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NumPy Tutorial メモ3 (Copies and Views)
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NumPyTutorial_3.ipynb
{
"cells": [
{
"metadata": {
"toc": "true"
},
"cell_type": "markdown",
"source": "# Table of Contents\n <p><div class=\"lev1\"><a href=\"#NumPyTutorial_3-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>NumPyTutorial_3</a></div><div class=\"lev2\"><a href=\"#Copies-and-Views（CopyとView）-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Copies and Views（CopyとView）</a></div><div class=\"lev3\"><a href=\"#No-Copy-at-All（全くコピーを行わない）-1.1.1\"><span class=\"toc-item-num\">1.1.1&nbsp;&nbsp;</span>No Copy at All（全くコピーを行わない）</a></div><div class=\"lev3\"><a href=\"#View-or-Shallow-Copy-1.1.2\"><span class=\"toc-item-num\">1.1.2&nbsp;&nbsp;</span>View or Shallow Copy</a></div><div class=\"lev3\"><a href=\"#Deep-Copy-1.1.3\"><span class=\"toc-item-num\">1.1.3&nbsp;&nbsp;</span>Deep Copy</a></div><div class=\"lev3\"><a href=\"#Functions-and-Methods-Overview-（関数とメソッドの概要）-1.1.4\"><span class=\"toc-item-num\">1.1.4&nbsp;&nbsp;</span>Functions and Methods Overview （関数とメソッドの概要）</a></div><div class=\"lev4\"><a href=\"#Array-Creation（配列の作成）-1.1.4.1\"><span class=\"toc-item-num\">1.1.4.1&nbsp;&nbsp;</span>Array Creation（配列の作成）</a></div><div class=\"lev4\"><a href=\"#Conversions（変換）-1.1.4.2\"><span class=\"toc-item-num\">1.1.4.2&nbsp;&nbsp;</span>Conversions（変換）</a></div><div class=\"lev4\"><a href=\"#Manipulations（操作）-1.1.4.3\"><span class=\"toc-item-num\">1.1.4.3&nbsp;&nbsp;</span>Manipulations（操作）</a></div><div class=\"lev4\"><a href=\"#Questions-1.1.4.4\"><span class=\"toc-item-num\">1.1.4.4&nbsp;&nbsp;</span>Questions</a></div><div class=\"lev4\"><a href=\"#Ordering（順番）-1.1.4.5\"><span class=\"toc-item-num\">1.1.4.5&nbsp;&nbsp;</span>Ordering（順番）</a></div><div class=\"lev4\"><a href=\"#Operations（演算）-1.1.4.6\"><span class=\"toc-item-num\">1.1.4.6&nbsp;&nbsp;</span>Operations（演算）</a></div><div class=\"lev4\"><a href=\"#Basic-Statistics（基本統計）-1.1.4.7\"><span class=\"toc-item-num\">1.1.4.7&nbsp;&nbsp;</span>Basic Statistics（基本統計）</a></div><div class=\"lev4\"><a href=\"#Basic-Linear-Algebra（基本的な線形代数）-1.1.4.8\"><span class=\"toc-item-num\">1.1.4.8&nbsp;&nbsp;</span>Basic Linear Algebra（基本的な線形代数）</a></div><div class=\"lev2\"><a href=\"#参考リンク-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>参考リンク</a></div>"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "# NumPyTutorial_3"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- [QuickStartTutorial](https://docs.scipy.org/doc/numpy-dev/user/quickstart.html)\n- [私訳「暫定的 NumPy チュートリアル」](http://naoyat.hatenablog.jp/entry/2011/12/29/021414)"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Copies and Views（CopyとView）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "When operating and manipulating arrays,\ntheir data is sometimes copied into a new array and sometimes not. \n（配列の演算や操作のとき、それらのデータは、新しい配列にコピーされる時もあればそうでない時もある。）\n\nThis is often a source of confusion for beginners. \n（これは時として初心者にとって混乱の元となる。）\n\nThere are three cases（3ケースある）:"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### No Copy at All（全くコピーを行わない）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Simple assignments make no copy of array objects or of their data.\n（シンプルな代入では、配列オブジェクトもそれらのデータもコピーされない。）"
},
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "import numpy as np",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "a = np.arange(12)\nb = a # no new object is create 新しいオブジェクトを作らない\nb is a # a and b are two names for the same ndarray object aとbは同じndarray objectを指す",
"execution_count": 2,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "True"
},
"metadata": {},
"execution_count": 2
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "b.shape = (3, 4) # changes the shape of a\na.shape",
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "(3, 4)"
},
"metadata": {},
"execution_count": 3
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Python passes mutable objects as references, so function calls make no copy.\n（Python は、書き換え可能なオブジェクトを参照を渡すため、\n関数コールはコピーしない。）"
},
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "def f(x):\n print(id(x))",
"execution_count": 4,
"outputs": []
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "id(a) # id is a unique identifier of an object（id はオブジェクトのユニークな識別子）",
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "1864188480048"
},
"metadata": {},
"execution_count": 5
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "f(a)",
"execution_count": 6,
"outputs": [
{
"output_type": "stream",
"text": "1864188480048\n",
"name": "stdout"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### View or Shallow Copy"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Different array objects can share the same data. \n（異なる配列オブジェクトが、同じデータを共有することができる。）\n\nThe `view` method creates a new array object that looks at the same data.\n（`view`メソッドは、同じデータに見える新しい配列オブジェクトを作成する。）"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "c = a.view()\nc is a ",
"execution_count": 7,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "False"
},
"metadata": {},
"execution_count": 7
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "c.base is a # c is a view of the data owned by a （c は、a が所有しているデータのビュー）",
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "True"
},
"metadata": {},
"execution_count": 8
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "c.flags.owndata",
"execution_count": 9,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "False"
},
"metadata": {},
"execution_count": 9
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "c.shape = (2, 6) # a's shape doesn't change\na.shape",
"execution_count": 10,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "(3, 4)"
},
"metadata": {},
"execution_count": 10
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "c[0, 4] = 1234 # a's data changes （a のデータは変更される）\na",
"execution_count": 11,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "array([[ 0, 1, 2, 3],\n [1234, 5, 6, 7],\n [ 8, 9, 10, 11]])"
},
"metadata": {},
"execution_count": 11
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Slicing an array returns a `view` of it\n（配列をスライスすると、その view が返される）:"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "s = a[ : , 1:3] # spaces added for clarity; could also be written \"s = a[:,1:3]\"\ns",
"execution_count": 12,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "array([[ 1, 2],\n [ 5, 6],\n [ 9, 10]])"
},
"metadata": {},
"execution_count": 12
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "s[:] = 10 # s[:] is a view of s. Note the difference between s=10 and s[:]=10 \ns #（s[:] はs のview。s=10 と s[:]=10 の違いに注意。）",
"execution_count": 13,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "array([[10, 10],\n [10, 10],\n [10, 10]])"
},
"metadata": {},
"execution_count": 13
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "a # aのデータも書き換わる",
"execution_count": 14,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "array([[ 0, 10, 10, 3],\n [1234, 10, 10, 7],\n [ 8, 10, 10, 11]])"
},
"metadata": {},
"execution_count": 14
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "test = [1,2,3,4,5]\ntest",
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "[1, 2, 3, 4, 5]"
},
"metadata": {},
"execution_count": 15
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "_slice = test[1:4]\n_slice",
"execution_count": 16,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "[2, 3, 4]"
},
"metadata": {},
"execution_count": 16
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "_slice = [0,0,0]\n_slice",
"execution_count": 17,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "[0, 0, 0]"
},
"metadata": {},
"execution_count": 17
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "test # pythonのlist は、sliceしても別オブジェクト",
"execution_count": 18,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "[1, 2, 3, 4, 5]"
},
"metadata": {},
"execution_count": 18
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Deep Copy"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "The `copy` method makes a complete copy of the array and its data.\n（copyメソッドは、配列とそのデータの完全なコピーを作る。）"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "d = a.copy() # a new array object with new data is created（dは新たに作成されたデータを持つ新たな配列オブジェクト）\nd",
"execution_count": 19,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "array([[ 0, 10, 10, 3],\n [1234, 10, 10, 7],\n [ 8, 10, 10, 11]])"
},
"metadata": {},
"execution_count": 19
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "d is a",
"execution_count": 20,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "False"
},
"metadata": {},
"execution_count": 20
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "d.base is a # d doesn't share anything with a",
"execution_count": 21,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "False"
},
"metadata": {},
"execution_count": 21
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "d[0, 0] = 9999\nd",
"execution_count": 22,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "array([[9999, 10, 10, 3],\n [1234, 10, 10, 7],\n [ 8, 10, 10, 11]])"
},
"metadata": {},
"execution_count": 22
}
]
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "a",
"execution_count": 23,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "array([[ 0, 10, 10, 3],\n [1234, 10, 10, 7],\n [ 8, 10, 10, 11]])"
},
"metadata": {},
"execution_count": 23
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Functions and Methods Overview （関数とメソッドの概要）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Here is a list of some useful NumPy functions and methods names ordered in categories. See Routines for the full list.\n（NumPy の関数およびメソッドのカテゴリ別一覧(name order)である。）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Array Creation（配列の作成）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- [arange](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.arange.html)\n- [array](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.array.html)\n- [copy (deep copy)](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.copy.html)\n- [empty](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.empty.html)\n- [empty_like](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.empty_like.html#numpy.empty_like)\n- [eye （単位行列）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.eye.html)\n- [identity]()\n- [fromfile （ファイルからNumPy配列読み込み）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.fromfile.html)\n- [fromfunction](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.fromfunction.html)\n- [linspace](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.linspace.html)\n- [logspace](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.logspace.html)\n- [mgrid （多次元“meshgrid”を作る）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.mgrid.html)\n- [ogrid （1つの軸に長さをもった“meshgrid”を作る）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.ogrid.html)\n- [ones](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.ones.html)\n- [ones_like](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.ones_like.html#numpy.ones_like)\n- [r\\_](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.r_.html)\n- [zeros zero行列](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.zeros.html)\n- [zeros_like](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.zeros_like.html#numpy.zeros_like)"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Conversions（変換）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- [ndarray.astype （型変換）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.ndarray.astype.html)\n- [atleast_1d （少なくとも1軸をもった配列に変換）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.atleast_1d.html)\n- [atleast_2d （少なくとも2軸をもった配列に変換）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.atleast_2d.html#numpy.atleast_2d)\n- [atleast_3d（少なくとも3軸をもった配列に変換）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.atleast_3d.html#numpy.atleast_3d)\n- [mat （matrix型）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.mat.html)"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Manipulations（操作）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- [array_split](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.array_split.html)\n- [column_stack](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.column_stack.html)\n- [concatenate](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.concatenate.html)\n- [diagonal](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.diagonal.html)\n- [dsplit （第3軸に沿って分ける）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.dsplit.html)\n- [dstack （第3軸にスタック）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.dstack.html)\n- [hsplit](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.hsplit.html)\n- [hstack](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.hstack.html)\n- [ndarray.item （indexアクセス）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.ndarray.item.html) \n- [newaxis](https://docs.scipy.org/doc/numpy-dev/reference/arrays.indexing.html#numpy.newaxis)\n- [ravel](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.ravel.html)\n- [repeat](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.repeat.html)\n- [reshape](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.reshape.html)\n- [resize](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.resize.html)\n- [squeeze（single dimension を削除）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.squeeze.html)\n- [swapaxes（軸の交換）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.swapaxes.html)\n- [take](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.take.html)\n- [transpose（転置）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.transpose.html)\n- [vsplit](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.vsplit.html)\n- [vstack](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.vstack.html)"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Questions"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- [all](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.all.html)\n- [any](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.any.html)\n- [nonzero （zeroでないindexを返す）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.nonzero.html)\n- [where](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.where.html)"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Ordering（順番）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- [argmax](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.argmax.html)\n- [argmin](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.argmin.html)\n- [argsort （sort後のindexを返す）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.argsort.html)\n- [max](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.ndarray.max.html)\n- [min](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.ndarray.min.html)\n- [ptp （最小値から最大値の範囲を返す）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.ptp.html)\n- [searchsorted （ソート後のindexを返す）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.searchsorted.html)\n- [sort](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.sort.html)"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Operations（演算）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- [choose](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.choose.html)\n- [compress](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.compress.html)\n- [cumprod （cumulative productを返す）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.cumprod.html)\n- [cumsum（cumulative sum を返す）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.cumsum.html)\n- [inner](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.inner.html)\n- [ndarray.fill](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.ndarray.fill.html)\n- [imag （虚数のみの演算）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.imag.html)\n- [real（実数のみの演算）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.real.html)\n- [prod （すべての要素の積した値を返す）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.prod.html)\n- [put（要素のreplace）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.put.html)\n- [putmask](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.putmask.html) \n- [sum](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.sum.html)"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Basic Statistics（基本統計）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- [cov (共分散行列)](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.cov.html)\n- [mean（平均）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.mean.html)\n- [std （標準偏差）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.std.html)\n- [var（分散）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.var.html)"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "#### Basic Linear Algebra（基本的な線形代数）"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- [cross（クロス積）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.cross.html)\n- [dot(行列の積)](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.dot.html)\n- [outer（直積）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.outer.html#numpy.outer)\n- [linalg.svd（特異値分解）](http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.linalg.svd.html)\n- [vdot（内積）](http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.vdot.html)"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## 参考リンク"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "- [QuickStartTutorial](https://docs.scipy.org/doc/numpy-dev/user/quickstart.html)\n- [私訳「暫定的 NumPy チュートリアル」](http://naoyat.hatenablog.jp/entry/2011/12/29/021414)"
}
],
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"language_info": {
"nbconvert_exporter": "python",
"file_extension": ".py",
"mimetype": "text/x-python",
"codemirror_mode": {
"version": 3,
"name": "ipython"
},
"version": "3.5.1",
"name": "python",
"pygments_lexer": "ipython3"
},
"toc": {
"toc_window_display": false,
"toc_threshold": "6",
"toc_cell": true,
"toc_number_sections": true
},
"gist": {
"id": "",
"data": {
"description": "NumPy Tutorial メモ3 (Copies and Views)",
"public": true
}
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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