Class, standalone functions and miscellaneous methods (2/3)

Miscellaneous methods

Is matrix square?

A matrix is 'square' if it has the same number of rows as it does columns:

\[\begin{equation} \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \end{equation}\]

Code implementation

This is extremely simple:

def is_square(self):
    return self.size(0) == self.size(1)

Is matrix wide or tall?

If the matrix is not square, then it must either have more columns than rows (wide) or have more rows than columns (tall). We make a couple of methods to test those cases too:

def is_wide(self):
    return self.size(0) < self.size(1)

def is_tall(self):
    return self.size(0) > self.size(1)

Is matrix lower triangular?

Code implementation

We loop over each element in the upper triangular region and if we find a non-zero we return False, otherwise we return True:

def is_lower_tri(self):
    for i, row in enumerate(self.data):
        for col in range(i+1,len(row)):
            if row[col] != 0:
                return False
    else:
        return True

Is matrix upper triangular?

Code implementation

Here we simply call the is_lower_tri method on the transposed matrix:

def is_upper_tri(self):
    return self.tr().is_lower_tri()

Is matrix diagonal?

Code implementation

If the matrix qualifies as both lower and upper, then it must be diagonal. Therefore we use the previous two methods like so:

def is_diag(self):
    if self.is_lower_tri() and self.is_upper_tri():
        return True
    else:
        return False

Is matrix symmetric?

Code implementation

We loop over two ranges - one being the number of rows/columns, and the other being one less than that (since we don't need to check diagonal entries). If we find any $a_{ij} \neq a_{ji}$, we return False, otherwise we return True:

def is_symmetric(self):
    for i in range(self.size(0)):
        for j in range(i+1, self.size(0)):
            if self.ind(i,j) != self.ind(i,j):
                return False
    else:
        return True

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Combining matrices and getting the diagonal >

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