1 core.matrices.QuadraticForm
core.matrices.QuadraticForm(vector, matrix)Quadratic form: x’ @ Q @ x where Q is a constant matrix.
This represents the scalar expression xᵀQx, commonly used for: - Portfolio variance: w’ @ Σ @ w - Regularization terms: x’ @ I @ x = ||x||² - Quadratic objectives in optimization
1.1 Parameters
| Name | Type | Description | Default |
|---|---|---|---|
| vector | VectorVariable | VectorExpression | VectorVariable or VectorExpression (the x). | required |
| matrix | np.ndarray | 2D NumPy array (the Q matrix, should be square). | required |
1.2 Example
import numpy as np Q = np.array([[1, 0.5], [0.5, 2]]) x = VectorVariable(“x”, 2) qf = QuadraticForm(x, Q) qf.evaluate({“x[0]”: 1, “x[1]”: 1}) 4.0 # 11 + 20.511 + 2*1 = 1 + 1 + 2 = 4
1.3 Methods
| Name | Description |
|---|---|
| evaluate | Evaluate the quadratic form xᵀQx. |
| get_variables | Return all variables this expression depends on. |
1.3.1 evaluate
core.matrices.QuadraticForm.evaluate(values)Evaluate the quadratic form xᵀQx.
1.3.2 get_variables
core.matrices.QuadraticForm.get_variables()Return all variables this expression depends on.