|
484 | 484 | "cell_type": "markdown", |
485 | 485 | "metadata": {}, |
486 | 486 | "source": [ |
487 | | - "Theano" |
| 487 | + "`Theano` 中可以定义共享的变量，它们可以在多个函数中被共享。" |
| 488 | + ] |
| 489 | + }, |
| 490 | + { |
| 491 | + "cell_type": "code", |
| 492 | + "execution_count": 19, |
| 493 | + "metadata": { |
| 494 | + "collapsed": false |
| 495 | + }, |
| 496 | + "outputs": [ |
| 497 | + { |
| 498 | + "name": "stdout", |
| 499 | + "output_type": "stream", |
| 500 | + "text": [ |
| 501 | + "TensorType(float64, matrix)\n" |
| 502 | + ] |
| 503 | + } |
| 504 | + ], |
| 505 | + "source": [ |
| 506 | + "shared_var = theano.shared(np.array([[1.0, 2.0], [3.0, 4.0]]))\n", |
| 507 | + "\n", |
| 508 | + "print shared_var.type" |
| 509 | + ] |
| 510 | + }, |
| 511 | + { |
| 512 | + "cell_type": "markdown", |
| 513 | + "metadata": {}, |
| 514 | + "source": [ |
| 515 | + "可以通过 `set_value` 方法改变它的值：" |
| 516 | + ] |
| 517 | + }, |
| 518 | + { |
| 519 | + "cell_type": "code", |
| 520 | + "execution_count": 20, |
| 521 | + "metadata": { |
| 522 | + "collapsed": true |
| 523 | + }, |
| 524 | + "outputs": [], |
| 525 | + "source": [ |
| 526 | + "shared_var.set_value(np.array([[3.0, 4], [2, 1]]))" |
| 527 | + ] |
| 528 | + }, |
| 529 | + { |
| 530 | + "cell_type": "markdown", |
| 531 | + "metadata": {}, |
| 532 | + "source": [ |
| 533 | + "通过 `get_value()` 方法返回它的值：" |
| 534 | + ] |
| 535 | + }, |
| 536 | + { |
| 537 | + "cell_type": "code", |
| 538 | + "execution_count": 21, |
| 539 | + "metadata": { |
| 540 | + "collapsed": false |
| 541 | + }, |
| 542 | + "outputs": [ |
| 543 | + { |
| 544 | + "data": { |
| 545 | + "text/plain": [ |
| 546 | + "array([[ 3., 4.],\n", |
| 547 | + " [ 2., 1.]])" |
| 548 | + ] |
| 549 | + }, |
| 550 | + "execution_count": 21, |
| 551 | + "metadata": {}, |
| 552 | + "output_type": "execute_result" |
| 553 | + } |
| 554 | + ], |
| 555 | + "source": [ |
| 556 | + "shared_var.get_value()" |
| 557 | + ] |
| 558 | + }, |
| 559 | + { |
| 560 | + "cell_type": "markdown", |
| 561 | + "metadata": {}, |
| 562 | + "source": [ |
| 563 | + "共享变量进行运算：" |
| 564 | + ] |
| 565 | + }, |
| 566 | + { |
| 567 | + "cell_type": "code", |
| 568 | + "execution_count": 22, |
| 569 | + "metadata": { |
| 570 | + "collapsed": false |
| 571 | + }, |
| 572 | + "outputs": [ |
| 573 | + { |
| 574 | + "name": "stdout", |
| 575 | + "output_type": "stream", |
| 576 | + "text": [ |
| 577 | + "[[ 9. 16.]\n", |
| 578 | + " [ 4. 1.]]\n" |
| 579 | + ] |
| 580 | + } |
| 581 | + ], |
| 582 | + "source": [ |
| 583 | + "shared_square = shared_var ** 2\n", |
| 584 | + "\n", |
| 585 | + "f = theano.function([], shared_square)\n", |
| 586 | + "\n", |
| 587 | + "print f()" |
| 588 | + ] |
| 589 | + }, |
| 590 | + { |
| 591 | + "cell_type": "markdown", |
| 592 | + "metadata": {}, |
| 593 | + "source": [ |
| 594 | + "这里函数不需要参数，因为共享变量隐式地被认为是一个参数。\n", |
| 595 | + "\n", |
| 596 | + "得到的结果会随这个共享变量的变化而变化：" |
| 597 | + ] |
| 598 | + }, |
| 599 | + { |
| 600 | + "cell_type": "code", |
| 601 | + "execution_count": 23, |
| 602 | + "metadata": { |
| 603 | + "collapsed": false |
| 604 | + }, |
| 605 | + "outputs": [ |
| 606 | + { |
| 607 | + "name": "stdout", |
| 608 | + "output_type": "stream", |
| 609 | + "text": [ |
| 610 | + "[[ 1. 4.]\n", |
| 611 | + " [ 9. 16.]]\n" |
| 612 | + ] |
| 613 | + } |
| 614 | + ], |
| 615 | + "source": [ |
| 616 | + "shared_var.set_value(np.array([[1.0, 2], [3, 4]]))\n", |
| 617 | + "\n", |
| 618 | + "print f()" |
| 619 | + ] |
| 620 | + }, |
| 621 | + { |
| 622 | + "cell_type": "markdown", |
| 623 | + "metadata": {}, |
| 624 | + "source": [ |
| 625 | + "一个共享变量的值可以用 `updates` 关键词在 `theano` 函数中被更新：" |
| 626 | + ] |
| 627 | + }, |
| 628 | + { |
| 629 | + "cell_type": "code", |
| 630 | + "execution_count": 24, |
| 631 | + "metadata": { |
| 632 | + "collapsed": true |
| 633 | + }, |
| 634 | + "outputs": [], |
| 635 | + "source": [ |
| 636 | + "subtract = T.matrix('subtract')\n", |
| 637 | + "\n", |
| 638 | + "f_update = theano.function([subtract], shared_var, updates={shared_var: shared_var - subtract})" |
| 639 | + ] |
| 640 | + }, |
| 641 | + { |
| 642 | + "cell_type": "markdown", |
| 643 | + "metadata": {}, |
| 644 | + "source": [ |
| 645 | + "这个函数先返回当前的值，然后将当前值更新为原来的值减去参数：" |
| 646 | + ] |
| 647 | + }, |
| 648 | + { |
| 649 | + "cell_type": "code", |
| 650 | + "execution_count": 25, |
| 651 | + "metadata": { |
| 652 | + "collapsed": false |
| 653 | + }, |
| 654 | + "outputs": [ |
| 655 | + { |
| 656 | + "name": "stdout", |
| 657 | + "output_type": "stream", |
| 658 | + "text": [ |
| 659 | + "before update:\n", |
| 660 | + "[[ 1. 2.]\n", |
| 661 | + " [ 3. 4.]]\n", |
| 662 | + "the return value:\n", |
| 663 | + "[[ 1. 2.]\n", |
| 664 | + " [ 3. 4.]]\n", |
| 665 | + "after update:\n", |
| 666 | + "[[ 0. 1.]\n", |
| 667 | + " [ 2. 3.]]\n" |
| 668 | + ] |
| 669 | + } |
| 670 | + ], |
| 671 | + "source": [ |
| 672 | + "print 'before update:'\n", |
| 673 | + "print shared_var.get_value()\n", |
| 674 | + "\n", |
| 675 | + "print 'the return value:'\n", |
| 676 | + "print f_update(np.array([[1.0, 1], [1, 1]]))\n", |
| 677 | + "\n", |
| 678 | + "print 'after update:'\n", |
| 679 | + "print shared_var.get_value()" |
| 680 | + ] |
| 681 | + }, |
| 682 | + { |
| 683 | + "cell_type": "markdown", |
| 684 | + "metadata": {}, |
| 685 | + "source": [ |
| 686 | + "## 导数" |
| 687 | + ] |
| 688 | + }, |
| 689 | + { |
| 690 | + "cell_type": "markdown", |
| 691 | + "metadata": {}, |
| 692 | + "source": [ |
| 693 | + "`Theano` 的一大好处在于它对符号变量计算导数的能力。\n", |
| 694 | + "\n", |
| 695 | + "我们用 `T.grad()` 来计算导数，之前我们定义了 `foo` 和 `bar` （分别是 $x$ 和 $x^2$）,我们来计算 `bar` 关于 `foo` 的导数（应该是 $2x$）：" |
| 696 | + ] |
| 697 | + }, |
| 698 | + { |
| 699 | + "cell_type": "code", |
| 700 | + "execution_count": 26, |
| 701 | + "metadata": { |
| 702 | + "collapsed": false |
| 703 | + }, |
| 704 | + "outputs": [ |
| 705 | + { |
| 706 | + "data": { |
| 707 | + "text/plain": [ |
| 708 | + "array(20.0)" |
| 709 | + ] |
| 710 | + }, |
| 711 | + "execution_count": 26, |
| 712 | + "metadata": {}, |
| 713 | + "output_type": "execute_result" |
| 714 | + } |
| 715 | + ], |
| 716 | + "source": [ |
| 717 | + "bar_grad = T.grad(bar, foo) # 表示 bar (x^2) 关于 foo (x) 的导数\n", |
| 718 | + "\n", |
| 719 | + "bar_grad.eval({foo: 10})" |
| 720 | + ] |
| 721 | + }, |
| 722 | + { |
| 723 | + "cell_type": "markdown", |
| 724 | + "metadata": {}, |
| 725 | + "source": [ |
| 726 | + "再如，对之前的 $y = Ax + b$ 求 $y$ 关于 $x$ 的雅可比矩阵（应当是 $A$）：" |
| 727 | + ] |
| 728 | + }, |
| 729 | + { |
| 730 | + "cell_type": "code", |
| 731 | + "execution_count": 27, |
| 732 | + "metadata": { |
| 733 | + "collapsed": false |
| 734 | + }, |
| 735 | + "outputs": [ |
| 736 | + { |
| 737 | + "name": "stdout", |
| 738 | + "output_type": "stream", |
| 739 | + "text": [ |
| 740 | + "[[ 9. 8. 7.]\n", |
| 741 | + " [ 4. 5. 6.]]\n" |
| 742 | + ] |
| 743 | + }, |
| 744 | + { |
| 745 | + "name": "stderr", |
| 746 | + "output_type": "stream", |
| 747 | + "text": [ |
| 748 | + "C:\\Anaconda\\lib\\site-packages\\theano\\scan_module\\scan_perform_ext.py:133: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n", |
| 749 | + " from scan_perform.scan_perform import *\n" |
| 750 | + ] |
| 751 | + } |
| 752 | + ], |
| 753 | + "source": [ |
| 754 | + "y_J = theano.gradient.jacobian(y, x)\n", |
| 755 | + "\n", |
| 756 | + "print y_J.eval({A: np.array([[9.0, 8, 7], [4, 5, 6]]), #A\n", |
| 757 | + " x: np.array([1.0, 2, 3]), #x\n", |
| 758 | + " b: np.array([4.0, 5])}) #b" |
| 759 | + ] |
| 760 | + }, |
| 761 | + { |
| 762 | + "cell_type": "markdown", |
| 763 | + "metadata": {}, |
| 764 | + "source": [ |
| 765 | + "`theano.gradient.jacobian` 用来计算雅可比矩阵，而 `theano.gradient.hessian` 可以用来计算 `Hessian` 矩阵。" |
488 | 766 | ] |
489 | 767 | } |
490 | 768 | ], |
|
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