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+# Memory layout of the Numpy matrices
+{:.no_toc}
 
+<nav markdown="1" class="toc-class">
+* TOC
+{:toc}
+</nav>
+
+## The goal
+
+More information about the Numpy matrices and the memory structure behind it. 
+
+Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
+
+
+
+## [Memory layouts​ (row-major vs column-major)](https://en.wikipedia.org/wiki/Row-_and_column-major_order)
+
+C order (or row-major)
+
+> In row-major order, the last dimension is contiguous, so that the memory-offset of this element is given by:
 
 $$ n_{d}+N_{d}\cdot (n_{d-1}+N_{d-1}\cdot (n_{d-2}+N_{d-2}\cdot (\cdots +N_{2}n_{1})\cdots )))=\sum _{k=1}^{d}\left(\prod _{\ell =k+1}^{d}N_{\ell }\right)n_{k} $$
 
-$$ n_{1}+N_{1}\cdot (n_{2}+N_{2}\cdot (n_{3}+N_{3}\cdot (\cdots +N_{d-1}n_{d})\cdots )))=\sum _{k=1}^{d}\left(\prod _{\ell =1}^{k-1}N_{\ell }\right)n_{k} $$
 
+Fortran (or column-major)
+
+> In column-major order, the first dimension is contiguous, so that the memory-offset of this element is given by:
+
+$$ n_{1}+N_{1}\cdot (n_{2}+N_{2}\cdot (n_{3}+N_{3}\cdot (\cdots +N_{d-1}n_{d})\cdots )))=\sum _{k=1}^{d}\left(\prod _{\ell =1}^{k-1}N_{\ell }\right)n_{k} $$
 
 
 ![Row_and_column_major_order.svg](Row_and_column_major_order.svg)
 
 [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)
 
+## Information about the inner-workings of the matrix
+
+### [numpy.ndarray.flags](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flags.html)
+
+```python
+ndarray.flags
+```
+
+> Information about the memory layout of the array.
+
+
+Attributes:
+
+|||
+|---|---|
+|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
+
+```python
+import numpy as np
+
+a = np.zeros((1, 2))
+print(a.flags)
+```
+
+Output
+
+```python
+  C_CONTIGUOUS : True
+  F_CONTIGUOUS : True
+  OWNDATA : True
+  WRITEABLE : True
+  ALIGNED : True
+  WRITEBACKIFCOPY : False
+```
+
+#### 2d
+
+```python
+import numpy as np
+
+a = np.zeros((2, 2))
+print(a.flags)
+```
+
+Output
+
+```python
+  C_CONTIGUOUS : True
+  F_CONTIGUOUS : False
+  OWNDATA : True
+  WRITEABLE : True
+  ALIGNED : True
+  WRITEBACKIFCOPY : False
+```