Therefore, the Jacobian matrix \\\( ext{d}\\\bar{ext{X}}_{ext{i}} /ext{d}\\\bar{ext{X}}_{{ext{sys}}} \\\) of the boundary variable vector \\\( {\\\bar{ext{X}}}_{ext{i}} \\\) with respect to the system variable vector \\\( {\\\bar{ext{X}}}_{{ext{...
The Jacobian of a vector function is a matrix of the partial derivatives of that function. Compute the Jacobian matrix of [x*y*z,y^2,x + z] with respect to [x,y,z]. Get syms x y z jacobian([x*y*z,y^2,x + z],[x,y,z]) ans = ⎛⎜⎜⎝y z01x z2 y...
Therefore, the Jacobian matrix \( ext{d}\bar{ext{X}}_{ext{i}} /ext{d}\bar{ext{X}}_{{ext{sys}}} \) of the boundary variable vector \( {\bar{ext{X}}}_{ext{i}} \) with respect to the system variable vector \( {\bar{ext{X}}}_{{ext{sys}}} \) is of crucial ...
As of Version 9.0, vector analysis functionality is built into the Wolfram Language» JacobianMatrix[pt] gives the Jacobian matrix of the transformation from the default coordinate system to the Cartesian coordinate system at the pointpt.
matrix-vector multiplication. [A(t+dt)] generally depends on {u(t+dt)} as well as the current stresses and additional state variables. For linear elastic or viscoelastic problems with constant time step size, A is a constant (after the elastic solution). {b(t+dt)} ...
Vector radiative transferJacobian matrix calculationAerosol scatteringDue to the polarization effects of the Earth's surface reflection and atmospheric particles' scattering, high-precision retrieval of atmospheric parameters from near-infrared satellite data requires accurate vector atmospheric radiative transfer ...
This paper studies the impact that the method of computing Jacobian-vector products has on the overall performance and accuracy of the time integration process. The analysis shows that the most beneficial approach is the direct computation of exact Jacobian-vector products in the context of matrix-...
We explore a class of vectorial total variation (VTV) measures formed as the spatial sum of a pixel-wise matrix norm of the Jacobian of a vector field. We give a theoretical treatment that indicates that, while color smearing and affine-coupling bias (often reported as gray-scale bias) are...
TheJacobian(f,v) command computes theJacobian Matrixof a list or Vector of expressionsfwith respect to the variables inv. • Ifvis not provided, the differentiation variables are determined from the coordinate system off, iffis a Vector, and otherwise from the ambient coordinate system (seeSet...
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-valued function in several variables generalizes the gradient of a scalar-valued function in several variables, which in turn generalizes the derivative...