Guide to NumPy - SciPy
Guide to NumPy
Travis E. Oliphant, PhD Dec 7, 2006
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Contents
I NumPy from Python
12
1 Origins of NumPy
13
2 Object Essentials
18
2.1 Data-Type Descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Basic indexing (slicing) . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Memory Layout of ndarray . . . . . . . . . . . . . . . . . . . . . . 26
2.3.1 Contiguous Memory Layout . . . . . . . . . . . . . . . . . . . 26
2.3.2 Non-contiguous memory layout . . . . . . . . . . . . . . . . . 28
2.4 Universal Functions for arrays . . . . . . . . . . . . . . . . . . . . . . 30
2.5 Summary of new features . . . . . . . . . . . . . . . . . . . . . . . . 32
2.6 Summary of differences with Numeric . . . . . . . . . . . . . . . . . 34
2.6.1 First-step changes . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6.2 Second-step changes . . . . . . . . . . . . . . . . . . . . . . . 37
2.6.3 Updating code that uses Numeric using alter codeN . . . . . 38
2.6.4 Changes to think about . . . . . . . . . . . . . . . . . . . . . 39
2.7 Summary of differences with Numarray . . . . . . . . . . . . . . . . 40
2.7.1 First-step changes . . . . . . . . . . . . . . . . . . . . . . . . 41
2.7.1.1 Import changes . . . . . . . . . . . . . . . . . . . . . 41
2.7.1.2 Attribute and method changes . . . . . . . . . . . . 42
2.7.2 Second-step changes . . . . . . . . . . . . . . . . . . . . . . . 43
2.7.3 Additional Extension modules . . . . . . . . . . . . . . . . . . 43
3 The Array Object
45
3.1 ndarray Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1.1 Memory Layout attributes . . . . . . . . . . . . . . . . . . . . 45
3.1.2 Data Type attributes . . . . . . . . . . . . . . . . . . . . . . 49
2
3.1.3 Other attributes . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.1.4 Array Interface attributes . . . . . . . . . . . . . . . . . . . . 52 3.2 ndarray Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.2.1 Array conversion . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.2.2 Array shape manipulation . . . . . . . . . . . . . . . . . . . . 59 3.2.3 Array item selection and manipulation . . . . . . . . . . . . . 61 3.2.4 Array calculation . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3 Array Special Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3.1 Methods for standard library functions . . . . . . . . . . . . . 71 3.3.2 Basic customization . . . . . . . . . . . . . . . . . . . . . . . 72 3.3.3 Container customization . . . . . . . . . . . . . . . . . . . . . 74 3.3.4 Arithmetic customization . . . . . . . . . . . . . . . . . . . . 75
3.3.4.1 Binary . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.3.4.2 In-place . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.3.4.3 Unary operations . . . . . . . . . . . . . . . . . . . 78 3.4 Array indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4.1 Basic Slicing . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4.2 Advanced selection . . . . . . . . . . . . . . . . . . . . . . . . 81 3.4.2.1 Integer . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.4.2.2 Boolean . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.4.3 Flat Iterator indexing . . . . . . . . . . . . . . . . . . . . . . 84
4 Basic Routines
85
4.1 Creating arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.2 Operations on two or more arrays . . . . . . . . . . . . . . . . . . . . 90
4.3 Printing arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.4 Functions redundant with methods . . . . . . . . . . . . . . . . . . 94
4.5 Dealing with data types . . . . . . . . . . . . . . . . . . . . . . . . . 94
5 Additional Convenience Routines
96
5.1 Shape functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2 Basic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.3 Polynomial functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.4 Set Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.5 Array construction using index tricks . . . . . . . . . . . . . . . . . . 112
5.6 Other indexing devices . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.7 Two-dimensional functions . . . . . . . . . . . . . . . . . . . . . . . . 116
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5.8 More data type functions . . . . . . . . . . . . . . . . . . . . . . . . 118 5.9 Functions that behave like ufuncs . . . . . . . . . . . . . . . . . . . . 121 5.10 Miscellaneous Functions . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.11 Utility functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6 Scalar objects
126
6.1 Attributes of array scalars . . . . . . . . . . . . . . . . . . . . . . . . 127
6.2 Methods of array scalars . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.3 Defining New Types . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7 Data-type (dtype) Objects
131
7.1 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.2 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8 Standard Classes
138
8.1 Special attributes and methods recognized by NumPy . . . . . . . . 139
8.2 Matrix Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8.3 Memory-mapped-file arrays . . . . . . . . . . . . . . . . . . . . . . . 142
8.4 Character arrays (numpy.char) . . . . . . . . . . . . . . . . . . . . . 143
8.5 Record Arrays (numpy.rec) . . . . . . . . . . . . . . . . . . . . . . . 144
8.6 Masked Arrays (numpy.ma) . . . . . . . . . . . . . . . . . . . . . . . 148
8.7 Standard container class . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.8 Array Iterators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.8.1 Default iteration . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.8.2 Flat iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.8.3 N-dimensional enumeration . . . . . . . . . . . . . . . . . . . 151
8.8.4 Iterator for broadcasting . . . . . . . . . . . . . . . . . . . . . 151
9 Universal Functions
153
9.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
9.1.1 Broadcasting . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
9.1.2 Output type determination . . . . . . . . . . . . . . . . . . . 154
9.1.3 Use of internal buffers . . . . . . . . . . . . . . . . . . . . . . 155
9.1.4 Error handling . . . . . . . . . . . . . . . . . . . . . . . . . . 155
9.1.5 Optional keyword arguments . . . . . . . . . . . . . . . . . . 156
9.2 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
9.3 Casting Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
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9.4 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 9.4.1 Reduce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 9.4.2 Accumulate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 9.4.3 Reduceat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 9.4.4 Outer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.5 Available ufuncs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 9.5.1 Math operations . . . . . . . . . . . . . . . . . . . . . . . . . 164 9.5.2 Trigonometric functions . . . . . . . . . . . . . . . . . . . . . 167 9.5.3 Bit-twiddling functions . . . . . . . . . . . . . . . . . . . . . . 168 9.5.4 Comparison functions . . . . . . . . . . . . . . . . . . . . . . 169 9.5.5 Floating functions . . . . . . . . . . . . . . . . . . . . . . . . 171
10 Basic Modules
174
10.1 Linear Algebra (linalg) . . . . . . . . . . . . . . . . . . . . . . . . 174
10.2 Discrete Fourier Transforms (fft) . . . . . . . . . . . . . . . . . . . 177
10.3 Random Numbers (random) . . . . . . . . . . . . . . . . . . . . . . 181
10.3.1 Discrete Distributions . . . . . . . . . . . . . . . . . . . . . . 181
10.3.2 Continuous Distributions . . . . . . . . . . . . . . . . . . . . 184
10.3.3 Miscellaneous utilities . . . . . . . . . . . . . . . . . . . . . . 190
10.4 Matrix-specific functions (matlib) . . . . . . . . . . . . . . . . . . . . 191
10.5 Ctypes utiltity functions (ctypeslib) . . . . . . . . . . . . . . . . . . 191
11 Testing and Packaging
192
11.1 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
11.2 NumPy Distutils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
11.2.1 misc util . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
11.2.2 Other modules . . . . . . . . . . . . . . . . . . . . . . . . . . 202
11.3 Conversion of .src files . . . . . . . . . . . . . . . . . . . . . . . . . . 203
11.3.1 Fortran files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
11.3.1.1 Named repeat rule . . . . . . . . . . . . . . . . . . . 204
11.3.1.2 Short repeat rule . . . . . . . . . . . . . . . . . . . . 204
11.3.1.3 Pre-defined names . . . . . . . . . . . . . . . . . . . 204
11.3.2 Other files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
II C-API
206
12 New Python Types and C-Structures
207
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