -12,  22,  13,   30,   2,   -23, -54, -48,\n      34,  16,  -42, -39, -26, 82,  89,   76,  -84,  30,   9,   27,  30,  -21,\n      -43, -48, 60,  20,  24,  -78, -91,  -63, -12,  24,   21,  28,  48,  35,\n      -6,  27,  33,  53,  -81, -71, 61,   -27, 11,   -48,  -82, 8,   -12, -19,\n      -10, -48, -81, 0,   13,  32,  41,   0,   -100, -120, 16,  124, 152, 45,\n      60,  -28, 24,  21,  -12, -14, -16,  8,   9,    -33,  5,   -12, -48, 4,\n      8,   9,   0,   -31, 16,  -98, -9,   4,   -22,  38,   2,   -96\n    ]);\n  });\n\n  it('A^t x B^t', async () => {\n    const a = tf.tensor3d(\n        [\n          -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3,  7,  -2, 5,\n          -6, 3,  8,  7, -8, 1,  4, -4, 6,  4,  -4, -9, -5, 2,  -2\n        ],\n        [5, 3, 2]);\n    const b = tf.tensor3d(\n        [\n          -8, -4, -1, 0,  -7, 0, 3,  3,  6,   2,  -1, 8, -4, 9, -6,\n          5,  8,  9,  -9, 7,  0, -1, -1, -10, -7, 3,  4, 6,  3, -4\n        ],\n        [5, 2, 3]);\n\n    const transposeA = true;\n    const transposeB = true;\n    const c = tf.matMul(a, b, transposeA, transposeB);\n    expectArraysClose(await c.data(), [\n      66,  42, 16,  -56, -12, 6,   -30, 19,  -1, 102,\n      -94, 14, -56, 32,  100, -56, -47, -11, 5,  -31\n    ]);\n  });\n\n  it('A has more batch dimensions than B', async () => {\n    const a = tf.tensor4d(\n        [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [2, 2, 2, 2]);\n    const b = tf.tensor3d([1, 2, 3, 4], [2, 2, 1]);\n\n    const c = tf.matMul(a, b);\n    expectArraysClose(await c.data(), [5, 11, 39, 53, 29, 35, 95, 109]);\n  });\n\n  it('batch dimensions do not match', () => {\n    const a = tf.tensor3d(\n        [\n          -5, -5, -6, 8,  -2, -8, 4, -7, -6, -9, -1, 3,\n          7,  -2, 5,  -6, 3,  8,  7, -8, 1,  4,  -4, 6\n        ],\n        [4, 3, 2]);\n    const b = tf.tensor3d(\n        [\n          -8, -4, -1, 0,  -7, 0, 3,  3,  6,   2,  -1, 8, -4, 9, -6,\n          5,  8,  9,  -9, 7,  0, -1, -1, -10, -7, 3,  4, 6,  3, -4\n        ],\n        [5, 2, 3]);\n\n    const f = () => {\n      tf.matMul(a, b, false, false);\n    };\n    expect(f).toThrowError();\n  });\n\n  it('gradients: A x B', async () => {\n    const a = tf.tensor3d(\n        [\n          -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3,  7,  -2, 5,\n          -6, 3,  8,  7, -8, 1,  4, -4, 6,  4,  -4, -9, -5, 2,  -2\n        ],\n        [5, 2, 3]);\n    const b = tf.tensor3d(\n        [\n          -8, -4, -1, 0,  -7, 0, 3,  3,  6,   2,  -1, 8, -4, 9, -6,\n          5,  8,  9,  -9, 7,  0, -1, -1, -10, -7, 3,  4, 6,  3, -4\n        ],\n        [5, 3, 2]);\n    const dy = tf.tensor3d(\n        [8, 2, -3, -2, -8, 4, 5, 7, 4, -4, -4, 5, 8, 10, 1, 0, 6, 6, -4, 7],\n        [5, 2, 2]);\n\n    const grads = tf.grads(\n        (a: tf.Tensor3D, b: tf.Tensor3D) => tf.matMul(a, b, false, false));\n    const [da, db] = grads([a, b], dy);\n\n    // da = dy * bT\n    expect(da.shape).toEqual(a.shape);\n    expectArraysClose(await da.data(), [\n      -72, -8, -56, 32, 3,   21,   -12, -40, 40, 36,  44, 51, -52, -44, -4,\n      61,  49, 13,  -2, -10, -108, -9,  0,   -1, -24, 60, -6, 49,  26,  -40\n    ]);\n\n    // db = aT * dy\n    expect(db.shape).toEqual(b.shape);\n    expectArraysClose(await db.data(), [\n      -64, -26, -34, -6, -24, 4,   -77, -47, 51, -35, 63,  -3,  52,  -58, -20,\n      23,  -12, 20,  60, 70,  -68, -80, 14,  10, 44,  -11, -32, -10, -46, -68\n    ]);\n  });\n\n  it('4d gradients: A x B', async () => {\n    const a = tf.tensor4d(\n        [\n          -2, 3,  5,  -5, 3,  9,  -3, -5, 1,   1,  -9, 9,   -6, 6,  -8,\n          -7, -1, 3,  9,  -7, -7, 2,  10, -6,  -8, -6, 9,   -6, 4,  -1,\n          9,  -6, 10, 8,  -9, 5,  -8, -7, 0,   2,  -5, -1,  -9, -4, 3,\n          -2, 6,  -4, 7,  1,  -5, -4, 9,  -8,  -6, -8, 4,   -1, 4,  3,\n          -7, 8,  -7, 5,  -3, -2, -4, 9,  2,   -1, 1,  -10, -3, 5,  -4,\n          6,  -8, -8, 9,  -3, -5, 10, 3,  -3,  -3, 9,  3,   -3, 2,  -8,\n          10, 1,  9,  -2, -2, -3, -4, 6,  -10, -1, 8,  -8,  7,  3,  -2,\n          3,  6,  -2, -2, -4, 1,  -5, -4, 0,   5,  1,  9,   -8, -2, -1\n        ],\n        [4, 5, 2, 3]);\n    const b = tf.tensor4d(\n        [\n          -4, -3, -2, -6, 6,  -1, -4, -1, 7,  -4, 8,  -9,  -9, 0,   -1,\n          -4, -6, -7, -3, -4, -7, 6,  -8, 1,  -2, 1,  -1,  -3, 8,   -5,\n          9,  -2, 5,  9,  -2, 2,  -5, -5, -8, -1, -2, -3,  -2, -10, 6,\n          -3, 0,  1,  6,  7,  1,  2,  -4, -5, 2,  -5, -7,  9,  3,   -6,\n          6,  4,  -4, 6,  10, -3, -2, 8,  10, -8, 10, -1,  -9, -7,  -8,\n          -3, 1,  1,  -2, -9, -7, -6, -1, 0,  7,  -9, -7,  -5, 0,   -4,\n          -4, -7, 2,  4,  6,  6,  -4, -6, -8, 3,  -8, -9,  6,  9,   -4,\n          1,  -1, 0,  8,  9,  0,  -5, 3,  -1, 5,  0,  -10, 7,  -2,  6\n        ],\n        [4, 5, 3, 2]);\n    const dy = tf.tensor4d(\n        [\n          8,  -7, 0,  -9,  -5, -5, 0,  3,  7,  -4, 6,  -8,  -8, 0,  -1, -8,\n          -9, -7, -4, -9,  2,  3,  5,  8,  -5, -7, 3,  -10, -5, -9, -5, 1,\n          7,  1,  -9, -10, 8,  5,  0,  8,  -6, 4,  0,  -5,  8,  -7, -2, 1,\n          -8, 9,  9,  -7,  1,  7,  -2, 5,  -2, 9,  1,  -5,  7,  5,  -7, -6,\n          6,  7,  -8, 7,   4,  -5, 4,  -5, 3,  -4, -5, 4,   -6, 3,  -8, 10\n        ],\n        [4, 5, 2, 2]);\n\n    const grads = tf.grads(\n        (a: tf.Tensor4D, b: tf.Tensor4D) => tf.matMul(a, b, false, false));\n    const [da, db] = grads([a, b], dy);\n\n    // da = dy * bT\n    expect(da.shape).toEqual(a.shape);\n    expectArraysClose(await da.data(), [\n      -11,  26,  55,  27,  54,  9,   25,  -15, 5,   -3,   -12, -27, -63, 9,\n      -14,  -54, 26,  20,  24,  56,  64,  35,  -41, 0,    11,  30,  -37, -1,\n      31,   13,  12,  37,  2,   29,  97,  6,   60,  47,   31,  35,  -14, 24,\n      100,  -3,  -9,  0,   -33, 1,   49,  9,   -33, -124, -29, 86,  -9,  -11,\n      -6,   -40, 72,  -48, -20, 48,  -72, -20, -30, 15,   -72, 136, 87,  12,\n      -28,  -21, 9,   37,  1,   -32, -51, 2,   -65, -49,  -1,  -41, -16, 2,\n      -95,  -31, -36, 52,  18,  20,  -63, 34,  72,  70,   -38, -78, -66, -27,\n      -111, -10, 85,  1,   -21, -21, -4,  -21, -21, -4,   -12, 20,  13,  -4,\n      -20,  -19, -30, 81,  30,  -40, 150, 76\n    ]);\n\n    // db = aT * dy\n    expect(db.shape).toEqual(b.shape);\n    expectArraysClose(await db.data(), [\n      -16, 59,  24,  -48,  40,   -116, 15,  18,  25,  -2,  -5,  22,  -84, 80,\n      36,  -16, -38, 8,    -74,  -16,  46,  -80, 62,  48,  96,  110, 38,  6,\n      -77, -54, 58,  91,   -57,  -90,  45,  70,  46,  36,  20,  99,  -3,  10,\n      55,  79,  -10, 42,   5,    -31,  85,  47,  -74, -89, 37,  75,  -48, -38,\n      -64, -8,  32,  44,   42,   -53,  -48, 47,  42,  -18, -30, 27,  70,  -62,\n      36,  -24, 78,  -69,  -112, 101,  -40, 20,  -11, 113, -9,  -6,  1,   -50,\n      3,   -12, -16, 71,   -14,  67,   84,  62,  21,  17,  84,  63,  -16, -35,\n      -28, 98,  4,   -126, 40,   -50,  36,  -45, -16, 20,  19,  -12, 8,   0,\n      3,   -4,  34,  -65,  10,   -17,  -46, 17\n    ]);\n  });\n\n  it('gradients: A x B^t', async () => {\n    const a = tf.tensor3d(\n        [\n          -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3,  7,  -2, 5,\n          -6, 3,  8,  7, -8, 1,  4, -4, 6,  4,  -4, -9, -5, 2,  -2\n        ],\n        [5, 3, 2]);\n    const b = tf.tensor3d(\n        [\n          -8, -4, -1, 0,  -7, 0, 3,  3,  6,   2,  -1, 8, -4, 9, -6,\n          5,  8,  9,  -9, 7,  0, -1, -1, -10, -7, 3,  4, 6,  3, -4\n        ],\n        [5, 3, 2]);\n    const dy = tf.tensor3d(\n        [\n          -0, 7,  5, 0,  -9, 5, -7, 6,  -5, -3,  -2, -2, -4, 10, -3,\n          5,  -1, 3, -2, -9, 4, -5, 7,  9,  -10, -8, -8, -5, -0, -1,\n          3,  3,  4, 9,  -7, 6, -2, -9, 5,  1,   -5, -3, -1, 9,  4\n        ],\n        [5, 3, 3]);\n\n    const grads = tf.grads(\n        (a: tf.Tensor3D, b: tf.Tensor3D) => tf.matMul(a, b, false, true));\n    const [da, db] = grads([a, b], dy);\n\n    expect(da.shape).toEqual(a.shape);\n    expectArraysClose(await da.data(), [\n      -42, 0,  -26,  0,  85,  28,  -19, -29, 51, -16, 6,   37,  94,  -27, 50,\n      71,  24, -202, 46, -25, -31, -22, -87, 10, -7,  -80, -36, -15, 55,  35\n    ]);\n\n    expect(db.shape).toEqual(b.shape);\n    expectArraysClose(await db.data(), [\n      14,  56, 7,    -155, -45, 55, 7,   72,  -67, -79, 7, 50, -69, -46, -52,\n      -88, 49, -126, -68,  106, 31, -30, -27, 60,  -19, 5, 27, 43,  55,  -13\n    ]);\n  });\n\n  it('4d gradients: A x B^t', async () => {\n    const a = tf.tensor4d(\n        [\n          -2, 3,  5,  -5, 3,  9,  -3, -5, 1,   1,  -9, 9,   -6, 6,  -8,\n          -7, -1, 3,  9,  -7, -7, 2,  10, -6,  -8, -6, 9,   -6, 4,  -1,\n          9,  -6, 10, 8,  -9, 5,  -8, -7, 0,   2,  -5, -1,  -9, -4, 3,\n          -2, 6,  -4, 7,  1,  -5, -4, 9,  -8,  -6, -8, 4,   -1, 4,  3,\n          -7, 8,  -7, 5,  -3, -2, -4, 9,  2,   -1, 1,  -10, -3, 5,  -4,\n          6,  -8, -8, 9,  -3, -5, 10, 3,  -3,  -3, 9,  3,   -3, 2,  -8,\n          10, 1,  9,  -2, -2, -3, -4, 6,  -10, -1, 8,  -8,  7,  3,  -2,\n          3,  6,  -2, -2, -4, 1,  -5, -4, 0,   5,  1,  9,   -8, -2, -1\n        ],\n        [4, 5, 3, 2]);\n    const b = tf.tensor4d(\n        [\n          -4, -3, -2, -6, 6,  -1, -4, -1, 7,  -4, 8,  -9,  -9, 0,   -1,\n          -4, -6, -7, -3, -4, -7, 6,  -8, 1,  -2, 1,  -1,  -3, 8,   -5,\n          9,  -2, 5,  9,  -2, 2,  -5, -5, -8, -1, -2, -3,  -2, -10, 6,\n          -3, 0,  1,  6,  7,  1,  2,  -4, -5, 2,  -5, -7,  9,  3,   -6,\n          6,  4,  -4, 6,  10, -3, -2, 8,  10, -8, 10, -1,  -9, -7,  -8,\n          -3, 1,  1,  -2, -9, -7, -6, -1, 0,  7,  -9, -7,  -5, 0,   -4,\n          -4, -7, 2,  4,  6,  6,  -4, -6, -8, 3,  -8, -9,  6,  9,   -4,\n          1,  -1, 0,  8,  9,  0,  -5, 3,  -1, 5,  0,  -10, 7,  -2,  6\n        ],\n        [4, 5, 3, 2]);\n    const dy = tf.tensor4d(\n        [\n          5,  -1, -5, -4, -1,  9,  1,   -2, 10,  7,  -1, 6,   -8, 8,  -3,\n          9,  -4, 2,  -4, -8,  8,  4,   8,  -10, -8, -8, 6,   6,  -5, 9,\n          -1, -7, -5, -3, -3,  2,  -6,  5,  8,   -9, 5,  -8,  -3, 8,  6,\n          2,  8,  5,  9,  7,   6,  2,   -3, 10,  7,  7,  -3,  4,  -3, -6,\n          -8, -8, 9,  0,  -8,  -3, -2,  -2, 8,   2,  3,  -6,  3,  6,  -3,\n          7,  7,  -9, -3, 8,   7,  7,   -1, -6,  5,  2,  -1,  -1, 1,  5,\n          0,  -4, 3,  -4, -10, 1,  -2,  -8, -9,  -6, 4,  4,   -7, -1, -1,\n          -9, 7,  1,  -1, 8,   0,  -2,  -7, 5,   7,  8,  9,   -3, -8, -6,\n          -7, -8, -1, 8,  -4,  7,  5,   -9, 9,   3,  0,  -10, 7,  -9, 4,\n          -7, 5,  -2, -2, 3,   3,  -6,  2,  0,   8,  -5, -10, 3,  -7, 0,\n          -6, 2,  3,  -1, 3,   3,  -10, 1,  3,   -7, -1, 8,   -2, -1, -1,\n          -3, -9, 7,  4,  -6,  3,  0,   -7, -4,  -5, -8, -6,  10, -6, 4\n        ],\n        [4, 5, 3, 3]);\n\n    const grads = tf.grads(\n        (a: tf.Tensor4D, b: tf.Tensor4D) => tf.matMul(a, b, false, true));\n    const [da, db] = grads([a, b], dy);\n\n    expect(da.shape).toEqual(a.shape);\n    expectArraysClose(await da.data(), [\n      -48, -4,   72,  9,   60,  -1,  13,   -57, 64,  3,   -48, -11, -4,  -24,\n      16,  38,   44,  -10, -55, -45, 92,   -43, 14,  -4,  71,  -61, -51, 16,\n      46,  -57,  48,  78,  104, 57,  -17,  -11, -85, -33, 16,  1,   86,  21,\n      -48, 21,   -8,  34,  14,  -35, 36,   48,  85,  108, -38, -40, 3,   -8,\n      -7,  -1,   6,   -16, 46,  -33, 26,   -79, -70, -29, 92,  -84, -6,  -47,\n      98,  -129, -55, -17, 79,  40,  -118, -64, 68,  75,  71,  111, 5,   -48,\n      98,  -36,  21,  13,  112, -34, 26,   57,  32,  44,  28,  50,  88,  27,\n      44,  -39,  -16, 15,  -21, -6,  -67,  -89, -46, -64, -19, -12, -3,  11,\n      41,  63,   78,  -73, 67,  -92, 102,  -18\n    ]);\n\n    expect(db.shape).toEqual(b.shape);\n    expectArraysClose(await db.data(), [\n      -27,  44,   -9,  -16, 85,  30,  -110, 38,  47,  -23, -39, -15, 0,    -76,\n      -8,   -128, 26,  136, 31,  -26, -26,  39,  136, -85, -45, 93,  37,   -68,\n      -112, -6,   90,  70,  169, -7,  15,   68,  -16, -33, -16, -47, -21,  0,\n      6,    -4,   84,  24,  15,  20,  -41,  -1,  79,  -86, 87,  -23, -26,  -64,\n      18,   9,    52,  64,  34,  -16, 122,  -66, -1,  47,  1,   43,  -11,  -33,\n      -17,  27,   -45, -73, -60, -66, -92,  -42, 32,  -85, -44, -44, -28,  -13,\n      8,    -20,  9,   -9,  -49, 79,  -76,  15,  73,  -7,  7,   -8,  -110, 93,\n      106,  -39,  64,  -84, -29, -19, 13,   14,  63,  2,   -15, 23,  17,   49,\n      -3,   -31,  -65, 30,  -95, 63,  -82,  40\n    ]);\n  });\n\n  it('gradients: A^t x B', async () => {\n    const a = tf.tensor3d(\n        [\n          -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3,  7,  -2, 5,\n          -6, 3,  8,  7, -8, 1,  4, -4, 6,  4,  -4, -9, -5, 2,  -2\n        ],\n        [5, 3, 2]);\n    const b = tf.tensor3d(\n        [\n          -8, -4, -1, 0,  -7, 0, 3,  3,  6,   2,  -1, 8, -4, 9, -6,\n          5,  8,  9,  -9, 7,  0, -1, -1, -10, -7, 3,  4, 6,  3, -4\n        ],\n        [5, 3, 2]);\n    const dy = tf.tensor3d(\n        [8, 2, -3, -2, -8, 4, 5, 7, 4, -4, -4, 5, 8, 10, 1, 0, 6, 6, -4, 7],\n        [5, 2, 2]);\n\n    const grads = tf.grads(\n        (a: tf.Tensor3D, b: tf.Tensor3D) => tf.matMul(a, b, true, false));\n    const [da, db] = grads([a, b], dy);\n\n    expect(da.shape).toEqual(a.shape);\n    expectArraysClose(await da.data(), [\n      -72, 32, -8, 3,  -56, 21,  -12, 36,   -40, 44,  40, 51, -52, 61, -44,\n      49,  -4, 13, -2, -9,  -10, 0,   -108, -1,  -24, 49, 60, 26,  -6, -40\n    ]);\n\n    expect(db.shape).toEqual(b.shape);\n    expectArraysClose(await db.data(), [\n      -25, 0,   -72, -28, 8,  12, -67, -33, 3,   -87, 23, 17,  36,  -38, 44,\n      -50, -20, 28,  48,  70, 12, 10,  -26, -40, 40,  -4, -34, -89, 20,  -2\n    ]);\n  });\n\n  it('gradients: A^t x B^t', async () => {\n    const a = tf.tensor3d(\n        [\n          -5, -5, -6, 8, -2, -8, 4, -7, -6, -9, -1, 3,  7,  -2, 5,\n          -6, 3,  8,  7, -8, 1,  4, -4, 6,  4,  -4, -9, -5, 2,  -2\n        ],\n        [5, 3, 2]);\n    const b = tf.tensor3d(\n        [\n          -8, -4, -1, 0,  -7, 0, 3,  3,  6,   2,  -1, 8, -4, 9, -6,\n          5,  8,  9,  -9, 7,  0, -1, -1, -10, -7, 3,  4, 6,  3, -4\n        ],\n        [5, 2, 3]);\n    const dy = tf.tensor3d(\n        [8, 2, -3, -2, -8, 4, 5, 7, 4, -4, -4, 5, 8, 10, 1, 0, 6, 6, -4, 7],\n        [5, 2, 2]);\n\n    const grads = tf.grads(\n        (a: tf.Tensor3D, b: tf.Tensor3D) => tf.matMul(a, b, true, true));\n    const [da, db] = grads([a, b], dy);\n\n    expect(da.shape).toEqual(a.shape);\n    expectArraysClose(await da.data(), [\n      -64, 24,  -46, 26,  -8, 3,  -16, 29,   -28, 8,  -16, 86, -36, 41, 4,\n      4,   -60, 69,  -82, -9, 46, 7,   -100, 0,   -6, 70,  36, 9,   0,  -44\n    ]);\n\n    expect(db.shape).toEqual(b.shape);\n    expectArraysClose(await db.data(), [\n      -25, -72, 8,  0,  -28, 12,  -67, 3,  23,  -33, -87, 17, 36, 44,  -20,\n      -38, -50, 28, 48, 12,  -26, 70,  10, -40, 40,  -34, 20, -4, -89, -2\n    ]);\n  });\n});\n\ndescribeWithFlags('dot', ALL_ENVS, () => {\n  let a: tf.Tensor1D;\n  let b: tf.Tensor2D;\n  let c: tf.Tensor2D;\n  let d: tf.Tensor3D;\n  let e: tf.Scalar;\n  let f: tf.Tensor3D;\n\n  beforeEach(() => {\n    a = tf.tensor1d([1, 2]);\n    b = tf.tensor2d([[1, 2], [3, 4]]);\n    c = tf.tensor2d([[1, 2, 3], [4, 5, 6]]);\n    d = tf.tensor3d([1, 2], [1, 1, 2]);\n    e = tf.scalar(1);\n    f = tf.tensor3d([1, 2, 1, 2], [2, 1, 2]);\n  });\n\n  it('vector-vector', async () => {\n    const aa = tf.dot(a, a);\n    expectArraysClose(await aa.data(), [5]);\n    expect(aa.shape).toEqual([]);\n  });\n\n  it('vector-matrix', async () => {\n    const ab = tf.dot(a, b);\n    const ac = tf.dot(a, c);\n    expect(ab.shape).toEqual([2]);\n    expect(ac.shape).toEqual([3]);\n    expectArraysClose(await ab.data(), [7, 10]);\n    expectArraysClose(await ac.data(), [9, 12, 15]);\n  });\n\n  it('matrix-vector', async () => {\n    const ba = b.dot(a);\n    expect(ba.shape).toEqual([2]);\n    expectArraysClose(await ba.data(), [5, 11]);\n  });\n\n  it('matrix-matrix', async () => {\n    const bb = tf.dot(b, b);\n    const bc = tf.dot(b, c);\n    expect(bb.shape).toEqual([2, 2]);\n    expect(bc.shape).toEqual([2, 3]);\n    expectArraysClose(await bb.data(), [7, 10, 15, 22]);\n    expectArraysClose(await bc.data(), [9, 12, 15, 19, 26, 33]);\n  });\n\n  it('matmul A x B asymmetric', async () => {\n    const a = tf.tensor2d([1, 2, 3, 4], [2, 2]);\n    const b = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);\n\n    const c = tf.matMul(a, b);\n    const cData = await c.data();\n\n    expect(c.shape).toEqual([2, 3]);\n    expectArraysClose(cData, [9, 12, 15, 19, 26, 33]);\n  });\n\n  it('broadcast batch shape', async () => {\n    const a = tf.tensor3d([1, 2, 3, 4], [1, 2, 2]);\n    const b = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);\n\n    const c = tf.matMul(a, b);\n    const cData = await c.data();\n\n    expect(c.shape).toEqual([1, 2, 3]);\n    expectArraysClose(cData, [9, 12, 15, 19, 26, 33]);\n  });\n\n  it('throws error on incompatible dimensions', () => {\n    expect(() => tf.dot(c, f)).toThrowError();\n  });\n\n  it('throws error when inputs are not rank 1 or 2', () => {\n    expect(() => tf.dot(a, d)).toThrowError();\n    expect(() => tf.dot(a, e)).toThrowError();\n  });\n\n  it('accepts a tensor-like object', async () => {\n    const a = [1, 2, 3];\n    const res = tf.dot(a, a);\n    expectArraysClose(await res.data(), [14]);\n    expect(res.shape).toEqual([]);\n  });\n\n  it('throws error for string tensors', () => {\n    expect(() => tf.dot('a', 'b'))\n        .toThrowError(/Argument 't1' passed to 'dot' must be numeric tensor/);\n  });\n\n  it('ensure no memory leak', async () => {\n    const numTensorsBefore = tf.memory().numTensors;\n    const numDataIdBefore = tf.engine().backend.numDataIds();\n    const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);\n    const b = tf.tensor2d([0, 1, -3, 2, 2, 1], [3, 2]);\n\n    const c = tf.matMul(a, b);\n\n    expect(c.shape).toEqual([2, 2]);\n    expectArraysClose(await c.data(), [0, 8, -3, 20]);\n\n    a.dispose();\n    b.dispose();\n    c.dispose();\n\n    const numTensorsAfter = tf.memory().numTensors;\n    const numDataIdAfter = tf.engine().backend.numDataIds();\n    expect(numTensorsAfter).toBe(numTensorsBefore);\n    expect(numDataIdAfter).toBe(numDataIdBefore);\n  });\n});\n"]}
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