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添加了线性代数和THEANO的卷积神经网络部分,修复了第一节显示的问题
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{
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"cells": [
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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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"# 稀疏矩阵的线性代数"
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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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"对于稀疏矩阵来说,其线性代数操作可以使用 `scipy.sparse.linalg` 实现:"
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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": 1,
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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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"import scipy.sparse.linalg"
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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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"## 矩阵操作"
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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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"- `scipy.sparse.linalg.inv`\n",
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" - 稀疏矩阵求逆\n",
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"- `scipy.sparse.linalg.expm`\n",
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" - 求稀疏矩阵的指数函数"
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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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"## 矩阵范数"
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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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"- `scipy.sparse.linalg.norm`\n",
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" - 稀疏矩阵求范数"
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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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"## 线性方程组求解"
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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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"提供了一系列求解方法:\n",
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"http://docs.scipy.org/doc/scipy/reference/sparse.linalg.html#solving-linear-problems\n",
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"\n",
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"主要使用的是迭代方法求解。"
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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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"## 特征值分解和奇异值分解"
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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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"对于特别大的矩阵,原来的方法可能需要太大的内存,考虑使用这两个方法替代:\n",
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"\n",
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"- `scipy.sparse.linalg.eigs`\n",
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" - 返回前 k 大的特征值和特征向量\n",
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"- `scipy.sparse.linalg.svds`\n",
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" - 返回前 k 大的奇异值和奇异向量"
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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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"## <font color=\"red\">所有的这些操作既可以在稀疏矩阵上使用,也可以在普通矩阵上使用。</font>"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 2",
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"language": "python",
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"name": "python2"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 2
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython2",
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"version": "2.7.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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