numpy

NUMPY

• normal list built-in methods don't work on numpy arrays

• in python + just concatenates

• in numpy + it does element-wise vector addition

• has instance methods: dot(), sum()

• has linalg methods:

  • np.linalg.norm(A)
  • np.linalg.inv(A)
  • np.linalg.det(A)
  • np.linalg.diag(A)

• matrix datatypes

  • np.matrix, np.array (just use the array always)
  • can be sliced

• matrix methods:

  • np.mean(), .var()
  • np.trace(a) -- sum of the diagonal

INNER (DOT) PRODUCT

C = sum over i {A(i)B(i)} a.dot(b) SAME AS np.inner(a,b)

MATRIX PRODUCTS

• inner dimensions of the 2 matrices have to match
• sum of dot products for each pair
• using * in numpy

OUTER PRODUCT

• when calculating the covariance of
• C(i,j) = A(i)B(j)
• np.outer()

Eigenvalues, eigenvectors

• often apply this to covariance matrix of a dataset (symmetrical)
• to get covariance: np.cov(X.T)
• np.linalg.eig() for
• np.linalg.eigh(cov) for symmetric (equal to the transpose of itself) / Hermitian matrices (equal to the conjugate transpose of itself)

Solving linear systems

Ax = b

A - a matrix x - column we are trying to solve for b = vector of numbers

solution: multiply by A(-1) (A inverse) on both sides

x = np.linalg.inv(A).dot(b)

-- alternatively: x = np.linalg.solve(A,b)