This is used to profile https://github.com/pygae/galgebra/issues/41 .

The following code uses https://github.com/pygae/galgebra/tree/new_printer .



In [1]:

    
!pip install pyprof2calltree









    



Requirement already satisfied: pyprof2calltree in /Users/utensil/.julia/conda/3/lib/python3.7/site-packages (1.4.4)



In [2]:

    
!brew install qcachegrind









    



Warning: qcachegrind 18.04.3_1 is already installed and up-to-date
To reinstall 18.04.3_1, run `brew reinstall qcachegrind`



In [3]:

    
%%writefile test_41.py
from galgebra.ga import Ga

GA = Ga('e*1|2|3')
a = GA.mv('a', 'vector')
b = GA.mv('b', 'vector')
c = GA.mv('c', 'vector')

def cross(x, y):
    return (x ^ y).dual()

xx = cross(a, cross(b, c))









    



Overwriting test_41.py



In [4]:

    
!python -m cProfile -o test_41.cprof test_41.py



In [5]:

    
!python -m pyprof2calltree -i test_41.cprof -k









    



launching kcachegrind
Selected  "Function cross"
CallGraphView::refresh
CallGraphView::refresh: Starting process 0x7fd353f8f380, 'dot -Tplain'
CallGraphView::readDotOutput: QProcess 0x7fd353f8f380
CallGraphView::dotExited: QProcess 0x7fd353f8f380

With View options set to:

The profiling result is like:



In [6]:

    
%%writefile test_41.py
from galgebra.ga import Ga

GA = Ga('e*1|2|3', norm=False)
a = GA.mv('a', 'vector')
b = GA.mv('b', 'vector')
c = GA.mv('c', 'vector')

def cross(x, y):
    return (x ^ y).dual()

xx = cross(a, cross(b, c))









    



Overwriting test_41.py



In [7]:

    
!python -m cProfile -o test_41.cprof test_41.py



In [8]:

    
!python -m pyprof2calltree -i test_41.cprof -k









    



launching kcachegrind
Selected  "Function cross"
CallGraphView::refresh
CallGraphView::refresh: Starting process 0x7f97aede0940, 'dot -Tplain'
CallGraphView::readDotOutput: QProcess 0x7f97aede0940
CallGraphView::dotExited: QProcess 0x7f97aede0940



In [14]:

    
from galgebra.ga import Ga

GA = Ga('e*1|2|3')
a = GA.mv('a', 'vector')
b = GA.mv('b', 'vector')
c = GA.mv('c', 'vector')

def cross(x, y):
    return (x ^ y).dual()

xx = cross(a, cross(b, c))
xx









    Out[14]:





\begin{equation*} \left ( \left ( e_{1}\cdot e_{2}\right )  a^{1} b^{1} c^{2} - \left ( e_{1}\cdot e_{2}\right )  a^{1} b^{2} c^{1} + \left ( e_{1}\cdot e_{3}\right )  a^{1} b^{1} c^{3} - \left ( e_{1}\cdot e_{3}\right )  a^{1} b^{3} c^{1} + \left ( e_{2}\cdot e_{2}\right )  a^{2} b^{1} c^{2} - \left ( e_{2}\cdot e_{2}\right )  a^{2} b^{2} c^{1} + \left ( e_{2}\cdot e_{3}\right )  a^{2} b^{1} c^{3} - \left ( e_{2}\cdot e_{3}\right )  a^{2} b^{3} c^{1} + \left ( e_{2}\cdot e_{3}\right )  a^{3} b^{1} c^{2} - \left ( e_{2}\cdot e_{3}\right )  a^{3} b^{2} c^{1} + \left ( e_{3}\cdot e_{3}\right )  a^{3} b^{1} c^{3} - \left ( e_{3}\cdot e_{3}\right )  a^{3} b^{3} c^{1}\right ) \boldsymbol{e}_{1} + \left ( - \left ( e_{1}\cdot e_{1}\right )  a^{1} b^{1} c^{2} + \left ( e_{1}\cdot e_{1}\right )  a^{1} b^{2} c^{1} - \left ( e_{1}\cdot e_{2}\right )  a^{2} b^{1} c^{2} + \left ( e_{1}\cdot e_{2}\right )  a^{2} b^{2} c^{1} + \left ( e_{1}\cdot e_{3}\right )  a^{1} b^{2} c^{3} - \left ( e_{1}\cdot e_{3}\right )  a^{1} b^{3} c^{2} - \left ( e_{1}\cdot e_{3}\right )  a^{3} b^{1} c^{2} + \left ( e_{1}\cdot e_{3}\right )  a^{3} b^{2} c^{1} + \left ( e_{2}\cdot e_{3}\right )  a^{2} b^{2} c^{3} - \left ( e_{2}\cdot e_{3}\right )  a^{2} b^{3} c^{2} + \left ( e_{3}\cdot e_{3}\right )  a^{3} b^{2} c^{3} - \left ( e_{3}\cdot e_{3}\right )  a^{3} b^{3} c^{2}\right ) \boldsymbol{e}_{2} + \left ( - \left ( e_{1}\cdot e_{1}\right )  a^{1} b^{1} c^{3} + \left ( e_{1}\cdot e_{1}\right )  a^{1} b^{3} c^{1} - \left ( e_{1}\cdot e_{2}\right )  a^{1} b^{2} c^{3} + \left ( e_{1}\cdot e_{2}\right )  a^{1} b^{3} c^{2} - \left ( e_{1}\cdot e_{2}\right )  a^{2} b^{1} c^{3} + \left ( e_{1}\cdot e_{2}\right )  a^{2} b^{3} c^{1} - \left ( e_{1}\cdot e_{3}\right )  a^{3} b^{1} c^{3} + \left ( e_{1}\cdot e_{3}\right )  a^{3} b^{3} c^{1} - \left ( e_{2}\cdot e_{2}\right )  a^{2} b^{2} c^{3} + \left ( e_{2}\cdot e_{2}\right )  a^{2} b^{3} c^{2} - \left ( e_{2}\cdot e_{3}\right )  a^{3} b^{2} c^{3} + \left ( e_{2}\cdot e_{3}\right )  a^{3} b^{3} c^{2}\right ) \boldsymbol{e}_{3} \end{equation*}



In [15]:

    
GA.E()









    Out[15]:





\begin{equation*}  \boldsymbol{e}_{1}\wedge \boldsymbol{e}_{2}\wedge \boldsymbol{e}_{3} \end{equation*}



In [16]:

    
GA.I()









    Out[16]:





\begin{equation*} \frac{1}{\sqrt{\left ( e_{1}\cdot e_{1}\right )  \left ( e_{2}\cdot e_{2}\right )  \left ( e_{3}\cdot e_{3}\right )  - \left ( e_{1}\cdot e_{1}\right )  \left ( e_{2}\cdot e_{3}\right ) ^{2} - \left ( e_{1}\cdot e_{2}\right ) ^{2} \left ( e_{3}\cdot e_{3}\right )  + 2 \left ( e_{1}\cdot e_{2}\right )  \left ( e_{1}\cdot e_{3}\right )  \left ( e_{2}\cdot e_{3}\right )  - \left ( e_{1}\cdot e_{3}\right ) ^{2} \left ( e_{2}\cdot e_{2}\right ) }} \boldsymbol{e}_{1}\wedge \boldsymbol{e}_{2}\wedge \boldsymbol{e}_{3} \end{equation*}



In [12]:

    
from galgebra.ga import Ga

GA = Ga('e*1|2|3', norm=False)
a = GA.mv('a', 'vector')
b = GA.mv('b', 'vector')
c = GA.mv('c', 'vector')

def cross(x, y):
    return (x ^ y).dual()

xx = cross(a, cross(b, c))
xx









    Out[12]:





\begin{equation*} \left ( \left ( e_{1}\cdot e_{2}\right )  a^{1} b^{1} c^{2} - \left ( e_{1}\cdot e_{2}\right )  a^{1} b^{2} c^{1} + \left ( e_{1}\cdot e_{3}\right )  a^{1} b^{1} c^{3} - \left ( e_{1}\cdot e_{3}\right )  a^{1} b^{3} c^{1} + \left ( e_{2}\cdot e_{2}\right )  a^{2} b^{1} c^{2} - \left ( e_{2}\cdot e_{2}\right )  a^{2} b^{2} c^{1} + \left ( e_{2}\cdot e_{3}\right )  a^{2} b^{1} c^{3} - \left ( e_{2}\cdot e_{3}\right )  a^{2} b^{3} c^{1} + \left ( e_{2}\cdot e_{3}\right )  a^{3} b^{1} c^{2} - \left ( e_{2}\cdot e_{3}\right )  a^{3} b^{2} c^{1} + \left ( e_{3}\cdot e_{3}\right )  a^{3} b^{1} c^{3} - \left ( e_{3}\cdot e_{3}\right )  a^{3} b^{3} c^{1}\right ) \boldsymbol{e}_{1} + \left ( - \left ( e_{1}\cdot e_{1}\right )  a^{1} b^{1} c^{2} + \left ( e_{1}\cdot e_{1}\right )  a^{1} b^{2} c^{1} - \left ( e_{1}\cdot e_{2}\right )  a^{2} b^{1} c^{2} + \left ( e_{1}\cdot e_{2}\right )  a^{2} b^{2} c^{1} + \left ( e_{1}\cdot e_{3}\right )  a^{1} b^{2} c^{3} - \left ( e_{1}\cdot e_{3}\right )  a^{1} b^{3} c^{2} - \left ( e_{1}\cdot e_{3}\right )  a^{3} b^{1} c^{2} + \left ( e_{1}\cdot e_{3}\right )  a^{3} b^{2} c^{1} + \left ( e_{2}\cdot e_{3}\right )  a^{2} b^{2} c^{3} - \left ( e_{2}\cdot e_{3}\right )  a^{2} b^{3} c^{2} + \left ( e_{3}\cdot e_{3}\right )  a^{3} b^{2} c^{3} - \left ( e_{3}\cdot e_{3}\right )  a^{3} b^{3} c^{2}\right ) \boldsymbol{e}_{2} + \left ( - \left ( e_{1}\cdot e_{1}\right )  a^{1} b^{1} c^{3} + \left ( e_{1}\cdot e_{1}\right )  a^{1} b^{3} c^{1} - \left ( e_{1}\cdot e_{2}\right )  a^{1} b^{2} c^{3} + \left ( e_{1}\cdot e_{2}\right )  a^{1} b^{3} c^{2} - \left ( e_{1}\cdot e_{2}\right )  a^{2} b^{1} c^{3} + \left ( e_{1}\cdot e_{2}\right )  a^{2} b^{3} c^{1} - \left ( e_{1}\cdot e_{3}\right )  a^{3} b^{1} c^{3} + \left ( e_{1}\cdot e_{3}\right )  a^{3} b^{3} c^{1} - \left ( e_{2}\cdot e_{2}\right )  a^{2} b^{2} c^{3} + \left ( e_{2}\cdot e_{2}\right )  a^{2} b^{3} c^{2} - \left ( e_{2}\cdot e_{3}\right )  a^{3} b^{2} c^{3} + \left ( e_{2}\cdot e_{3}\right )  a^{3} b^{3} c^{2}\right ) \boldsymbol{e}_{3} \end{equation*}



In [11]:

    
GA.E()









    Out[11]:





\begin{equation*}  \boldsymbol{e}_{1}\wedge \boldsymbol{e}_{2}\wedge \boldsymbol{e}_{3} \end{equation*}



In [17]:

    
GA.I()









    Out[17]:





\begin{equation*} \frac{1}{\sqrt{\left ( e_{1}\cdot e_{1}\right )  \left ( e_{2}\cdot e_{2}\right )  \left ( e_{3}\cdot e_{3}\right )  - \left ( e_{1}\cdot e_{1}\right )  \left ( e_{2}\cdot e_{3}\right ) ^{2} - \left ( e_{1}\cdot e_{2}\right ) ^{2} \left ( e_{3}\cdot e_{3}\right )  + 2 \left ( e_{1}\cdot e_{2}\right )  \left ( e_{1}\cdot e_{3}\right )  \left ( e_{2}\cdot e_{3}\right )  - \left ( e_{1}\cdot e_{3}\right ) ^{2} \left ( e_{2}\cdot e_{2}\right ) }} \boldsymbol{e}_{1}\wedge \boldsymbol{e}_{2}\wedge \boldsymbol{e}_{3} \end{equation*}



In [ ]: