1 core.vectors.DotProduct

core.vectors.DotProduct(left, right)

Dot product of two vectors: x · y = x[0]y[0] + x[1]y[1] + … + x[n-1]*y[n-1].

This is a scalar expression representing the inner product.

1.1 Parameters

Name	Type	Description	Default
left	VectorVariable | VectorExpression	First vector.	required
right	VectorVariable | VectorExpression	Second vector.	required

1.2 Example

x = VectorVariable(“x”, 3) y = VectorVariable(“y”, 3) d = DotProduct(x, y) d.evaluate({“x[0]”: 1, “x[1]”: 2, “x[2]”: 3, “y[0]”: 4, “y[1]”: 5, “y[2]”: 6}) 32.0

1.3 Methods

Name	Description
evaluate	Evaluate the dot product given variable values.
get_variables	Return all variables this expression depends on.
jacobian_row	Return Jacobian row in O(n) for special cases.

1.3.1 evaluate

core.vectors.DotProduct.evaluate(values)

Evaluate the dot product given variable values.

1.3.2 get_variables

core.vectors.DotProduct.get_variables()

Return all variables this expression depends on.

1.3.3 jacobian_row

core.vectors.DotProduct.jacobian_row(variables)

Return Jacobian row in O(n) for special cases.

For DotProduct(x, x) (same VectorVariable), gradient is 2*x[i]. For DotProduct(x, y) with two different VectorVariables, gradient is y[i] for x[i] and x[i] for y[i].

1.3.3.1 Returns

Name	Type	Description
	list[Expression] | None	List of expressions, or None if optimization not applicable.