@tensorflow/tfjs-core
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Hardware-accelerated JavaScript library for machine intelligence
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JavaScript
/**
* @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.
* =============================================================================
*/
import * as tf from '../index';
import { ALL_ENVS, describeWithFlags } from '../jasmine_util';
import { expectArraysClose, expectArraysEqual } from '../test_util';
describeWithFlags('div', ALL_ENVS, () => {
it('same shape', async () => {
const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
const c = tf.tensor2d([1, 2, 3, 4, 2, 5], [2, 3]);
const r = tf.div(a, c);
expectArraysClose(await r.data(), [1, 1, 1, 1, 2.5, 6 / 5]);
});
it('vec4 same shape', async () => {
const a = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const b = tf.tensor2d([5, 3, 4, -7], [2, 2]);
const expected = [0.2, 0.666, -0.75, 0.571];
const result = tf.div(a, b);
expect(result.shape).toEqual([2, 2]);
expectArraysClose(await result.data(), expected);
});
it('TensorLike', async () => {
const a = [0, 1, -2, -4, 4, -4];
const b = [0.15, 0.2, 0.25, 0.5, 0.7, 1.2];
const result = tf.div(a, b);
expect(result.shape).toEqual([6]);
expectArraysClose(await result.data(), [0, 5.0, -8.0, -8.0, 5.714285850524902, -3.3333332538604736]);
});
it('TensorLike chained', async () => {
const a = tf.tensor1d([0, 1, -2, -4, 4, -4]);
const b = [0.15, 0.2, 0.25, 0.5, 0.7, 1.2];
const result = a.div(b);
expect(result.shape).toEqual(a.shape);
expectArraysClose(await result.data(), [0, 5.0, -8.0, -8.0, 5.714285850524902, -3.3333332538604736]);
});
it('division by zero results in infinity', async () => {
const r = tf.div(1, 0);
const rData = await r.data();
expect(Array.from(rData)).toEqual([Infinity]);
});
it('integer division implements floor divide', async () => {
const a = tf.tensor1d([-6, -6, -5, -4, -3, -3, 3, 3, 2], 'int32');
const c = tf.tensor1d([-2, 2, 3, 2, -3, 3, 2, 3, 2], 'int32');
const r = tf.div(a, c);
expect(r.dtype).toEqual('int32');
expectArraysClose(await r.data(), [3, -3, -2, -2, 1, -1, 1, 1, 1]);
});
it('integer division broadcasts', async () => {
const a = tf.tensor1d([-5, -4, 3, 2], 'int32');
const c = tf.scalar(2, 'int32');
const r = tf.div(a, c);
expect(r.dtype).toEqual('int32');
expectArraysClose(await r.data(), [-3, -2, 1, 1]);
});
it('propagates NaNs', async () => {
const a = tf.tensor2d([1, 2], [2, 1]);
const c = tf.tensor2d([3, NaN], [2, 1]);
const r = tf.div(a, c);
expectArraysClose(await r.data(), [1 / 3, NaN]);
});
it('broadcasting same rank Tensors different shape', async () => {
const a = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const b = tf.tensor2d([2, 3], [2, 1]);
const result = tf.div(a, b);
expect(result.shape).toEqual([2, 2]);
const expected = [1 / 2, 1, -1, -4 / 3];
expectArraysClose(await result.data(), expected);
});
it('broadcast scalar', async () => {
const a = tf.tensor2d([1, 2, 3, 4], [2, 2]);
const b = [2];
const result = tf.div(a, b);
expect(result.shape).toEqual([2, 2]);
const expected = [0.5, 1, 1.5, 2];
expectArraysClose(await result.data(), expected);
});
it('broadcast 2D + 1D', async () => {
const a = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const b = tf.tensor1d([1, 2]);
const result = tf.div(a, b);
expect(result.shape).toEqual([2, 2]);
const expected = [1, 1, -3, -2];
expectArraysClose(await result.data(), expected);
});
it('upcasts when dtypes dont match', async () => {
let res = tf.div(tf.scalar(6, 'int32'), tf.scalar(3, 'float32'));
expect(res.dtype).toBe('float32');
expectArraysClose(await res.data(), [2]);
res = tf.div(tf.scalar(6, 'int32'), tf.scalar(true, 'bool'));
expect(res.dtype).toBe('int32');
expectArraysClose(await res.data(), [6]);
});
it('throws when passed tensors of different shapes', () => {
const a = tf.tensor2d([1, 2, -3, -4, 5, 6], [2, 3]);
const b = tf.tensor2d([5, 3, 4, -7], [2, 2]);
expect(() => tf.div(a, b)).toThrowError();
expect(() => tf.div(b, a)).toThrowError();
});
it('scalar divided by array', async () => {
const c = tf.scalar(2);
const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
const r = tf.div(c, a);
expectArraysClose(await r.data(), [2 / 1, 2 / 2, 2 / 3, 2 / 4, 2 / 5, 2 / 6]);
});
it('scalar divided by array propagates NaNs', async () => {
const c = tf.scalar(NaN);
const a = tf.tensor2d([1, 2, 3], [1, 3]);
const r = tf.div(c, a);
expectArraysEqual(await r.data(), [NaN, NaN, NaN]);
});
it('array divided by scalar', async () => {
const a = tf.tensor2d([1, 2, 3, 4, 5, 6], [2, 3]);
const c = tf.scalar(2);
const r = tf.div(a, c);
expectArraysClose(await r.data(), [1 / 2, 2 / 2, 3 / 2, 4 / 2, 5 / 2, 6 / 2]);
});
it('array divided by scalar propagates NaNs', async () => {
const a = tf.tensor2d([1, 2, NaN], [1, 3]);
const c = tf.scalar(2);
const r = tf.div(a, c);
expectArraysClose(await r.data(), [1 / 2, 2 / 2, NaN]);
});
it('gradient: Scalar', async () => {
const a = tf.scalar(5);
const b = tf.scalar(2);
const dy = tf.scalar(4);
const before = tf.memory().numTensors;
const grads = tf.grads((a, b) => tf.div(a, b));
const [da, db] = grads([a, b], dy);
const now = tf.memory().numTensors;
expect(now).toBe(before + 2);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [4 / 2]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [-4 * 5 / (2 * 2)]);
});
it('gradient with clones', async () => {
const grads = tf.grads((a, b) => tf.div(a.clone(), b.clone()).clone());
const [da, db] = grads([5, 2]);
expect(da.shape).toEqual([]);
expect(db.shape).toEqual([]);
expectArraysClose(await da.data(), [1 / 2]);
expectArraysClose(await db.data(), [-5 / 4]);
});
it('gradient: Tensor1D', async () => {
const a = tf.tensor1d([1, 2, 3]);
const b = tf.tensor1d([3, 4, 5]);
const dy = tf.tensor1d([1, 10, 20]);
const grads = tf.grads((a, b) => tf.div(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await da.data(), [1 / 3, 10 / 4, 20 / 5]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [-1 * 1 / 9, -10 * 2 / 16, -20 * 3 / 25]);
});
it('gradient: Tensor1D with int32', async () => {
const a = tf.tensor1d([1, 2, 3], 'int32');
const b = tf.tensor1d([3, 4, 5], 'int32');
const dy = tf.tensor1d([1, 10, 20]);
const grads = tf.grads((a, b) => tf.div(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await da.data(), [1 / 3, 10 / 4, 20 / 5]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [-1 * 1 / 9, -10 * 2 / 16, -20 * 3 / 25]);
});
it('gradient: 1d<int32> with 1d<bool> ', async () => {
const a = tf.tensor1d([true, false, true], 'bool');
const b = tf.tensor1d([1, 2, 3], 'int32');
const dy = tf.tensor1d([1, 19, 20]);
const grads = tf.grads((a, b) => tf.div(a.toInt(), b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await da.data(), [1, 19 / 2, 20 / 3]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [-1 / 1, 0, -20 / 9]);
});
it('gradient: Tensor2D', async () => {
const a = tf.tensor2d([3, 1, 2, 3], [2, 2]);
const b = tf.tensor2d([1, 3, 4, 5], [2, 2]);
const dy = tf.tensor2d([1, 10, 15, 20], [2, 2]);
const grads = tf.grads((a, b) => tf.div(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [1 / 1, 10 / 3, 15 / 4, 20 / 5]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [-1 * 3 / 1, -10 * 1 / 9, -15 * 2 / 16, -20 * 3 / 25]);
});
it('gradient: scalar / Tensor1D', async () => {
const a = tf.scalar(2);
const b = tf.tensor1d([3, 4, 5]);
const dy = tf.tensor1d([6, 7, 8]);
const grads = tf.grads((a, b) => tf.div(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [6 / 3 + 7 / 4 + 8 / 5]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [-6 * 2 / 9, -7 * 2 / 16, -8 * 2 / 25]);
});
it('gradient: Tensor2D / scalar', async () => {
const a = tf.tensor2d([[2, 3], [4, 5]], [2, 2]);
const b = tf.scalar(2);
const dy = tf.tensor2d([[6, 7], [8, 9]], [2, 2]);
const grads = tf.grads((a, b) => tf.div(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [6 / 2, 7 / 2, 8 / 2, 9 / 2]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [-6 * 2 / 4 + -7 * 3 / 4 + -8 * 4 / 4 + -9 * 5 / 4]);
});
it('gradient: Tensor2D / Tensor2D w/ broadcast', async () => {
const a = tf.tensor2d([3, 4], [2, 1]);
const b = tf.tensor2d([[2, 3], [4, 5]], [2, 2]);
const dy = tf.tensor2d([[6, 7], [8, 9]], [2, 2]);
const grads = tf.grads((a, b) => tf.div(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [6 / 2 + 7 / 3, 8 / 4 + 9 / 5]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [-6 * 3 / 4, -7 * 3 / 9, -8 * 4 / 16, -9 * 4 / 25]);
});
it('throws when passed a as a non-tensor', () => {
expect(() => tf.div({}, tf.scalar(1)))
.toThrowError(/Argument 'a' passed to 'div' must be a Tensor/);
});
it('throws when passed b as a non-tensor', () => {
expect(() => tf.div(tf.scalar(1), {}))
.toThrowError(/Argument 'b' passed to 'div' must be a Tensor/);
});
it('accepts a tensor-like object', async () => {
const r = tf.div([[1, 2, 3], [4, 5, 6]], 2);
expect(r.shape).toEqual([2, 3]);
expectArraysClose(await r.data(), [1 / 2, 2 / 2, 3 / 2, 4 / 2, 5 / 2, 6 / 2]);
});
});
describeWithFlags('mul', ALL_ENVS, () => {
it('same-shaped tensors', async () => {
const a = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const b = tf.tensor2d([5, 3, 4, -7], [2, 2]);
const expected = [5, 6, -12, 28];
const result = tf.mul(a, b);
expect(result.shape).toEqual([2, 2]);
expectArraysClose(await result.data(), expected);
});
it('TensorLike', async () => {
const a = [[1, 2], [-3, -4]];
const b = [[5, 3], [4, -7]];
const expected = [5, 6, -12, 28];
const result = tf.mul(a, b);
expect(result.shape).toEqual([2, 2]);
expectArraysClose(await result.data(), expected);
});
it('TensorLike chained', async () => {
const a = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const b = [[5, 3], [4, -7]];
const expected = [5, 6, -12, 28];
const result = a.mul(b);
expect(result.shape).toEqual([2, 2]);
expectArraysClose(await result.data(), expected);
});
it('broadcasting tensors', async () => {
const a = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const b = tf.scalar(2);
const expected = [2, 4, -6, -8];
const result = tf.mul(a, b);
expect(result.shape).toEqual([2, 2]);
expectArraysClose(await result.data(), expected);
});
it('broadcasting same rank Tensors different shape', async () => {
const a = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const b = tf.tensor2d([2, 3], [2, 1]);
const result = tf.mul(a, b);
expect(result.shape).toEqual([2, 2]);
const expected = [2, 4, -9, -12];
expectArraysClose(await result.data(), expected);
});
it('broadcast 2D + 1D', async () => {
const a = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const b = tf.tensor1d([1, 2]);
const result = tf.mul(a, b);
expect(result.shape).toEqual([2, 2]);
const expected = [1, 4, -3, -8];
expectArraysClose(await result.data(), expected);
});
it('broadcast 5D + 2D', async () => {
const a = tf.range(1, 33).reshape([2, 2, 2, 2, 2]);
const b = tf.tensor([2, 3], [2, 1]);
const result = tf.mul(a, b);
expect(result.shape).toEqual([2, 2, 2, 2, 2]);
const expected = [
2, 4, 9, 12, 10, 12, 21, 24, 18, 20, 33, 36, 26, 28, 45, 48,
34, 36, 57, 60, 42, 44, 69, 72, 50, 52, 81, 84, 58, 60, 93, 96
];
expectArraysClose(await result.data(), expected);
});
it('broadcast 6D + 2D', async () => {
const a = tf.range(1, 65).reshape([2, 2, 2, 2, 2, 2]);
const b = tf.tensor([2, 3], [2, 1]);
const result = tf.mul(a, b);
expect(result.shape).toEqual([2, 2, 2, 2, 2, 2]);
const expected = [
2, 4, 9, 12, 10, 12, 21, 24, 18, 20, 33, 36, 26,
28, 45, 48, 34, 36, 57, 60, 42, 44, 69, 72, 50, 52,
81, 84, 58, 60, 93, 96, 66, 68, 105, 108, 74, 76, 117,
120, 82, 84, 129, 132, 90, 92, 141, 144, 98, 100, 153, 156,
106, 108, 165, 168, 114, 116, 177, 180, 122, 124, 189, 192
];
expectArraysClose(await result.data(), expected);
});
it('gradient: Scalar', async () => {
const a = tf.scalar(5);
const b = tf.scalar(2);
const dy = tf.scalar(4);
const grads = tf.grads((a, b) => tf.mul(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), await b.mul(dy).data());
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), await a.mul(dy).data());
});
it('gradient with clones', async () => {
const grads = tf.grads((a, b) => tf.mul(a.clone(), b.clone()).clone());
const [da, db] = grads([4, 2]);
expect(da.shape).toEqual([]);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), 2);
expect(db.shape).toEqual([]);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), 4);
});
it('gradient: Tensor1D', async () => {
const a = tf.tensor1d([1, 2, 3]);
const b = tf.tensor1d([3, 4, 5]);
const dy = tf.tensor1d([1, 10, 20]);
const grads = tf.grads((a, b) => tf.mul(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [3 * 1, 4 * 10, 5 * 20]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [1 * 1, 2 * 10, 3 * 20]);
});
it('gradient: Tensor1D with dtype int32', async () => {
const a = tf.tensor1d([1, 2, 3], 'int32');
const b = tf.tensor1d([3, 4, 5], 'int32');
const dy = tf.tensor1d([1, 10, 20]);
const grads = tf.grads((a, b) => tf.mul(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await da.data(), [3 * 1, 4 * 10, 5 * 20]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [1 * 1, 2 * 10, 3 * 20]);
});
it('gradient: Tensor2D', async () => {
const a = tf.tensor2d([3, 1, 2, 3], [2, 2]);
const b = tf.tensor2d([1, 3, 4, 5], [2, 2]);
const dy = tf.tensor2d([1, 10, 15, 20], [2, 2]);
const grads = tf.grads((a, b) => tf.mul(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [1 * 1, 3 * 10, 4 * 15, 5 * 20]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [3 * 1, 1 * 10, 2 * 15, 3 * 20]);
});
it('gradient: scalar * Tensor1D', async () => {
const a = tf.scalar(2);
const b = tf.tensor1d([3, 4, 5]);
const dy = tf.tensor1d([6, 7, 8]);
const grads = tf.grads((a, b) => tf.mul(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [3 * 6 + 4 * 7 + 5 * 8]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [2 * 6, 2 * 7, 2 * 8]);
});
it('gradient: Tensor2D * scalar', async () => {
const a = tf.tensor2d([[2, 3], [4, 5]], [2, 2]);
const b = tf.scalar(2);
const dy = tf.tensor2d([[6, 7], [8, 9]], [2, 2]);
const grads = tf.grads((a, b) => tf.mul(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [2 * 6, 2 * 7, 2 * 8, 2 * 9]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [2 * 6 + 3 * 7 + 4 * 8 + 5 * 9]);
});
it('gradient: Tensor2D * Tensor2D w/ broadcast', async () => {
const a = tf.tensor2d([3, 4], [2, 1]);
const b = tf.tensor2d([[2, 3], [4, 5]], [2, 2]);
const dy = tf.tensor2d([[6, 7], [8, 9]], [2, 2]);
const grads = tf.grads((a, b) => tf.mul(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [2 * 6 + 3 * 7, 4 * 8 + 5 * 9]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [6 * 3, 7 * 3, 8 * 4, 9 * 4]);
});
it('complex number multiplication', async () => {
const real1 = tf.tensor1d([2]);
const imag1 = tf.tensor1d([3]);
const complex1 = tf.complex(real1, imag1);
const real2 = tf.tensor1d([4]);
const imag2 = tf.tensor1d([5]);
const complex2 = tf.complex(real2, imag2);
const result = complex1.mul(complex2);
expect(result.dtype).toBe('complex64');
expect(result.shape).toEqual([1]);
expectArraysClose(await result.data(), [2 * 4 - 3 * 5, 2 * 5 + 3 * 4]);
});
it('complex number broadcasting multiplication', async () => {
const real1 = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const imag1 = tf.tensor2d([10, 20, -30, -40], [2, 2]);
const complex1 = tf.complex(real1, imag1);
const real2 = tf.tensor1d([4]);
const imag2 = tf.tensor1d([5]);
const complex2 = tf.complex(real2, imag2);
const result = tf.mul(complex1, complex2);
expect(result.dtype).toEqual('complex64');
expect(result.shape).toEqual([2, 2]);
expectArraysClose(await result.data(), [
1 * 4 - 10 * 5, 1 * 5 + 10 * 4, 2 * 4 - 20 * 5, 2 * 5 + 20 * 4,
-3 * 4 + 30 * 5, -3 * 5 + -30 * 4, -4 * 4 + 40 * 5, -4 * 5 + -40 * 4
]);
});
it('throws when passed a as a non-tensor', () => {
expect(() => tf.mul({}, tf.scalar(1)))
.toThrowError(/Argument 'a' passed to 'mul' must be a Tensor/);
});
it('throws when passed b as a non-tensor', () => {
expect(() => tf.mul(tf.scalar(1), {}))
.toThrowError(/Argument 'b' passed to 'mul' must be a Tensor/);
});
it('upcasts when dtypes dont match', async () => {
let res = tf.mul(tf.scalar(2, 'int32'), tf.scalar(3, 'float32'));
expect(res.dtype).toBe('float32');
expectArraysClose(await res.data(), [6]);
res = tf.mul(tf.scalar(2, 'int32'), tf.scalar(true, 'bool'));
expect(res.dtype).toBe('int32');
expectArraysClose(await res.data(), [2]);
res = tf.mul(tf.scalar(2, 'int32'), tf.scalar(false, 'bool'));
expect(res.dtype).toBe('int32');
expectArraysClose(await res.data(), [0]);
});
it('accepts a tensor-like object', async () => {
const result = tf.mul([[1, 2], [-3, -4]], 2);
expect(result.shape).toEqual([2, 2]);
expectArraysClose(await result.data(), [2, 4, -6, -8]);
});
});
describeWithFlags('pow', ALL_ENVS, () => {
it('same-shaped tensors', async () => {
const a = tf.tensor2d([1, -2, -3, 0, 7, 1], [2, 3]);
const b = tf.tensor2d([5, 3, 4, 5, 2, -3], [2, 3], 'int32');
const expected = [1, -8, 81, 0, 49, 1];
const result = tf.pow(a, b);
expect(result.shape).toEqual([2, 3]);
expectArraysClose(await result.data(), expected, 0.01);
});
it('TensorLike', async () => {
const a = [1, 2, 3];
const exp = 2;
const result = tf.pow(a, exp);
expect(result.shape).toEqual([3]);
expect(result.dtype).toBe('float32');
expectArraysClose(await result.data(), [1, 4, 9]);
});
it('TensorLike chained', async () => {
const a = tf.tensor1d([1, 2, 3]);
const exp = 2;
const result = a.pow(exp);
expect(result.shape).toEqual([3]);
expect(result.dtype).toBe('float32');
expectArraysClose(await result.data(), [1, 4, 9]);
});
it('int32^int32 returns int32', async () => {
const a = tf.tensor1d([1, 2, 3], 'int32');
const exp = tf.scalar(2, 'int32');
const result = tf.pow(a, exp);
expect(result.shape).toEqual([3]);
expect(result.dtype).toBe('int32');
expectArraysEqual(await result.data(), [1, 4, 9]);
});
it('different-shaped tensors', async () => {
const a = tf.tensor2d([1, -2, -3, 0, 7, 1], [2, 3]);
const b = tf.scalar(2, 'int32');
const expected = [1, 4, 9, 0, 49, 1];
const result = tf.pow(a, b);
expect(result.shape).toEqual([2, 3]);
expectArraysClose(await result.data(), expected, 0.05);
});
it('propagates NaNs', async () => {
const a = tf.tensor2d([NaN, 3, NaN, 0], [2, 2]);
const b = tf.tensor2d([1, 3, 2, 3], [2, 2], 'int32');
const result = tf.pow(a, b);
expectArraysClose(await result.data(), [NaN, 27, NaN, 0], 0.05);
});
it('exponent of 0 returns 1', async () => {
const a = tf.tensor1d([-2, -1, 0, 1, 2]);
const b = tf.scalar(0);
const result = tf.pow(a, b);
expectArraysClose(await result.data(), [1, 1, 1, 1, 1]);
});
it('handles non int32 exponent param', async () => {
const a = tf.tensor1d([2, 4]);
const b = tf.tensor1d([.5, 1.2]);
const result = tf.pow(a, b);
const expected = [Math.pow(2, 0.5), Math.pow(4, 1.2)];
expectArraysClose(await result.data(), expected);
});
it('broadcasting same rank Tensors different shape', async () => {
const a = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const b = tf.tensor2d([2, 1], [2, 1], 'int32');
const result = tf.pow(a, b);
expect(result.shape).toEqual([2, 2]);
const expected = [1, 4, -3, -4];
expectArraysClose(await result.data(), expected);
});
it('broadcast 2D + 1D', async () => {
const a = tf.tensor2d([1, 2, -3, -4], [2, 2]);
const b = tf.tensor1d([1, 2], 'int32');
const result = tf.pow(a, b);
expect(result.shape).toEqual([2, 2]);
const expected = [1, 4, -3, 16];
expectArraysClose(await result.data(), expected);
});
it('gradients: Scalar ^ Scalar', async () => {
const a = tf.scalar(5);
const b = tf.scalar(2, 'int32');
const dy = tf.scalar(3);
const grads = tf.grads((a, b) => tf.pow(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [2 * 5 * 3]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [3 * Math.pow(5, 2) * Math.log(5)]);
});
it('gradient with clones', async () => {
const a = tf.scalar(5);
const b = tf.scalar(2, 'int32');
const grads = tf.grads((a, b) => tf.pow(a.clone(), b.clone()).clone());
const [da, db] = grads([a, b]);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [2 * 5]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [Math.pow(5, 2) * Math.log(5)]);
});
it('gradients: x ^ 2 where x = 0', async () => {
const f = (x) => x.pow(tf.scalar(2)).asScalar();
const g = tf.grad(f)(tf.scalar(0));
expectArraysClose(await g.data(), [0]);
});
it('gradients: Scalar ^ Scalar fractional exponent', async () => {
const a = tf.scalar(4.0);
const b = tf.scalar(1.5);
const dy = tf.scalar(3.0);
const grads = tf.grads((a, b) => tf.pow(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [1.5 * Math.pow(4, 0.5) * 3]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [3.0 * Math.pow(4, 1.5) * Math.log(4.0)]);
});
it('gradients: Tensor ^ Tensor', async () => {
const a = tf.tensor1d([-1, .5, 2]);
const b = tf.tensor1d([3, 2, -1], 'int32');
const dy = tf.tensor1d([1, 5, 10]);
const grads = tf.grads((a, b) => tf.pow(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [
3 * Math.pow(-1, 2) * 1, 2 * Math.pow(.5, 1) * 5,
-1 * Math.pow(2, -2) * 10
], 1e-1);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [
0, 5 * Math.pow(.5, 2) * Math.log(.5), 10 * Math.pow(2, -1) * Math.log(2)
]);
});
it('gradient wrt exponent with negative base', async () => {
const a = tf.tensor1d([-1, -.5, -2.7]);
const b = tf.tensor1d([3, 2, -1], 'int32');
const dy = tf.tensor1d([1, 1, 1]);
const grads = tf.grads((a, b) => tf.pow(a, b));
const [, db] = grads([a, b], dy);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [0, 0, 0]);
});
it('gradient: scalar / Tensor1D', async () => {
const a = tf.scalar(2);
const b = tf.tensor1d([3, 4, 5]);
const dy = tf.tensor1d([6, 7, 8]);
const grads = tf.grads((a, b) => tf.pow(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [
6 * 3 * Math.pow(2, 2) + 7 * 4 * Math.pow(2, 3) + 8 * 5 * Math.pow(2, 4)
]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [
6 * Math.pow(2, 3) * Math.log(2), 7 * Math.pow(2, 4) * Math.log(2),
8 * Math.pow(2, 5) * Math.log(2)
]);
});
it('gradient: Tensor2D / scalar', async () => {
const a = tf.tensor2d([[2, 3], [4, 5]], [2, 2]);
const b = tf.scalar(2);
const dy = tf.tensor2d([[6, 7], [8, 9]], [2, 2]);
const grads = tf.grads((a, b) => tf.pow(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [
6 * 2 * Math.pow(2, 1), 7 * 2 * Math.pow(3, 1), 8 * 2 * Math.pow(4, 1),
9 * 2 * Math.pow(5, 1)
]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [6 * Math.pow(2, 2) * Math.log(2) + 7 * Math.pow(3, 2) * Math.log(3) +
8 * Math.pow(4, 2) * Math.log(4) + 9 * Math.pow(5, 2) * Math.log(5)]);
});
it('gradient: Tensor2D / Tensor2D w/ broadcast', async () => {
const a = tf.tensor2d([3, 4], [2, 1]);
const b = tf.tensor2d([[2, 3], [.4, .5]], [2, 2]);
const dy = tf.tensor2d([[6, 7], [8, 9]], [2, 2]);
const grads = tf.grads((a, b) => tf.pow(a, b));
const [da, db] = grads([a, b], dy);
expect(da.shape).toEqual(a.shape);
expect(da.dtype).toEqual('float32');
expectArraysClose(await da.data(), [
6 * 2 * Math.pow(3, 1) + 7 * 3 * Math.pow(3, 2),
8 * .4 * Math.pow(4, .4 - 1) + 9 * .5 * Math.pow(4, .5 - 1)
]);
expect(db.shape).toEqual(b.shape);
expect(db.dtype).toEqual('float32');
expectArraysClose(await db.data(), [
6 * Math.pow(3, 2) * Math.log(3), 7 * Math.pow(3, 3) * Math.log(3),
8 * Math.pow(4, .4) * Math.log(4), 9 * Math.pow(4, .5) * Math.log(4)
]);
});
it('throws when passed base as a non-tensor', () => {
expect(() => tf.pow({}, tf.scalar(1)))
.toThrowError(/Argument 'base' passed to 'pow' must be a Tensor/);
});
it('throws when passed exp as a non-tensor', () => {
expect(() => tf.pow(tf.scalar(1), {}))
.toThrowError(/Argument 'exp' passed to 'pow' must be a Tensor/);
});
it('accepts a tensor-like object', async () => {
const result = tf.pow([1, 2, 3], 2);
expect(result.shape).toEqual([3]);
expect(result.dtype).toBe('float32');
expectArraysClose(await result.data(), [1, 4, 9]);
});
it('negative base and whole exponent not NaN', async () => {
const a = tf.tensor1d([-2, -3, -4], 'float32');
const b = tf.tensor1d([2, -3, 4], 'float32');
const expected = [Math.pow(-2, 2), Math.pow(-3, -3), Math.pow(-4, 4)];
const result = tf.pow(a, b);
expectArraysClose(await result.data(), expected);
});
it('negative base and whole exponent not NaN - vec4', async () => {
const a = tf.tensor1d([-2, -3, -4, -5], 'float32');
const b = tf.tensor1d([2, -3, 4, -5], 'float32');
const expected = [Math.pow(-2, 2), Math.pow(-3, -3), Math.pow(-4, 4), Math.pow(-5, -5)];
const result = tf.pow(a, b);
expectArraysClose(await result.data(), expected);
});
it('negative base and fract exponent NaN', async () => {
const a = tf.tensor1d([-2, -3, -4], 'float32');
const b = tf.tensor1d([2.1, -3.01, 4.1], 'float32');
const expected = [NaN, NaN, NaN];
const result = tf.pow(a, b);
expectArraysClose(await result.data(), expected);
});
});
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MsQ0FBQyxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLEVBQUUsQ0FBQyxDQUFDLEVBQUUsT0FBTyxDQUFDLENBQUM7UUFDL0MsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLE1BQU0sQ0FBQyxDQUFDLEVBQUUsT0FBTyxDQUFDLENBQUM7UUFFaEMsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLEdBQUcsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUM7UUFFdkIsTUFBTSxDQUFDLENBQUMsQ0FBQyxLQUFLLENBQUMsQ0FBQyxPQUFPLENBQUMsT0FBTyxDQUFDLENBQUM7UUFDakMsaUJBQWlCLENBQUMsTUFBTSxDQUFDLENBQUMsSUFBSSxFQUFFLEVBQUUsQ0FBQyxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUMsQ0FBQztJQUNwRCxDQUFDLENBQUMsQ0FBQztJQUVILEVBQUUsQ0FBQyxpQkFBaUIsRUFBRSxLQUFLLElBQUksRUFBRTtRQUMvQixNQUFNLENBQUMsR0FBRyxFQUFFLENBQUMsUUFBUSxDQUFDLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxDQUFDLENBQUM7UUFDdEMsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLFFBQVEsQ0FBQyxDQUFDLENBQUMsRUFBRSxHQUFHLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBRXhDLE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxHQUFHLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxDQUFDO1FBRXZCLGlCQUFpQixDQUFDLE1BQU0sQ0FBQyxDQUFDLElBQUksRUFBRSxFQUFFLENBQUMsQ0FBQyxHQUFHLENBQUMsRUFBRSxHQUFHLENBQUMsQ0FBQyxDQUFDO0lBQ2xELENBQUMsQ0FBQyxDQUFDO0lBRUgsRUFBRSxDQUFDLGdEQUFnRCxFQUFFLEtBQUssSUFBSSxFQUFFO1FBQzlELE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxRQUFRLENBQUMsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxFQUFFLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUMsQ0FBQztRQUM5QyxNQUFNLENBQUMsR0FBRyxFQUFFLENBQUMsUUFBUSxDQUFDLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxDQUFDLENBQUM7UUFFdEMsTUFBTSxNQUFNLEdBQUcsRUFBRSxDQUFDLEdBQUcsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUM7UUFFNUIsTUFBTSxDQUFDLE1BQU0sQ0FBQyxLQUFLLENBQUMsQ0FBQyxPQUFPLENBQUMsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUMsQ0FBQztRQUNyQyxNQUFNLFFBQVEsR0FBRyxDQUFDLENBQUMsR0FBRyxDQUFDLEVBQUUsQ0FBQyxFQUFFLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxHQUFHLENBQUMsQ0FBQyxDQUFDO1FBRXhDLGlCQUFpQixDQUFDLE1BQU0sTUFBTSxDQUFDLElBQUksRUFBRSxFQUFFLFFBQVEsQ0FBQyxDQUFDO0lBQ25ELENBQUMsQ0FBQyxDQUFDO0lBRUgsRUFBRSxDQUFDLGtCQUFrQixFQUFFLEtBQUssSUFBSSxFQUFFO1FBQ2hDLE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxRQUFRLENBQUMsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxFQUFFLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBQzVDLE1BQU0sQ0FBQyxHQUFHLENBQUMsQ0FBQyxDQUFDLENBQUM7UUFFZCxNQUFNLE1BQU0sR0FBRyxFQUFFLENBQUMsR0FBRyxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQztRQUU1QixNQUFNLENBQUMsTUFBTSxDQUFDLEtBQUssQ0FBQyxDQUFDLE9BQU8sQ0FBQyxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBQ3JDLE1BQU0sUUFBUSxHQUFHLENBQUMsR0FBRyxFQUFFLENBQUMsRUFBRSxHQUFHLEVBQUUsQ0FBQyxDQUFDLENBQUM7UUFFbEMsaUJBQWlCLENBQUMsTUFBTSxNQUFNLENBQUMsSUFBSSxFQUFFLEVBQUUsUUFBUSxDQUFDLENBQUM7SUFDbkQsQ0FBQyxDQUFDLENBQUM7SUFFSCxFQUFFLENBQUMsbUJBQW1CLEVBQUUsS0FBSyxJQUFJLEVBQUU7UUFDakMsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLFFBQVEsQ0FBQyxDQUFDLENBQUMsRUFBRSxDQUFDLEVBQUUsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBQzlDLE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxRQUFRLENBQUMsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUMsQ0FBQztRQUU5QixNQUFNLE1BQU0sR0FBRyxFQUFFLENBQUMsR0FBRyxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQztRQUU1QixNQUFNLENBQUMsTUFBTSxDQUFDLEtBQUssQ0FBQyxDQUFDLE9BQU8sQ0FBQyxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBQ3JDLE1BQU0sUUFBUSxHQUFHLENBQUMsQ0FBQyxFQUFFLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBRWhDLGlCQUFpQixDQUFDLE1BQU0sTUFBTSxDQUFDLElBQUksRUFBRSxFQUFFLFFBQVEsQ0FBQyxDQUFDO0lBQ25ELENBQUMsQ0FBQyxDQUFDO0lBRUgsRUFBRSxDQUFDLGdDQUFnQyxFQUFFLEtBQUssSUFBSSxFQUFFO1FBQzlDLElBQUksR0FBRyxHQUFHLEVBQUUsQ0FBQyxHQUFHLENBQUMsRUFBRSxDQUFDLE1BQU0sQ0FBQyxDQUFDLEVBQUUsT0FBTyxDQUFDLEVBQUUsRUFBRSxDQUFDLE1BQU0sQ0FBQyxDQUFDLEVBQUUsU0FBUyxDQUFDLENBQUMsQ0FBQztRQUNqRSxNQUFNLENBQUMsR0FBRyxDQUFDLEtBQUssQ0FBQyxDQUFDLElBQUksQ0FBQyxTQUFTLENBQUMsQ0FBQztRQUNsQyxpQkFBaUIsQ0FBQyxNQUFNLEdBQUcsQ0FBQyxJQUFJLEVBQUUsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDLENBQUM7UUFFekMsR0FBRyxHQUFHLEVBQUUsQ0FBQyxHQUFHLENBQUMsRUFBRSxDQUFDLE1BQU0sQ0FBQyxDQUFDLEVBQUUsT0FBTyxDQUFDLEVBQUUsRUFBRSxDQUFDLE1BQU0sQ0FBQyxJQUFJLEVBQUUsTUFBTSxDQUFDLENBQUMsQ0FBQztRQUM3RCxNQUFNLENBQUMsR0FBRyxDQUFDLEtBQUssQ0FBQyxDQUFDLElBQUksQ0FBQyxPQUFPLENBQUMsQ0FBQztRQUNoQyxpQkFBaUIsQ0FBQyxNQUFNLEdBQUcsQ0FBQyxJQUFJLEVBQUUsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDLENBQUM7SUFDM0MsQ0FBQyxDQUFDLENBQUM7SUFFSCxFQUFFLENBQUMsZ0RBQWdELEVBQUUsR0FBRyxFQUFFO1FBQ3hELE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxRQUFRLENBQUMsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxFQUFFLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxFQUFFLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBQ3BELE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxRQUFRLENBQUMsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxFQUFFLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxDQUFDLENBQUM7UUFFN0MsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLEVBQUUsQ0FBQyxHQUFHLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxDQUFDLENBQUMsWUFBWSxFQUFFLENBQUM7UUFDMUMsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLEVBQUUsQ0FBQyxHQUFHLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxDQUFDLENBQUMsWUFBWSxFQUFFLENBQUM7SUFDNUMsQ0FBQyxDQUFDLENBQUM7SUFFSCxFQUFFLENBQUMseUJBQXlCLEVBQUUsS0FBSyxJQUFJLEVBQUU7UUFDdkMsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLE1BQU0sQ0FBQyxDQUFDLENBQUMsQ0FBQztRQUN2QixNQUFNLENBQUMsR0FBRyxFQUFFLENBQUMsUUFBUSxDQUFDLENBQUMsQ0FBQyxFQUFFLENBQUMsRUFBRSxDQUFDLEVBQUUsQ0FBQyxFQUFFLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBRWxELE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxHQUFHLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxDQUFDO1FBRXZCLGlCQUFpQixDQUNiLE1BQU0sQ0FBQyxDQUFDLElBQUksRUFBRSxFQUFFLENBQUMsQ0FBQyxHQUFHLENBQUMsRUFBRSxDQUFDLEdBQUcsQ0FBQyxFQUFFLENBQUMsR0FBRyxDQUFDLEVBQUUsQ0FBQyxHQUFHLENBQUMsRUFBRSxDQUFDLEdBQUcsQ0FBQyxFQUFFLENBQUMsR0FBRyxDQUFDLENBQUMsQ0FBQyxDQUFDO0lBQ2xFLENBQUMsQ0FBQyxDQUFDO0lBRUgsRUFBRSxDQUFDLHlDQUF5QyxFQUFFLEtBQUssSUFBSSxFQUFFO1FBQ3ZELE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxNQUFNLENBQUMsR0FBRyxDQUFDLENBQUM7UUFDekIsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLFFBQVEsQ0FBQyxDQUFDLENBQUMsRUFBRSxDQUFDLEVBQUUsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUMsQ0FBQztRQUV6QyxNQUFNLENBQUMsR0FBRyxFQUFFLENBQUMsR0FBRyxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQztRQUV2QixpQkFBaUIsQ0FBQyxNQUFNLENBQUMsQ0FBQyxJQUFJLEVBQUUsRUFBRSxDQUFDLEdBQUcsRUFBRSxHQUFHLEVBQUUsR0FBRyxDQUFDLENBQUMsQ0FBQztJQUNyRCxDQUFDLENBQUMsQ0FBQztJQUVILEVBQUUsQ0FBQyx5QkFBeUIsRUFBRSxLQUFLLElBQUksRUFBRTtRQUN2QyxNQUFNLENBQUMsR0FBRyxFQUFFLENBQUMsUUFBUSxDQUFDLENBQUMsQ0FBQyxFQUFFLENBQUMsRUFBRSxDQUFDLEVBQUUsQ0FBQyxFQUFFLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBQ2xELE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxNQUFNLENBQUMsQ0FBQyxDQUFDLENBQUM7UUFFdkIsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLEdBQUcsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUM7UUFFdkIsaUJBQWlCLENBQ2IsTUFBTSxDQUFDLENBQUMsSUFBSSxFQUFFLEVBQUUsQ0FBQyxDQUFDLEdBQUcsQ0FBQyxFQUFFLENBQUMsR0FBRyxDQUFDLEVBQUUsQ0FBQyxHQUFHLENBQUMsRUFBRSxDQUFDLEdBQUcsQ0FBQyxFQUFFLENBQUMsR0FBRyxDQUFDLEVBQUUsQ0FBQyxHQUFHLENBQUMsQ0FBQyxDQUFDLENBQUM7SUFDbEUsQ0FBQyxDQUFDLENBQUM7SUFFSCxFQUFFLENBQUMseUNBQXlDLEVBQUUsS0FBSyxJQUFJLEVBQUU7UUFDdkQsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLFFBQVEsQ0FBQyxDQUFDLENBQUMsRUFBRSxDQUFDLEVBQUUsR0FBRyxDQUFDLEVBQUUsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUMsQ0FBQztRQUMzQyxNQUFNLENBQUMsR0FBRyxFQUFFLENBQUMsTUFBTSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBRXZCLE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxHQUFHLENBQUMsQ0FBQyxFQUFFLENBQUMsQ0FBQyxDQUFDO1FBQ3ZCLGlCQUFpQixDQUFDLE1BQU0sQ0FBQyxDQUFDLElBQUksRUFBRSxFQUFFLENBQUMsQ0FBQyxHQUFHLENBQUMsRUFBRSxDQUFDLEdBQUcsQ0FBQyxFQUFFLEdBQUcsQ0FBQyxDQUFDLENBQUM7SUFDekQsQ0FBQyxDQUFDLENBQUM7SUFFSCxFQUFFLENBQUMsa0JBQWtCLEVBQUUsS0FBSyxJQUFJLEVBQUU7UUFDaEMsTUFBTSxDQUFDLEdBQUcsRUFBRSxDQUFDLE1BQU0sQ0FBQyxDQUFDLENBQUMsQ0FBQztRQUN2QixNQUFNLENBQUMsR0FBRyxFQUFFLENBQUMsTUFBTSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBQ3ZCLE1BQU0sRUFBRSxHQUFHLEVBQUUsQ0FBQyxNQUFNLENBQUMsQ0FBQyxDQUFDLENBQUM7UUFFeEIsTUFBTSxNQUFNLEdBQUcsRUFBRSxDQUFDLE1BQU0sRUFBRSxDQUFDLFVBQVUsQ0FBQztRQUN0QyxNQUFNLEtBQUssR0FBRyxFQUFFLENBQUMsS0FBSyxDQUFDLENBQUMsQ0FBQyxFQUFFLENBQUMsRUFBRSxFQUFFLENBQUMsRUFBRSxDQUFDLEdBQUcsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUMsQ0FBQztRQUMvQyxNQUFNLENBQUMsRUFBRSxFQUFFLEVBQUUsQ0FBQyxHQUFHLEtBQUssQ0FBQyxDQUFDLENBQUMsRUFBRSxDQUFDLENBQUMsRUFBRSxFQUFFLENBQUMsQ0FBQztRQUNuQyxNQUFNLEdBQUcsR0FBRyxFQUFFLENBQUMsTUFBTSxFQUFFLENBQUMsVUFBVSxDQUFDO1FBQ25DLE1BQU0sQ0FBQyxHQUFHLENBQUMsQ0FBQyxJQUFJLENBQUMsTUFBTSxHQUFHLENBQUMsQ0FBQyxDQUFDO1FBRTdCLE1BQU0sQ0FBQyxFQUFFLENBQUMsS0FBSyxDQUFDLENBQUMsT0FBTyxDQUFDLENBQUMsQ0FBQyxLQUFLLENBQUMsQ0FBQztRQUNsQyxNQUFNLENBQUMsRUFBRSxDQUFDLEtBQUssQ0FBQyxDQUFDLE9BQU8sQ0FBQyxTQUFTLENBQUMsQ0FBQztRQUNwQyxpQkFBaUIsQ0FBQyxNQUFNLEVBQUUsQ0FBQyxJQUFJLEVBQUUsRUFBRSxDQUFDLENBQUMsR0FBRyxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBRTVDLE1BQU0sQ0FBQyxFQUFFLENBQUMsS0FBSyxDQUFDLENBQUMsT0FBTyxDQUFDLENBQUMsQ0FBQyxLQUFLLENBQUMsQ0FBQztRQUNsQyxNQUFNLENBQUMsRUFBRSxDQUFDLEtBQUssQ0FBQyxDQUFDLE9BQU8sQ0FBQyxTQUFTLENBQUMsQ0FBQztRQUNwQyxpQkFBaUIsQ0FBQyxNQUFNLEVBQUUsQ0FBQyxJQUFJLEVBQUUsRUFBRSxDQUFDLENBQUMsQ0FBQyxHQUFHLENBQUMsR0FBRyxDQUFDLENBQUMsR0FBRyxDQUFDLENBQUMsQ0FBQyxDQUFDLENBQUM7SUFDekQsQ0FBQyxDQUFDLENBQUM7SUFFSCxFQUFFLENBQUMsc0JBQXNCLEVBQUUsS0FBSyxJQUFJLEVBQUU7UUFDcEMsTUFBTSxLQUFLLEdBQUcsRUFBRSxDQUFDLEtBQUssQ0FBQyxDQUFDLENBQUMsRUFBRSxDQUFDLEVBQUUsRUFBRSxDQUFDLEVBQUUsQ0FBQyxHQUFHLENBQUMsQ0FBQyxDQUFDLEtBQUssRUFBRSxFQUFFLENBQUMsQ0FBQyxLQUFLLEVBQUUsQ0FBQyxDQUFDLEtBQUssRUFBRSxDQUFDLENBQUM7UUFDdkUsTUFBTSxDQUFDLEVBQUUsRUFBRSxFQUFFLENBQUMsR0FBRyxLQUFLLENBQUMsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxDQUFDLENBQUMsQ0FBQztRQUMvQixNQUFNLENBQUMsRUFBRSxDQUFDLEtBQUssQ0FBQyxDQUFDLE9BQU8sQ0FBQyxFQUFFLENBQUMsQ0FBQztRQUM3QixNQUFNLENBQUMsRUFBRSxDQUFDLEtBQUssQ0FBQyxDQUFDLE9BQU8sQ0FBQyxFQUFFLENBQUMsQ0FBQztRQUM3QixpQkFBaUIsQ0FBQyxNQUFNLEVBQUUsQ0FBQyxJQUFJLEVBQUUsRUFBRSxDQUFDLENBQUMsR0FBRyxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBQzVDLGlCQUFpQixDQUFDLE1BQU0sRUFBRSxDQUFDLElBQUksRUFBRSxFQUFFLENBQUMsQ0FBQyxDQUFDLEdBQUcsQ0FBQyxDQUFDLENBQUMsQ0FBQztJQUMvQyxDQUFDLENBQUMsQ0FBQztJQUVILEVBQUUsQ0FBQyxvQkFBb0IsRUFBRSxLQUFLLElBQUksRUFBRTtRQUNsQyxNQUFNLENBQUMsR0FBRyxFQUFFLENBQUMsUUFBUSxDQUFDLENBQUMsQ0FBQyxFQUFFLENBQUMsRUFBRSxDQUFDLENBQUMsQ0FBQyxDQUFDO1FBQ2pDLE1BQU0sQ0FBQyxHQUFHLEVBQUUsQ0FBQyxRQUFRLENBQUMsQ0FBQyxDQUFDLEVBQUUsQ0FBQyxFQUFFLENBQUMsQ0FBQyxDQUFDLENBQUM7UUFDakMsTUFBTSxFQUFFLE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