Update README.md

Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>

numpy_mat_files/README.md

@@ -92,4 +92,136 @@ ImportantMessage =
 
     'Hellp world!'
 ```
-### MATLAB == 7.3 format mat files
+
+### MATLAB == 7.3 format mat files (for very big files)
+
+#### Read
+Under Matlab we create another test file
+
+```matlab
+>> A = rand(10,100);
+>> B = rand(5, 10,100);
+>> save -v7.3 Test_3.mat A B
+```
+
+And we can read the data under Python. But be aware that the matrix is in reversed order now. 10x100 -> 100x10 and 5x10x100 -> 100x10x5
+
+```python
+import numpy as np
+import h5py
+
+file_handle = h5py.File("Test_3.mat", "r")
+
+print(file_handle.keys())  # --> <KeysViewHDF5 ['A']>
+
+hdf5_a = file_handle["A"]
+print(hdf5_a)  # --> <HDF5 dataset "A": shape (100, 10), type "<f8">
+a = np.array(hdf5_a)
+print(type(a))  # --> <class 'numpy.ndarray'>
+print(a.dtype)  # --> float64
+print(a.shape)  # --> (100, 10)
+
+hdf5_b = file_handle["B"]
+print(hdf5_b)  # --> <HDF5 dataset "B": shape (100, 10), type "<f8">
+b = np.array(hdf5_b)
+print(type(b))  # --> <class 'numpy.ndarray'>
+print(b.dtype)  # --> float64
+print(b.shape)  # --> (100, 10, 5)
+
+file_handle.close() #  optional
+```
+
+Note: If you -- in a real world example -- see a HDF5 group (e.g. <HDF5 group "/#refs#" (16 members)> ) instead of a HDF5 dataset then the variable is a container again (very similar to file_handle in the example). It will have keys and you can go down the tree until you find the HDF5 datasets. Especially in the case of Matlab structures you might need to go deeper. 
+
+#### Write
+
+Under Python we generate a .hd5 file:
+
+```python
+import numpy as np
+import h5py
+
+myrng = np.random.default_rng()
+
+a: np.ndarray = myrng.random((10, 100), dtype=np.float64)
+b: np.ndarray = myrng.random((2, 20, 200), dtype=np.float64)
+
+file_handle = h5py.File("Test_4.hd5", "w")
+
+dataset_a = file_handle.create_dataset("A", data=a)
+dataset_b = file_handle.create_dataset("B", data=b)
+file_handle.close() # optional
+```
+
+Under Matlab we now can extract information about the hd5 file:
+
+```matlab
+>> info = h5info('Test_4.hd5');
+>> length(info.Datasets)
+
+ans =
+
+     2
+
+>> info.Datasets(1)
+
+ans = 
+
+  struct with fields:
+
+          Name: 'A'
+      Datatype: [1x1 struct]
+     Dataspace: [1x1 struct]
+     ChunkSize: []
+     FillValue: 0
+       Filters: []
+    Attributes: []
+
+>> info.Datasets(2)
+
+ans = 
+
+  struct with fields:
+
+          Name: 'B'
+      Datatype: [1x1 struct]
+     Dataspace: [1x1 struct]
+     ChunkSize: []
+     FillValue: 0
+       Filters: []
+    Attributes: []
+```
+
+And now we read it in under Matlab:
+
+```matlab
+>> h5disp('Test_4.hd5')
+HDF5 Test_4.hd5 
+Group '/' 
+    Dataset 'A' 
+        Size:  100x10
+        MaxSize:  100x10
+        Datatype:   H5T_IEEE_F64LE (double)
+        ChunkSize:  []
+        Filters:  none
+        FillValue:  0.000000
+    Dataset 'B' 
+        Size:  200x20x2
+        MaxSize:  200x20x2
+        Datatype:   H5T_IEEE_F64LE (double)
+        ChunkSize:  []
+        Filters:  none
+        FillValue:  0.000000
+```
+
+Now we know that the databases are at '/A' and '/B'. With information we can read the matrices. But be aware that the matrices are in reversed order!
+
+```matlab
+>> a = h5read('Test_4.hd5','/A');
+>> b = h5read('Test_4.hd5','/B');
+>> whos
+  Name        Size              Bytes  Class     Attributes
+
+  a         100x10               8000  double              
+  b         200x20x2            64000  double
+```