Sample Code/Day_04_SampleCode.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"@webio":{"lastCommId":null,"lastKernelId":null},"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.7.4"},"colab":{"name":"範例程式.ipynb","provenance":[],"collapsed_sections":["RiQ4Jz8iaMmL","2oxeoLjKaMmr","6Gjo-MAZaMm6","AdwF2n4IaMm6","lT2Udi0QaMm_","xiKwVehjaMnE"]}},"cells":[{"cell_type":"markdown","metadata":{"id":"-3hwXy27aMk4"},"source":["<img width=150 src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/NumPy_logo.svg/200px-NumPy_logo.svg.png\"></img>\n","\n","# Part.2-1-04 NumPy 陣列邏輯函式 (Logic Functions)"]},{"cell_type":"markdown","metadata":{"id":"YPvtMscrC98d"},"source":["範例目標:<br>\r\n","實做\r\n","1. 陣列內容 (Array contents)\r\n","2. 陣列型別偵測 (Array type testing)\r\n","3. 比較 (Comparison)\r\n","4. 邏輯操作 (Logical operations)\r\n","5. Truth 值測試 (Truth value testing)\r\n"]},{"cell_type":"markdown","metadata":{"id":"mY0TcCTUDJiM"},"source":["範例重點:<br>\r\n","1. 在此介紹的函數應注意是否為 element-wise 的比較邏輯，因不同邏輯產生的輸出會不相同\r\n","2. np.inf表示無限數，np.nan表示Not a Number"]},{"cell_type":"code","metadata":{"id":"KVUgCAFhaMl4"},"source":["import numpy as np"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"CuZfWNd_aMl6"},"source":["## 1. 陣列內容"]},{"cell_type":"markdown","metadata":{"id":"BW0ZzLq6aMl6"},"source":["## 1.1 `isnan()`\n","\n","呼叫 `isnan()` 函式判斷陣列元素是否為 nan，如果是的話回傳 True，否則回傳 False。\n","\n","`numpy.nan` 與 `numpy.NAN` 都是 NumPy 常數，代表 Not a Number，不過在官方文件中建議統一使用小寫的 `nan`。"]},{"cell_type":"code","metadata":{"id":"T11udv63aMl7","outputId":"9155011d-061b-4bdb-b2d5-b372380209b7"},"source":["np.isnan(np.array([1.0, np.nan, 3.0]))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([False,  True, False])"]},"metadata":{"tags":[]},"execution_count":2}]},{"cell_type":"markdown","metadata":{"id":"HJdknPlwaMl_"},"source":["### 1.2 `isfinite()`\n","\n","判斷陣列元素是否為有限數 (finite number)，如果是的話回傳 True，如果元素值為正無限數、負無限數、或是 nan 則回傳 False。"]},{"cell_type":"code","metadata":{"id":"7wiOnx8paMl_","outputId":"b5f1caf9-5d1f-4a73-907e-097208068e3c"},"source":["np.isfinite(1.0)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":3}]},{"cell_type":"code","metadata":{"id":"dhG2f8ZVaMmF","outputId":"3f755cb0-b6f1-4369-a698-8d836cbb7df1"},"source":["np.isfinite(np.nan)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["False"]},"metadata":{"tags":[]},"execution_count":4}]},{"cell_type":"markdown","metadata":{"id":"2RCy-CmgaMmH"},"source":["## 1.3 `isinf()`、`isposinf()`、`isneginf()`\n","\n","判別元素是否為無限數。\n","\n","|函式|說明|\n","|---|---|\n","|isinf()|判斷陣列元素是否為正無限數或負無限數|\n","|isposinf()|判斷陣列元素是否為正無限數|\n","|isneginf()|判斷陣列元素是否為負無限數|\n","\n","在下列範例中我們會用到 NumPy 內建常數 (Constants) 來示範，無限數相關的常數如下表：\n","\n","|常數|說明|別名|\n","|---|---|---|\n","|np.inf|正無限數| np.Inf, np.Infinity, np.PINF, np.infty|\n","|np.Inf|正無限數||\n","|np.Infinity|正無限數||\n","|np.PINF|正無限數||\n","|np.infty|正無限數||\n","|np.NINF|負無限數||\n","\n","NumPy 文件建議正無限數使用 `np.inf` (小寫)。"]},{"cell_type":"code","metadata":{"id":"KLUuwEiDaMmI","outputId":"65065a24-73de-4ffe-f049-c96bb2c32570"},"source":["np.isinf([np.inf, -np.inf, 1.0, np.nan, np.PINF])"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ True,  True, False, False,  True])"]},"metadata":{"tags":[]},"execution_count":5}]},{"cell_type":"code","metadata":{"id":"5rH6UtqZaMmJ","outputId":"0fcfd23d-2ae3-42cb-f2e1-a8ff7d667fc5"},"source":["np.isposinf(np.PINF)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":6}]},{"cell_type":"code","metadata":{"id":"uVj_A9EnaMmJ","outputId":"4b0527cd-ed2d-444e-f3d4-a8e58f2a365d"},"source":["np.isneginf(np.NINF), np.isneginf(np.nan)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(True, False)"]},"metadata":{"tags":[]},"execution_count":7}]},{"cell_type":"markdown","metadata":{"id":"fZvjOo2TaMmK"},"source":["## 1.4 `isnat()`\n","\n","`isnat()` 的 nat (NaT) 是 not a time 的意思，用來判別陣列元素是否為日期時間。若非日期時間 (包括 datetime 或 timedelta) 的話回傳 True，若是的話則回傳 False。"]},{"cell_type":"code","metadata":{"id":"cLDCBXSoaMmL","outputId":"9a4965f3-e981-4241-9633-47f333d3e980"},"source":["np.isnat(np.array([\"NaT\", \"2020-06-26\"], dtype=\"datetime64[ns]\"))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ True, False])"]},"metadata":{"tags":[]},"execution_count":8}]},{"cell_type":"markdown","metadata":{"id":"NG6vYuk_aMmL"},"source":["## 2. 陣列型別偵測"]},{"cell_type":"markdown","metadata":{"id":"RiQ4Jz8iaMmL"},"source":["## 2.1 `isscalar()`\n","\n","如果陣列元素為純量或是數字物件 (例如實數、複數、有理數) 、內建常數、字串的話，`isscalar()` 回傳 True 。需要留意的是 `isscalar()` 不是 element-wise 的，所以傳入值須為元素。\n","\n","數字物件的詳細說明，參照 [PEP 3141](https://www.python.org/dev/peps/pep-3141/)。"]},{"cell_type":"code","metadata":{"id":"68udEtPeaMmQ"},"source":["a = np.array([1, 2, 3])"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"N1gGf3Z_aMmQ","outputId":"6fedf84e-24f1-4625-bf1b-8ff033e7e6e8"},"source":["np.isscalar(a[2])"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":10}]},{"cell_type":"markdown","metadata":{"id":"oznd-7rzaMmU"},"source":["如果傳傳整個陣列的話，會回傳 False。"]},{"cell_type":"code","metadata":{"id":"a4w9WJOMaMmU","outputId":"eae9c096-573a-4129-da1b-ef78a71e6be9"},"source":["np.isscalar(a)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["False"]},"metadata":{"tags":[]},"execution_count":11}]},{"cell_type":"markdown","metadata":{"id":"mTpVNxYzaMmW"},"source":["傳入內建常數 `np.pi`，回傳 True。"]},{"cell_type":"code","metadata":{"id":"9w1kBq1uaMmX","outputId":"b7540d2c-3c2a-4709-984c-7e971ffecbf1"},"source":["np.isscalar(np.pi)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":12}]},{"cell_type":"markdown","metadata":{"id":"GswvIwcSaMmY"},"source":["傳入 0 維陣列的話，仍然會回傳 False。"]},{"cell_type":"code","metadata":{"id":"quLk_sIgaMmY","outputId":"4da29018-48ef-4e00-f525-7a56276446da"},"source":["np.isscalar(np.array(3.0))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["False"]},"metadata":{"tags":[]},"execution_count":13}]},{"cell_type":"markdown","metadata":{"id":"2oxeoLjKaMmr"},"source":["## 2.2 `isreal()`、`iscomplex()`、`isrealobj()`、`iscomplexobj（）`\n","\n","判斷輸入的陣列元素為實數 (`isreal()`) 或是複數 (`iscomplex()`)。"]},{"cell_type":"code","metadata":{"id":"cRG0bTz-aMmr"},"source":["# 包含實數與複數的陣列\n","b = np.array([1+1j, 1+0j, 4.5, 3, 2, 2j])"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"E_fryzNtaMmr","outputId":"7039bf85-336f-49fb-f26c-df05167ec14c"},"source":["np.isreal(b)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([False,  True,  True,  True,  True, False])"]},"metadata":{"tags":[]},"execution_count":15}]},{"cell_type":"code","metadata":{"id":"iIQzB4bwaMms","outputId":"72faa0e4-f0ec-439f-d009-37678f7267a6"},"source":["np.iscomplex(b)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ True, False, False, False, False,  True])"]},"metadata":{"tags":[]},"execution_count":16}]},{"cell_type":"markdown","metadata":{"id":"yzwobFLlaMmu"},"source":["與上面 2 個函式類似的 `isrealobj()`、`iscomplexobj（）`，不同之處在於是判斷整個陣列物件是否為實數或是複數物件。"]},{"cell_type":"code","metadata":{"id":"a4AskDhHaMm4","outputId":"07d9add8-55a9-4dd2-d39f-7a832da7840d"},"source":["np.iscomplexobj(b)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":17}]},{"cell_type":"code","metadata":{"id":"qyY8Qw9-aMm4","outputId":"15bca92a-ec77-417b-ad2a-f1f9c12555b1"},"source":["# 陣列中有複數，所以回傳 False\n","np.isrealobj(b)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["False"]},"metadata":{"tags":[]},"execution_count":18}]},{"cell_type":"code","metadata":{"id":"TasEu-YwaMm5","outputId":"68dc1ddd-d431-40ea-d588-565b4d20f283"},"source":["# 陣列中全部是實數\n","np.isrealobj(np.array([1, 2.0, 3.1]))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":19}]},{"cell_type":"markdown","metadata":{"id":"6Gjo-MAZaMm6"},"source":["## 3. 比較\n","\n"]},{"cell_type":"markdown","metadata":{"id":"AdwF2n4IaMm6"},"source":["## 3.1 比較 2 個陣列是否相同：`np.array_equal()`、`np.array_equiv()`\n","\n","|函式|說明|\n","|---|---|\n","|np.array_equal()|若兩個陣列形狀與元素值均相同，回傳 True|\n","|np.array_equiv()|兩個陣列形狀元素值均相同，回傳 True；<br />如果兩個陣列維度不同的話，須符合廣播規則，且元素值均相同，則回傳 True|\n","\n","兩個函式不同之處在於 `array_equal()` 需要形狀完全一樣且元素值皆相同才為 True。"]},{"cell_type":"code","metadata":{"id":"kSV5OgAHaMm6","outputId":"351866de-79f1-4bee-dd46-ab18505a2c6c"},"source":["np.array_equal(np.array([1, 2, 3]), np.array([1, 2, 3]))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":20}]},{"cell_type":"code","metadata":{"id":"lpRh2syAaMm7","outputId":"ea878e1b-e8ea-4bab-a40f-0667a70fa64a"},"source":["np.array_equal(np.array([1, 2, 3]), np.array([1, 2, 5]))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["False"]},"metadata":{"tags":[]},"execution_count":21}]},{"cell_type":"markdown","metadata":{"id":"tBCAQ0vwaMm8"},"source":["下列 3 個 `array_equiv()` 範例均回傳 True。"]},{"cell_type":"code","metadata":{"id":"TcA7pap4aMm9","outputId":"2d94e6f3-b6d7-4bf6-bfa0-d76b331e27bb"},"source":["np.array_equiv(np.array([1, 2, 3]), np.array([1, 2, 3]))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":22}]},{"cell_type":"code","metadata":{"id":"d6N1M31vaMm-","outputId":"ab3ad993-7e98-4a80-a1d7-6e23d400454d"},"source":["np.array_equiv(np.array([1, 2, 3]), np.array([[1, 2, 3], [1, 2, 3]]))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":23}]},{"cell_type":"code","metadata":{"id":"O_1zaDdsaMm-","outputId":"78b4af2e-49d4-4c1c-f932-715154c2a55b"},"source":["np.array_equiv(np.array([1, 1, 1]), np.array([1]))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":24}]},{"cell_type":"markdown","metadata":{"id":"lT2Udi0QaMm_"},"source":["## 3.2 比較：等於/不等於、大於/大於或等於、小於/小於或等於\n","\n","|函式|說明|\n","|---|---|\n","|np.equal()|等於|\n","|np.not_equal()|不等於|\n","|np.greater()|大於|\n","|np.greater_equal()|大於或等於|\n","|np.less()|小於|\n","|np.less_equal()|小於或等於|\n","\n","上列的函式均可以比較兩個形狀相同的陣列，或是比較符合廣播規則的兩個陣列，若元素值相同的話就回傳 True。比較時均是 element-wise 的比較。"]},{"cell_type":"code","metadata":{"id":"rUsQ7QR0aMm_","outputId":"3f8e773b-9b8f-442f-b907-2d1a6b022ae2"},"source":["# 形狀與元素值均相同\n","np.equal(np.array([1, 2, 3]), np.array([1, 2, 3]))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ True,  True,  True])"]},"metadata":{"tags":[]},"execution_count":25}]},{"cell_type":"code","metadata":{"id":"rH4WGCTAaMm_","outputId":"f0f1f79a-b279-4b78-b620-a6bd5d255ff4"},"source":["# 符合廣播規則的相等\n","np.equal(np.array([1, 1, 1]), np.ones(1))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ True,  True,  True])"]},"metadata":{"tags":[]},"execution_count":26}]},{"cell_type":"code","metadata":{"id":"E839VHyDaMnC","outputId":"f57901c3-243a-4419-c0f0-9efface8a0fc"},"source":["# 不等於的比較，符合廣播規則\n","np.not_equal([1, 2], [[1, 3],[1, 4]])"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[False,  True],\n","       [False,  True]])"]},"metadata":{"tags":[]},"execution_count":27}]},{"cell_type":"markdown","metadata":{"id":"xiKwVehjaMnE"},"source":["## 4. 邏輯操作\n","\n","邏輯比較函式都是 element-wise，比較 2 個陣列元素。如果 2 個陣列的形狀不同的話，必須符合廣播 (broadcasting) 規則。\n","\n","|Logical operation|函式|\n","|---|---|\n","|AND|np.logical_and()|\n","|OR|np.logical_or()|\n","|NOT|np.logical_not()|\n","|XOR|np.logical_xor()|"]},{"cell_type":"code","metadata":{"id":"0YAHVq3uaMnG"},"source":["x = np.array([True, True, False, False])\n","y = np.array([True, False, True, False])"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"eqTbemVmaMnH","outputId":"f5f73338-1092-47d5-ca18-ba5e13594ad0"},"source":["np.logical_and(x, y)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ True, False, False, False])"]},"metadata":{"tags":[]},"execution_count":29}]},{"cell_type":"code","metadata":{"id":"vz_SVirHaMnI","outputId":"7201b55a-9c80-41ce-d612-898b1c407d1c"},"source":["np.logical_or(x, y)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ True,  True,  True, False])"]},"metadata":{"tags":[]},"execution_count":30}]},{"cell_type":"code","metadata":{"id":"7kygOOoHaMnJ","outputId":"061c788f-45da-4134-d6ba-9c66ee4a79b3"},"source":["np.logical_not(x)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([False, False,  True,  True])"]},"metadata":{"tags":[]},"execution_count":31}]},{"cell_type":"code","metadata":{"id":"gAkOlq_ZaMnK","outputId":"26ff2cdf-1b5a-4d28-c29b-07bc71fb1435"},"source":["np.logical_xor(x, y)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([False,  True,  True, False])"]},"metadata":{"tags":[]},"execution_count":32}]},{"cell_type":"markdown","metadata":{"id":"sS0mDQwHaMnL"},"source":["下面範例是透過廣播產生符合條件的 2 個 True/False 陣列，並且進行 logical AND 操作。"]},{"cell_type":"code","metadata":{"id":"7jtFjOv6aMnL","outputId":"413439f0-642e-41a9-994f-1667132d546c"},"source":["a = np.arange(5)\n","a"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([0, 1, 2, 3, 4])"]},"metadata":{"tags":[]},"execution_count":33}]},{"cell_type":"code","metadata":{"id":"2gKx8OfOaMny","outputId":"00301dd7-462d-4997-9ae1-49c336ae100f"},"source":["np.logical_and(a > 1, a < 4)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([False, False,  True,  True, False])"]},"metadata":{"tags":[]},"execution_count":34}]},{"cell_type":"markdown","metadata":{"id":"xyTwWSjMaMny"},"source":["## 5. `np.all()`、`np.any()`\n","\n","針對軸 (axis) 進行比較，兩個函式不同的地方在於 `np.all()` 是 AND 邏輯的比較，而 `np.any()` 是 OR 邏輯的比較。\n","\n","以下的值均認定為非 0，也就是屬於 True：True、NaN、正無限值、負無限值"]},{"cell_type":"code","metadata":{"id":"JIZVIiqtaMnz","outputId":"d1299ba8-f41f-41c2-fb4a-27a1c35eaf34"},"source":["np.all([-1, np.nan, 5])"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":35}]},{"cell_type":"code","metadata":{"id":"C2yNfNbgaMnz","outputId":"7b250a7e-186c-4fbb-c363-6bdad7bafe47"},"source":["np.all([-1, 4, 0])"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["False"]},"metadata":{"tags":[]},"execution_count":36}]},{"cell_type":"code","metadata":{"id":"CtsCC8JsaMnz","outputId":"9f0de446-5ac3-4c47-a8fb-54bab7b104b5"},"source":["np.any([[True, False], [True, True]])"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["True"]},"metadata":{"tags":[]},"execution_count":37}]},{"cell_type":"code","metadata":{"id":"lM5zmutdaMn5","outputId":"4676503a-8631-4b70-d776-d39b3b741ac4"},"source":["np.any([[True, False], [False, False]], axis=0)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ True, False])"]},"metadata":{"tags":[]},"execution_count":38}]},{"cell_type":"code","metadata":{"id":"tJ9zl9CZaMn7"},"source":[""],"execution_count":null,"outputs":[]}]}