Scipy 是以 Travis Oliphant 於 2006 年撰寫的 Numpy 套件為基礎所發展的 Python 科學計算套件, 2001 年 Travis Oliphant, Pearu Peterson, Eric Jones 等人將 Numpy 與他們所撰寫的程式整合為 SciPy, 並以 BSD 授權開源, 功能包含線性代數, 數值積分, 數值微分, 求矩陣特徵值, 解聯立方程式, 快速傅立葉變換, 統計分析, 影像處理, 數位信號處理, 非監督式機器學習等模組 (監督式是放在 scikit-learn 套件中) 等等. SciPy 裡面的很多底層函數都是用 Fortran 實作的, 因此運算效能優異, 可與 MATLAB 以及 Octave 等商業軟體相匹敵.
參考 :
# Wiki : SciPy
# https://en.wikipedia.org/wiki/SciPy
教學文件參考 :
# https://www.scipy.org/docs.html
# https://docs.scipy.org/doc/scipy/reference/index.html
SciPy 相關書籍參考 :
# SciPy and Numpy (Oreilly, 2013)
# Elegant SciPy: The Art of Scientific Python (Oreilly, 2017)
# Learning SciPy for Numerical and Scientific Computing 2nd Edition (Packt, 2015)
# Numerical Methods in Engineering with Python 3 (Cambridge, 2013)# Numerical Python: Scientific Computing and Data Science Applications With Numpy, Scipy and Matplotlib 2nd Edition (Apress, 2018)
一. 安裝 SciPy :
可在命令列下以 pip 安裝 SciPy (大約 31MB 左右) :
pip3 install scipy
或加 -U 參數更新到最新版 :
pip3 install scipy -U
D:\>pip3 install scipy -U
Collecting scipy
Downloading scipy-1.4.1-cp37-cp37m-win_amd64.whl (30.9 MB)
Requirement already satisfied, skipping upgrade: numpy>=1.13.3 in c:\python37\lib\site-packages (from scipy) (1.16.0)
Installing collected packages: scipy
Attempting uninstall: scipy
Found existing installation: scipy 1.2.0
Uninstalling scipy-1.2.0:
Successfully uninstalled scipy-1.2.0
Successfully installed scipy-1.4.1
因為 SciPy 是以 Numpy 為基礎, 故安裝 SciPy 時會先裝 Numpy.
完成後進入 Python IDLE 介面用 __version__ 屬性檢查 SciPy 版本, 使用前先匯入 scipy 套件 :
D:\>python
Python 3.7.2 (tags/v3.7.2:9a3ffc0492, Dec 23 2018, 23:09:28) [MSC v.1916 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import scipy
>>> scipy.__version__
'1.4.1'
使用 import scipy 方式匯入的話, 使用其屬性或模組時前面都要帶 scipy. 才行, 也可以直接匯入全部 SciPy 模組, 這樣就不需冠上 scipi. 了 (但要注意命名空間汙染問題) :
from scipy import *
>>> from scipy import *
>>> __version__
'1.4.1'
二. SciPy 的模組 :
SciPy 由許多子套件組成, 常用的子套件如下表 :
| SciPy 常用子套件 | 說明 |
| constants | 科學常數 |
| specials | 特殊函數 |
| integrate | 解積分或微分方程式 |
| linalg | 線性代數 |
| stats | 統計函數 |
| fftpack | 快速傅立葉轉換函數 |
| interpolate | 內插平滑函數 |
| optimize | 最佳化與求解函數 |
| sparse | 稀疏矩陣函數 |
| signal | 信號處理 |
SciPy 所有子套件可用 dir() 檢視 :
>>> import scipy
>>> dir(scipy)
['ALLOW_THREADS', 'AxisError', 'BUFSIZE', 'CLIP', 'ComplexWarning', 'DataSource', 'ERR_CALL', 'ERR_DEFAULT', 'ERR_IGNORE', 'ERR_LOG', 'ERR_PRINT', 'ERR_RAISE', 'ERR_WARN', 'FLOATING_POINT_SUPPORT', 'FPE_DIVIDEBYZERO', 'FPE_INVALID', 'FPE_OVERFLOW', 'FPE_UNDERFLOW', 'False_', 'Inf', 'Infinity', 'LowLevelCallable', 'MAXDIMS', 'MAY_SHARE_BOUNDS', 'MAY_SHARE_EXACT', 'MachAr', 'ModuleDeprecationWarning', 'NAN', 'NINF', 'NZERO', 'NaN', 'PINF', 'PZERO', 'RAISE', 'RankWarning', 'SHIFT_DIVIDEBYZERO', 'SHIFT_INVALID', 'SHIFT_OVERFLOW', 'SHIFT_UNDERFLOW', 'ScalarType', 'TooHardError', 'True_', 'UFUNC_BUFSIZE_DEFAULT', 'UFUNC_PYVALS_NAME', 'VisibleDeprecationWarning', 'WRAP', '_UFUNC_API', '__SCIPY_SETUP__', '__all__', '__builtins__', '__cached__', '__config__', '__doc__', '__file__', '__loader__', '__name__', '__numpy_version__', '__package__', '__path__', '__spec__', '__version__', '_add_newdoc_ufunc', '_arg', '_dep_fft', '_deprecated', '_distributor_init', '_fun', '_key', '_lib', '_msg', '_sci', 'absolute', 'absolute_import', 'add', 'add_docstring', 'add_newdoc', 'add_newdoc_ufunc', 'alen', 'all', 'allclose', 'alltrue', 'amax', 'amin', 'angle', 'any', 'append', 'apply_along_axis', 'apply_over_axes', 'arange', 'arccos', 'arccosh', 'arcsin', 'arcsinh', 'arctan', 'arctan2', 'arctanh', 'argmax', 'argmin', 'argpartition', 'argsort', 'argwhere', 'around', 'array', 'array2string', 'array_equal', 'array_equiv', 'array_repr', 'array_split', 'array_str', 'asanyarray', 'asarray', 'asarray_chkfinite', 'ascontiguousarray', 'asfarray', 'asfortranarray', 'asmatrix', 'asscalar', 'atleast_1d', 'atleast_2d', 'atleast_3d', 'average', 'bartlett', 'base_repr', 'binary_repr', 'bincount', 'bitwise_and', 'bitwise_not', 'bitwise_or', 'bitwise_xor', 'blackman', 'block', 'bmat', 'bool8', 'bool_', 'broadcast', 'broadcast_arrays', 'broadcast_to', 'busday_count', 'busday_offset', 'busdaycalendar', 'byte', 'byte_bounds', 'bytes0', 'bytes_', 'c_', 'can_cast', 'cast', 'cbrt', 'cdouble', 'ceil', 'cfloat', 'char', 'character', 'chararray', 'choose', 'clip', 'clongdouble', 'clongfloat', 'column_stack', 'common_type', 'compare_chararrays', 'complex128', 'complex64', 'complex_', 'complexfloating', 'compress', 'concatenate', 'conj', 'conjugate', 'convolve', 'copy', 'copysign', 'copyto', 'corrcoef', 'correlate', 'cos', 'cosh', 'count_nonzero', 'cov', 'cross', 'csingle', 'ctypeslib', 'cumprod', 'cumproduct', 'cumsum', 'datetime64', 'datetime_as_string', 'datetime_data', 'deg2rad', 'degrees', 'delete', 'deprecate', 'deprecate_with_doc', 'diag', 'diag_indices', 'diag_indices_from', 'diagflat', 'diagonal', 'diff', 'digitize', 'disp', 'divide', 'division', 'divmod', 'dot', 'double', 'dsplit', 'dstack', 'dtype', 'e', 'ediff1d', 'einsum', 'einsum_path', 'emath', 'empty', 'empty_like', 'equal', 'errstate', 'euler_gamma', 'exp', 'exp2', 'expand_dims', 'expm1', 'extract', 'eye', 'fabs', 'fastCopyAndTranspose', 'fft', 'fft_msg', 'fill_diagonal', 'find_common_type', 'finfo', 'fix', 'flatiter', 'flatnonzero', 'flexible', 'flip', 'fliplr', 'flipud', 'float16', 'float32', 'float64', 'float_', 'float_power', 'floating', 'floor', 'floor_divide', 'fmax', 'fmin', 'fmod', 'format_float_positional', 'format_float_scientific', 'format_parser', 'frexp', 'frombuffer', 'fromfile', 'fromfunction', 'fromiter', 'frompyfunc', 'fromregex', 'fromstring', 'full', 'full_like', 'fv', 'gcd', 'generic', 'genfromtxt', 'geomspace', 'get_array_wrap', 'get_include', 'get_printoptions', 'getbufsize', 'geterr', 'geterrcall', 'geterrobj', 'gradient', 'greater', 'greater_equal', 'half', 'hamming', 'hanning', 'heaviside', 'histogram', 'histogram2d', 'histogram_bin_edges', 'histogramdd', 'hsplit', 'hstack', 'hypot', 'i0', 'identity', 'ifft', 'iinfo', 'imag', 'in1d', 'index_exp', 'indices', 'inexact', 'inf', 'info', 'infty', 'inner', 'insert', 'int0', 'int16', 'int32', 'int64', 'int8', 'int_', 'int_asbuffer', 'intc', 'integer', 'interp', 'intersect1d', 'intp', 'invert', 'ipmt', 'irr', 'is_busday', 'isclose', 'iscomplex', 'iscomplexobj', 'isfinite', 'isfortran', 'isin', 'isinf', 'isnan', 'isnat', 'isneginf', 'isposinf', 'isreal', 'isrealobj', 'isscalar', 'issctype', 'issubclass_', 'issubdtype', 'issubsctype', 'iterable', 'ix_', 'kaiser', 'kron', 'lcm', 'ldexp', 'left_shift', 'less', 'less_equal', 'lexsort', 'linspace', 'little_endian', 'load', 'loads', 'loadtxt', 'log', 'log10', 'log1p', 'log2', 'logaddexp', 'logaddexp2', 'logical_and', 'logical_not', 'logical_or', 'logical_xor', 'logn', 'logspace', 'long', 'longcomplex', 'longdouble', 'longfloat', 'longlong', 'lookfor', 'ma', 'mafromtxt', 'mask_indices', 'mat', 'math', 'matmul', 'matrix', 'maximum', 'maximum_sctype', 'may_share_memory', 'mean', 'median', 'memmap', 'meshgrid', 'mgrid', 'min_scalar_type', 'minimum', 'mintypecode', 'mirr', 'mod', 'modf', 'moveaxis', 'msort', 'multiply', 'nan', 'nan_to_num', 'nanargmax', 'nanargmin', 'nancumprod', 'nancumsum', 'nanmax', 'nanmean', 'nanmedian', 'nanmin', 'nanpercentile', 'nanprod', 'nanquantile', 'nanstd', 'nansum', 'nanvar', 'nbytes', 'ndarray', 'ndenumerate', 'ndfromtxt', 'ndim', 'ndindex', 'nditer', 'negative', 'nested_iters', 'newaxis', 'nextafter', 'nonzero', 'not_equal', 'nper', 'npv', 'number', 'obj2sctype', 'object0', 'object_', 'ogrid', 'ones', 'ones_like', 'outer', 'packbits', 'pad', 'partition', 'percentile', 'pi', 'piecewise', 'place', 'pmt', 'poly', 'poly1d', 'polyadd', 'polyder', 'polydiv', 'polyfit', 'polyint', 'polymul', 'polysub', 'polyval', 'positive', 'power', 'ppmt', 'print_function', 'printoptions', 'prod', 'product', 'promote_types', 'ptp', 'put', 'put_along_axis', 'putmask', 'pv', 'quantile', 'r_', 'rad2deg', 'radians', 'rand', 'randn', 'random', 'rank', 'rate', 'ravel', 'ravel_multi_index', 'real', 'real_if_close', 'rec', 'recarray', 'recfromcsv', 'recfromtxt', 'reciprocal', 'record', 'remainder', 'repeat', 'require', 'reshape', 'resize', 'result_type', 'right_shift', 'rint', 'roll', 'rollaxis', 'roots', 'rot90', 'round_', 'row_stack', 's_', 'safe_eval', 'save', 'savetxt', 'savez', 'savez_compressed', 'sctype2char', 'sctypeDict', 'sctypeNA', 'sctypes', 'searchsorted', 'select', 'set_numeric_ops', 'set_printoptions', 'set_string_function', 'setbufsize', 'setdiff1d', 'seterr', 'seterrcall', 'seterrobj', 'setxor1d', 'shape', 'shares_memory', 'short', 'show_config', 'show_numpy_config', 'sign', 'signbit', 'signedinteger', 'sin', 'sinc', 'single', 'singlecomplex', 'sinh', 'size', 'sometrue', 'sort', 'sort_complex', 'source', 'spacing', 'split', 'sqrt', 'square', 'squeeze', 'stack', 'std', 'str0', 'str_', 'string_', 'subtract', 'sum', 'swapaxes', 'take', 'take_along_axis', 'tan', 'tanh', 'tensordot', 'test', 'tile', 'timedelta64', 'trace', 'tracemalloc_domain', 'transpose', 'trapz', 'tri', 'tril', 'tril_indices', 'tril_indices_from', 'trim_zeros', 'triu', 'triu_indices', 'triu_indices_from', 'true_divide', 'trunc', 'typeDict', 'typeNA', 'typecodes', 'typename', 'ubyte', 'ufunc', 'uint', 'uint0', 'uint16', 'uint32', 'uint64', 'uint8', 'uintc', 'uintp', 'ulonglong', 'unicode', 'unicode_', 'union1d', 'unique', 'unpackbits', 'unravel_index', 'unsignedinteger', 'unwrap', 'ushort', 'vander', 'var', 'vdot', 'vectorize', 'version', 'void', 'void0', 'vsplit', 'vstack', 'where', 'who', 'zeros', 'zeros_like']
可用 help() 查詢各子套件之說明資訊 :
>>> import scipy
>>> help(scipy.log)
Help on function log in module numpy.lib.scimath:
log(x)
scipy.log is deprecated and will be removed in SciPy 2.0.0, use numpy.lib.scimath.log instead
三. SciPy 的科學常數 :
SciPy 內建了一個 constants 子套件, 提供科學計算所需要的數學與自然常數, 且具有單位轉換功能. 用 dir() 可顯示 constants 子套件內容, 不過因為 constants 是子套件, 不是 scipy 的屬性, 所以 import scripy 後用 dir() 函數顯示 scipy.constants 會找不到 :
>>> import scipy
>>> dir(scipy.constants)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
AttributeError: module 'scipy' has no attribute 'constants'
要用 from scipy import constants 匯入 constants 子套件才行 :
>>> from scipy import constants
>>> dir(constants)
['Avogadro', 'Boltzmann', 'Btu', 'Btu_IT', 'Btu_th', 'ConstantWarning', 'G', 'Julian_year', 'N_A', 'Planck', 'R', 'Rydberg', 'Stefan_Boltzmann', 'Wien', '__all__', '__builtins__', '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__path__', '__spec__', '_obsolete_constants', 'absolute_import', 'acre', 'alpha', 'angstrom', 'arcmin', 'arcminute', 'arcsec', 'arcsecond', 'astronomical_unit', 'atm', 'atmosphere', 'atomic_mass', 'atto', 'au', 'bar', 'barrel', 'bbl', 'blob', 'c', 'calorie', 'calorie_IT', 'calorie_th', 'carat', 'centi', 'codata', 'constants', 'convert_temperature', 'day', 'deci', 'degree', 'degree_Fahrenheit', 'deka', 'division', 'dyn', 'dyne', 'e', 'eV', 'electron_mass', 'electron_volt', 'elementary_charge', 'epsilon_0', 'erg', 'exa', 'exbi', 'femto', 'fermi', 'find', 'fine_structure', 'fluid_ounce', 'fluid_ounce_US', 'fluid_ounce_imp', 'foot', 'g', 'gallon', 'gallon_US', 'gallon_imp', 'gas_constant', 'gibi', 'giga', 'golden', 'golden_ratio', 'grain', 'gram', 'gravitational_constant', 'h', 'hbar', 'hectare', 'hecto', 'horsepower', 'hour', 'hp', 'inch', 'k', 'kgf', 'kibi', 'kilo', 'kilogram_force', 'kmh', 'knot', 'lambda2nu', 'lb', 'lbf', 'light_year', 'liter', 'litre', 'long_ton', 'm_e', 'm_n', 'm_p', 'm_u', 'mach', 'mebi', 'mega', 'metric_ton', 'micro', 'micron', 'mil', 'mile', 'milli', 'minute', 'mmHg', 'mph', 'mu_0', 'nano', 'nautical_mile', 'neutron_mass', 'nu2lambda', 'ounce', 'oz', 'parsec', 'pebi', 'peta', 'physical_constants', 'pi', 'pico', 'point', 'pound', 'pound_force', 'precision', 'print_function', 'proton_mass', 'psi', 'pt', 'short_ton', 'sigma', 'slinch', 'slug', 'speed_of_light', 'speed_of_sound', 'stone', 'survey_foot', 'survey_mile', 'tebi', 'tera', 'test', 'ton_TNT', 'torr', 'troy_ounce', 'troy_pound', 'u', 'unit', 'value', 'week', 'yard', 'year', 'yobi', 'yotta', 'zebi', 'zepto', 'zero_Celsius', 'zetta']
這些都是 constants 的成員, 可直接用屬性取得其值, 以下是數學常數 :
>>> constants.pi #圓周率
3.141592653589793
>>> constants.golden_ratio #黃金比率 (同 golden)
1.618033988749895
>>> constants.golden #黃金比率
1.618033988749895
以下是物理常數 :
>>> constants.c #光速
299792458.0
>>> constants.speed_of_light #光速
299792458.0
>>> constants.speed_of_sound #音速
340.5
>>> constants.Planck #普郎克常數 (同 h)
6.62607015e-34
>>> constants.h #普郎克常數 (焦耳秒)
6.62607015e-34
>>> constants.Avogadro #亞佛加厥常數 (同 N_A)
6.02214076e+23
>>> constants.N_A #亞佛加厥常數 (莫耳 mol)
6.02214076e+23
>>> constants.Boltzmann #波茲曼常數 (同 k)
1.380649e-23
>>> constants.k #波茲曼常數 (J/K)
1.380649e-23
>>> constants.gravitational_constant #重力常數
6.6743e-11
>>> constants.gas_constant #氣體常數 (同 R)
8.314462618
>>> constants.R #氣體常數
8.314462618
>>> constants.G #牛頓重力常數 (m3*kg**(-1)s**(-2))
6.6743e-11
>>> constants.g #標準重力加速度 (m*s**(2))
9.80665
>>> constants.elementary_charge #電荷電量 (庫倫, 同 e)
1.602176634e-19
>>> constants.e #電荷電量 (庫倫)
1.602176634e-19
>>> constants.m_e #電子質量 (公斤)
9.1093837015e-31
>>> constants.electron_mass #電子質量 (公斤, 同 m_e)
9.1093837015e-31
>>> constants.m_p #質子質量 (公斤)
1.67262192369e-27
>>> constants.proton_mass #質子質量 (公斤, 同 m_p)
1.67262192369e-27
>>> constants.m_n #中子質量 (公斤)
1.67492749804e-27
>>> constants.neutron_mass #中子質量 (公斤, 同 m_n)
1.67492749804e-27
>>> constants.mu_0 #真空磁導率 (亨利/米)
1.2566370614359173e-06
>>> constants.epsilon_0 #真空電容率 (法拉/米)
8.854187817620389e-12
>>> constants.Wien #維恩位移常數 (mK) : 黑體輻射波長與溫度關係
0.002897771955
>>> constants.Rydberg #芮德柏常數 (1/m)
10973731.56816
注意, 如果用人名, 第一個字母均大寫, 例如波茲曼常數要用 Boltzmann.
完整的常數參見 :
# https://docs.scipy.org/doc/scipy/reference/constants.html
Thank you, Sir. This is just my learning notebook. I will be glad if it can help. Thanks a lot for your note.
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