View source for Memory layout of Numpy matrices

== The goal ==
More information about the Numpy matrices and the memory structure behind it.

Questions to [mailto:davrot@uni-bremen.de David Rotermund]

== [[wikipedia:Row-_and_column-major_order|Memory layouts (row-major vs column-major)]] ==
C order (or row-major)<blockquote>In row-major order, the last dimension is contiguous, so that the memory-offset of this element is given by:</blockquote><math display="block"> 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} </math>

Fortran (or column-major)<blockquote>In column-major order, the first dimension is contiguous, so that the memory-offset of this element is given by:</blockquote><math display="block"> 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} </math><div class="figure">
[[File:2025-10-17 15-34.png]]
</div>[[wikipedia:Row-_and_column-major_order#/media/File:Row_and_column_major_order.svg|Illustration of difference between row- and column-major ordering]] (by CMG Lee. CC BY-SA 4.0)

== [https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flags.html numpy.ndarray.flags] ==
<syntaxhighlight lang="python">ndarray.flags</syntaxhighlight><blockquote>Information about the memory layout of the array.</blockquote>Attributes:
{| class="wikitable"
|C_CONTIGUOUS (C)
|The data is in a single, C-style contiguous segment.
|-
|F_CONTIGUOUS (F)
|The data is in a single, Fortran-style contiguous segment.
|-
|OWNDATA (O)
|The array owns the memory it uses or borrows it from another object.
|-
|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.
|-
|ALIGNED (A)
|The data and all elements are aligned appropriately for the hardware.
|-
|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.
|-
|FNC
|F_CONTIGUOUS and not C_CONTIGUOUS.
|-
|FORC
|F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).
|-
|BEHAVED (B)
|ALIGNED and WRITEABLE.
|-
|CARRAY (CA)
|BEHAVED and C_CONTIGUOUS.
|-
|FARRAY (FA)
|BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
|}

=== 1d ===
<syntaxhighlight lang="python">import numpy as np

a = np.zeros((1, 2))
print(a.flags)</syntaxhighlight>Output<syntaxhighlight lang="python">  C_CONTIGUOUS : True
  F_CONTIGUOUS : True
  OWNDATA : True
  WRITEABLE : True
  ALIGNED : True
  WRITEBACKIFCOPY : False</syntaxhighlight>

=== 2d ===
<syntaxhighlight lang="python">import numpy as np

a = np.zeros((2, 2))
print(a.flags)</syntaxhighlight>Output<syntaxhighlight lang="python">  C_CONTIGUOUS : True
  F_CONTIGUOUS : False
  OWNDATA : True
  WRITEABLE : True
  ALIGNED : True
  WRITEBACKIFCOPY : False</syntaxhighlight>

== C - contigousness ==
There are situations when you need a C_CONTIGUOUS matrix. Examples are PyBind11 and numba.<syntaxhighlight lang="python">import numpy as np

a = np.arange(1, 10)

print(a.flags["C_CONTIGUOUS"])  # -> True

print(a[::1].flags["C_CONTIGUOUS"])  # -> True
print(a[::2].flags["C_CONTIGUOUS"])  # -> False

print(a[::2].copy().flags["C_CONTIGUOUS"])  # -> True</syntaxhighlight>'''You may want to make a copy of B for PyBind11 and numba or…'''

== [https://numpy.org/doc/stable/reference/generated/numpy.ascontiguousarray.html numpy.ascontiguousarray] ==
<syntaxhighlight lang="python">numpy.ascontiguousarray(a, dtype=None, *, like=None)</syntaxhighlight><blockquote>Return a contiguous array (ndim &#x3E;= 1) in memory (C order).</blockquote><syntaxhighlight lang="python">import numpy as np

a = np.arange(1, 10)

print(a.flags["C_CONTIGUOUS"])  # -> True
print(a[::2].flags["C_CONTIGUOUS"])  # -> False
print(np.ascontiguousarray(a[::2]).flags["C_CONTIGUOUS"])  # -> True</syntaxhighlight>