symsx[1 3]matrixf = sin(x)*sin(x).' f =sin(x) sin(x)T g = gradient(f,x) g =2 (cos(x)⊙I3) sin(x)T To express the gradient in terms of the elements ofx, convert the result to a vector of symbolic scalar
The exact value of the gradient off(x,y)=x2y3at the point (1,-2) is (∇f)(1,−2)=2xy3ˆi+3x2y2ˆj=−16ˆi+12ˆj. Input Arguments collapse all Input array, specified as a vector, matrix, or multidimensional array. ...
The term "gradient" has several meanings in mathematics. The simplest is as a synonym for slope. The more general gradient, called simply "the" gradient in vector analysis, is a vector operator denoted del and sometimes also called del or nabla. It is m
gradientcalculates values along the edges of the matrix withsingle-sided differences: G(:,1) = A(:,2) - A(:,1); G(:,N) = A(:,N) - A(:,N-1); If you specify the point spacing, thengradientscales the differences appropriately. If you specify two or more outputs, then the func...
Picasso is a high quality vector graphic rendering library. It has high performance and low footprint. Picasso provides a set of high level 2D graphics API, which can be used to a GUI system, rendering postscript, rendering svg images and so on. It support path, matrix, gradient, pattern...
Fortunately, this problem can be solved by the gradient vector flow (GVF), which can overcome the defect of the traditional external flow and move the active contour towards the desired object edge more efficiently. So far, the ACM method has been proposed for the segmentation of touching, ...
注意,这里 X 和Y 可以是scalar, vector, and matrix。 定义L(θ) ,其中 θ∈Rm 。对应的gradient descent就是 θk+1=θk−η∂L∂θ(θk).令η→0+ , 我们得到了相应的gradient flow dθdt=−∂L∂θ(θ).注意continuous time的gradient flow和discrete time的gradient descent肯定是有...
定义$X$为输入特征图,则$W^T X$为输出特征图,$e=\frac{1}{\sqrt{M}}1$为$M$位单位向量(unit vector),$I\in\mathbb{R}^{M\times M}$为单位矩阵(identity matrix)。 Formulation of GC 对于卷积层或全连接层的权值向量$wi$,通过反向传播得到其梯度$\nabla{wi}\mathcal{L}$,然后如图b所示...
The function df , which maps x to dfx , is called the differential or exterior derivative of f and is an example of a differential 1-form. 2 Jacobian matrix 雅可比矩阵的重要性在于它体现了一个可微方程与给出点的最优线性逼近。 因此,雅可比矩阵类似于多元函数的导数。 The Jacobian of a vector...
where σ is the coefficient of the surface tension (N/m), к is the curvature of the interface (m), n→ is the vector of interface, ∇sσ is the surface tension gradient. The first term at the right of Eq. (58) is a net force caused by the local curvature of the interface. ...