vautodiff

dual_constant(v)

Wraps v as a Dual representing a fixed constant.

dual_constant(5)

dual_variable(v)

dual_variable(3.0)

dual_coerce(value)

Coerces value to a Dual, leaving an existing Dual unchanged.

dual_coerce(5)

dual_add(a, b)

Adds two Duals (or Dual-and-Number mixes), propagating both derivatives.

dual_add(dual_variable(2.0), dual_constant(3.0))

dual_subtract(a, b)

Subtracts two Duals (or Dual-and-Number mixes), propagating both derivatives.

dual_subtract(dual_variable(5.0), dual_constant(2.0))

dual_multiply(a, b)

Multiplies two Duals (or Dual-and-Number mixes) using the product rule.

dual_multiply(dual_variable(3.0), dual_variable(3.0))

dual_divide(a, b)

Divides two Duals (or Dual-and-Number mixes) using the quotient rule.

dual_divide(dual_variable(6.0), dual_constant(2.0))

dual_negate(a)

Negates a Dual (or Number), flipping the sign of both value and derivative.

dual_negate(dual_variable(4.0))

dual_power(a, n)

Raises a Dual (or Number) to a CONSTANT real exponent n.

dual_power(dual_variable(2.0), 3)

dual_sqrt(a)

Gives back the square root of a Dual (or Number), with its derivative.

dual_sqrt(dual_variable(4.0))

dual_exp(a)

Gives back e raised to a Dual (or Number), with its derivative.

dual_exp(dual_variable(0.0))

dual_natural_log(a)

Gives back the natural logarithm of a Dual (or Number), with its derivative.

dual_natural_log(dual_variable(2.0))

dual_sin(a)

Gives back the sine of a Dual (or Number), with its derivative.

dual_sin(dual_variable(0.0))

dual_cos(a)

Gives back the cosine of a Dual (or Number), with its derivative.

dual_cos(dual_variable(0.0))

dual_tan(a)

Gives back the tangent of a Dual (or Number), with its derivative.

dual_tan(dual_variable(0.0))

dual_equals(a, b)

Tests whether two Duals (or Dual-and-Number mixes) have equal value AND equal derivative.

dual_equals(dual_variable(2.0), dual_constant(2.0))

dual_display(a)

Renders a Dual as "value + deriv*epsilon" Text.

dual_display(dual_variable(2.0))

derivative(f, x0)

THE MAIN ENTRY POINT: gives back the exact derivative of f at x0.

make f(x)
    give dual_sin(dual_multiply(x, x))

derivative(f, 2.0)

value_and_derivative(f, x0)

make f(x)
    give dual_sin(dual_multiply(x, x))

value_and_derivative(f, 2.0)