141 lines
4.1 KiB
Markdown
141 lines
4.1 KiB
Markdown
# Memory layout of Numpy matrices
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{:.no_toc}
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<nav markdown="1" class="toc-class">
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* TOC
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{:toc}
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</nav>
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## The goal
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More information about the Numpy matrices and the memory structure behind it.
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Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
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## [Memory layouts (row-major vs column-major)](https://en.wikipedia.org/wiki/Row-_and_column-major_order)
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C order (or row-major)
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> In row-major order, the last dimension is contiguous, so that the memory-offset of this element is given by:
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$$ n_{d}+N_{d}\cdot (n_{d-1}+N_{d-1}\cdot (n_{d-2}+N_{d-2}\cdot (\cdots +N_{2}n_{1})\cdots )))=\sum _{k=1}^{d}\left(\prod _{\ell =k+1}^{d}N_{\ell }\right)n_{k} $$
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Fortran (or column-major)
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> In column-major order, the first dimension is contiguous, so that the memory-offset of this element is given by:
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$$ n_{1}+N_{1}\cdot (n_{2}+N_{2}\cdot (n_{3}+N_{3}\cdot (\cdots +N_{d-1}n_{d})\cdots )))=\sum _{k=1}^{d}\left(\prod _{\ell =1}^{k-1}N_{\ell }\right)n_{k} $$
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[Illustration of difference between row- and column-major ordering](https://en.wikipedia.org/wiki/Row-_and_column-major_order#/media/File:Row_and_column_major_order.svg) (by CMG Lee. CC BY-SA 4.0)
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## [numpy.ndarray.flags](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flags.html)
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```python
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ndarray.flags
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```
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> Information about the memory layout of the array.
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Attributes:
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|C_CONTIGUOUS (C)|The data is in a single, C-style contiguous segment.|
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|F_CONTIGUOUS (F)|The data is in a single, Fortran-style contiguous segment.|
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|OWNDATA (O)|The array owns the memory it uses or borrows it from another object.|
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|WRITEABLE (W)| The data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception.|
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|ALIGNED (A)|The data and all elements are aligned appropriately for the hardware.|
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|WRITEBACKIFCOPY (X)|This array is a copy of some other array. The C-API function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.|
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|FNC|F_CONTIGUOUS and not C_CONTIGUOUS.|
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|FORC|F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).|
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|BEHAVED (B)|ALIGNED and WRITEABLE.|
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|CARRAY (CA)|BEHAVED and C_CONTIGUOUS.|
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|FARRAY (FA)|BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.|
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### 1d
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```python
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import numpy as np
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a = np.zeros((1, 2))
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print(a.flags)
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```
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Output
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```python
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C_CONTIGUOUS : True
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F_CONTIGUOUS : True
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OWNDATA : True
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WRITEABLE : True
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ALIGNED : True
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WRITEBACKIFCOPY : False
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```
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### 2d
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```python
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import numpy as np
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a = np.zeros((2, 2))
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print(a.flags)
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```
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Output
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```python
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C_CONTIGUOUS : True
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F_CONTIGUOUS : False
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OWNDATA : True
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WRITEABLE : True
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ALIGNED : True
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WRITEBACKIFCOPY : False
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```
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## C - contigousness
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There are situations when you need a C_CONTIGUOUS matrix. Examples are PyBind11 and numba.
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```python
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import numpy as np
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a = np.arange(1, 10)
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print(a.flags["C_CONTIGUOUS"]) # -> True
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print(a[::1].flags["C_CONTIGUOUS"]) # -> True
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print(a[::2].flags["C_CONTIGUOUS"]) # -> False
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print(a[::2].copy().flags["C_CONTIGUOUS"]) # -> True
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```
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**You may want to make a copy of B for PyBind11 and numba or...**
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## [numpy.ascontiguousarray](https://numpy.org/doc/stable/reference/generated/numpy.ascontiguousarray.html)
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```python
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numpy.ascontiguousarray(a, dtype=None, *, like=None)
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```
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> Return a contiguous array (ndim >= 1) in memory (C order).
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```python
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import numpy as np
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a = np.arange(1, 10)
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print(a.flags["C_CONTIGUOUS"]) # -> True
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print(a[::2].flags["C_CONTIGUOUS"]) # -> False
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print(np.ascontiguousarray(a[::2]).flags["C_CONTIGUOUS"]) # -> True
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```
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