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更新了09.02
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‎09. theano/09.02 theano basics.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Theano"
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"`Theano` 中可以定义共享的变量，它们可以在多个函数中被共享。"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"TensorType(float64, matrix)\n"
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]
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}
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],
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"source": [
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"shared_var = theano.shared(np.array([[1.0, 2.0], [3.0, 4.0]]))\n",
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"\n",
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"print shared_var.type"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"可以通过 `set_value` 方法改变它的值："
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"shared_var.set_value(np.array([[3.0, 4], [2, 1]]))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"通过 `get_value()` 方法返回它的值："
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[ 3., 4.],\n",
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" [ 2., 1.]])"
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]
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},
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"execution_count": 21,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"shared_var.get_value()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"共享变量进行运算："
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[ 9. 16.]\n",
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" [ 4. 1.]]\n"
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]
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}
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],
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"source": [
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"shared_square = shared_var ** 2\n",
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"\n",
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"f = theano.function([], shared_square)\n",
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"\n",
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"print f()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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",
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"\n",
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"得到的结果会随这个共享变量的变化而变化："
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[ 1. 4.]\n",
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" [ 9. 16.]]\n"
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]
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}
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],
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"source": [
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"shared_var.set_value(np.array([[1.0, 2], [3, 4]]))\n",
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"\n",
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"print f()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"一个共享变量的值可以用 `updates` 关键词在 `theano` 函数中被更新："
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]
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"subtract = T.matrix('subtract')\n",
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"\n",
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"f_update = theano.function([subtract], shared_var, updates={shared_var: shared_var - subtract})"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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："
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"before update:\n",
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"[[ 1. 2.]\n",
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" [ 3. 4.]]\n",
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"the return value:\n",
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"[[ 1. 2.]\n",
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" [ 3. 4.]]\n",
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"after update:\n",
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"[[ 0. 1.]\n",
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" [ 2. 3.]]\n"
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]
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}
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],
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"source": [
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"print 'before update:'\n",
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"print shared_var.get_value()\n",
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"\n",
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"print 'the return value:'\n",
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"print f_update(np.array([[1.0, 1], [1, 1]]))\n",
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"\n",
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"print 'after update:'\n",
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"print shared_var.get_value()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 导数"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"`Theano` 的一大好处在于它对符号变量计算导数的能力。\n",
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"\n",
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"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 $2x$）："
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array(20.0)"
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]
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},
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"execution_count": 26,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"bar_grad = T.grad(bar, foo) # 表示 bar (x^2) 关于 foo (x) 的导数\n",
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"\n",
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"bar_grad.eval({foo: 10})"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"再如，对之前的 $y = Ax + b$ 求 $y$ 关于 $x$ 的雅可比矩阵（应当是 $A$）："
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[ 9. 8. 7.]\n",
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" [ 4. 5. 6.]]\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"C:\\Anaconda\\lib\\site-packages\\theano\\scan_module\\scan_perform_ext.py:133: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n",
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" from scan_perform.scan_perform import *\n"
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]
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}
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],
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"source": [
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"y_J = theano.gradient.jacobian(y, x)\n",
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"\n",
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"print y_J.eval({A: np.array([[9.0, 8, 7], [4, 5, 6]]), #A\n",
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" x: np.array([1.0, 2, 3]), #x\n",
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" b: np.array([4.0, 5])}) #b"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"`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。"
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]
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}
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],

‎README.md

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- [08.11 接口](08. object-oriented programming/08.11 interfaces.ipynb)
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- [08.12 共有，私有和特殊方法和属性](08. object-oriented programming/08.12 public private special in python.ipynb)
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- [08.13 多重继承](08. object-oriented programming/08.13 multiple inheritance.ipynb)
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- [09. **Theano**](09. theano)
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- [09.01 Theano 简介及其安装](09. theano/09.01 introduction and installation.ipynb)
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- [09.02 Theano 基础](09. theano/09.02 theano basics.ipynb)
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- [10. **有趣的主题**](10. something interesting)
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- [10.01 使用 basemap 画地图](10. something interesting/10.01 maps using basemap.ipynb)
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- [10.02 使用 cartopy 画地图](10. something interesting/10.02 maps using cartopy.ipynb)
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- [10.02 使用 cartopy 画地图](10. something interesting/10.02 maps using cartopy.ipynb)

‎generate index.ipynb

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" '06. matplotlib',\n",
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" '07. interfacing with other languages',\n",
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" '08. object-oriented programming',\n",
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" '09. theano',\n",
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" '10. something interesting'\n",
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" ]"
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]
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" '06. **Matplotlib**',\n",
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" '07. **使用其他语言进行扩展**',\n",
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" '08. **面向对象编程**',\n",
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" '09. **Theano**',\n",
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" '10. **有趣的主题**']"
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]
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},
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" 08.11 接口\n",
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" 08.12 共有，私有和特殊方法和属性\n",
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" 08.13 多重继承\n",
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"09. Theano\n",
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" 09.01 Theano 简介及其安装\n",
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" 09.02 Theano 基础\n",
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"10. 有趣的主题\n",
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" 10.01 使用 basemap 画地图\n",
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" 10.02 使用 cartopy 画地图\n"

‎index.ipynb

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"\t - [08.11 接口](08. object-oriented programming/08.11 interfaces.ipynb)\n",
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"\t - [08.12 共有，私有和特殊方法和属性](08. object-oriented programming/08.12 public private special in python.ipynb)\n",
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"\t - [08.13 多重继承](08. object-oriented programming/08.13 multiple inheritance.ipynb)\n",
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"- [09. **Theano**](09. theano)\n",
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"\t - [09.01 Theano 简介及其安装](09. theano/09.01 introduction and installation.ipynb)\n",
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"\t - [09.02 Theano 基础](09. theano/09.02 theano basics.ipynb)\n",
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"- [10. **有趣的主题**](10. something interesting)\n",
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"\t - [10.01 使用 basemap 画地图](10. something interesting/10.01 maps using basemap.ipynb)\n",
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"\t - [10.02 使用 cartopy 画地图](10. something interesting/10.02 maps using cartopy.ipynb)\n"

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