The algorithm of high number gradient is that the gradient is equal to the sum of the square of the directional derivative of X plus the square of the directional derivative of Y, and then squared.

Calculation formula of gradient: gradu=a? (? u/？ x)+a？ (? u/？ y)+az(？ u/？ z)

A gradient is a vector, which means that the directional derivative of a function at that point gets the maximum in that direction, that is, the function changes the fastest at that point in that direction (the direction of this gradient) and the rate of change is the largest (the modulus of this gradient).

Gradient is a special form of Jacobian matrix;

When m= 1, the Jacobian matrix of the function is gradient. This concept was originally set for field theory, and any field can be used to understand gradient. Later, it was quoted in mathematics to represent the direction and size of the fastest change rate of a function at a specified point, which is a digital abstraction of efficiency change.

For example, to build a cable car leading to the top of the mountain, there may be a mountain peak in the middle of a straight line from the top of the mountain to the bottom of the mountain. Raising the arrival station at the top of the mountain is not only unsafe, but also increases the construction efficiency. When adjusting the construction angle of the cable car, the angle change rate is gradient. If the angle is too low, the gradient direction angle is zero and the direction derivative is zero.

In vector calculus, the gradient of scalar field is a vector field. The gradient of a point in the scalar field points to the fastest growing direction of the scalar field, and the length of the gradient is the maximum change rate. More strictly speaking, the gradient of a function from Euclidean space Rn to R is the best linear approximation of a point in Rn. In this sense, gradient is a special case of Jacobian matrix.

In the case of unary real functions, the gradient is only the derivative, or, for linear functions, the slope of a straight line.