robotics代写|寻路算法代写Path Planning Algorithms|Visibility-Based Optimal Path Planning

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  • Longitudinal Data Analysis 纵向数据分析
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robotics代写|寻路算法代写Path Planning Algorithms|Visibility-Based Optimal Path Planning

robotics代写|寻路算法代写Path Planning Algorithms|Existence of Solutions

First, we consider Problem 4.1. The following result ensures that the set of all admissible paths $\Gamma$ satisfying condition (1) is nonempty.

Proposition 4.1 Under the conditions of Theorem 3.3, there exists an admissible path $\Gamma \in \Omega$ that satisfies condition (4.2).

Proof 4.I From Theorem $3.3$, there exists a finite point set $P^{(N)}=\left{x^{(k)}, k=\right.$ $1, \ldots, N} \subset \Omega$ that satisfies the total visibility constraint (1). If the specified end points $x_{o}$ and $x_{f} \in P^{(N)}$, then under the assumption that $\Omega$ is simply connected, it is always possible to construct a path $\Gamma$ in $\Omega$ corresponding to a Jordan arc passing through all the points in $P^{(N)}$. In particular, if the line segment joining any pair of points in $P^{(N)}$ lies in $\Omega$, then a Jordan arc composed of straightline segments joining the successive points in $P^{(N)}$ can always be constructed. A trivial case is where $\Omega$ is a compact convex subset of $\mathbb{R}^{2}$. If $x_{o}$ and/or $x_{f} \notin P^{(N)}$, we augment $P^{(N)}$ by these points, and proceed with the construction of a Jordan arc. Finally, from the constructed $\Gamma$, the corresponding path $\Gamma_{\mathcal{P}}$ in $\mathcal{P}$ can be determined from ${(x, g(x)): x \in \Gamma} .$

Remark 4.3 Proposition $4.1$ implies the existence of a Jordan arc passing through a finite set of observation points $\left(x^{(k)}, f_{h_{v}}\left(x^{(k)}\right)\right) \in G_{f_{b_{E}}}$ such that $G_{f}$ is totally visible. In general, the set of observation points for total visibility is not unique. Moreover, the cardinality of this set depends on $f$.

Remark 4.4 Suppose that the line segment $L$ joining the points $x_{o}$ and $x_{f}$ lies in $\Omega$, and $\bigcup_{x \in L} \mathcal{V}\left(\left(x, f_{h_{E}}(x)\right)\right)=G_{f}$, then $L$ is an optimal path. If $\bigcup_{x \in L} \mathcal{V}\left(\left(x, f_{h_{v}}(x)\right)\right) \subset$ $G_{f}$, then for a certain class of $G_{f}$, the optimal path $\Gamma^{*}$ is close to $L$ in the sense of arc length. Minimal excursions from $L$ can be introduced so that the invisible part $G_{f}-\bigcup_{x \in L} \mathcal{V}\left(\left(x, f_{h_{v}}(x)\right)\right)$ becomes visible.

For Problem 4.1″, we first construct the set $\tilde{\Omega} \stackrel{\text { def }}{=}\left{x \in \Omega:|\nabla f(x)| \leq f_{\max }^{\prime}\right}$, and then find the shortest admissible path $\Gamma^{} \subset \bar{\Omega}$ such that $\bigcup_{x \in \Gamma^{}} \mathcal{V}\left(\left(x, f_{h_{v}}(x)\right)\right)=$ $G_{f}$. In general, it is possible that $\bar{\Omega}$ consists of disjoint subsets of $\Omega$, and there may not exist admissible paths in $\bar{\Omega}$ (e.g. $x_{o}$ and $x_{f}$ lie in two disjoint subsets of $\Omega$ separated by a strip on which $|\nabla f(x)|>f_{\max }^{\prime}$ for all points $x$ on this strip). Consequently, Problem 4.1″ has no solution. Note also that the line segment $L$ joining $x_{o}$ and $x_{f}$ may not lie in $\bar{\Omega}$.

Since $f$ is a $C_{1}$-function, the set $\bar{\Omega}$ is compact. Assuming the existence of an admissible path in $\bar{\Omega}$, the observations given in Remarks $4.3$ and $4.4$ are also applicable to this case.

robotics代写|寻路算法代写Path Planning Algorithms|Optimality Conditions

Here, we develop optimality conditions for Problem $4.1$ under the assumption that a solution exists. From Theorem $3.3$, there exists a finite point set $P^{(N)}=\left{x^{(k)}, k=\right.$ $1, \ldots, N} \subset \Omega$ with $x^{(1)}=x_{o}$ and $x^{(N)}=x_{f}$ such that
\bigcup_{k=1}^{N} \mathcal{V}\left(\left(x^{(k)}, f_{h_{v}}\left(x^{(k)}\right)\right)\right)=G_{f}
is satisfied. Let $P$ denote the set of all such $P^{(N)}$ ‘s with $2 \leq N<\infty$. The cardinality of $P$ is generally infinite. Now, for a given $P^{(N)} \subset P$, let $\tilde{\mathcal{A}}{P(N)}$ denote the set of all admissible paths $\Gamma$ formed by line segments joining distinct pairs of points in $P^{(N)}$. The cardinality of $\overline{\mathcal{A}}{P(N)}$ is $\leq(N-2)$ !. Thus, Problem $4.1$ reduces to finding a finite point set $P^{(N)} \subset P$ and an admissible path $\Gamma \in \tilde{\mathcal{A}}{P(N)}$ such that the arc length $$ \Lambda(\Gamma)=\sum{k=1}^{N-1}\left|x^{(k+1)}-x^{(k)}\right|
is minimized. For convenience, the points $x^{(k)}, k=2, \ldots, N-1$ are indexed consecutively along the path $\Gamma$ initiating from $x_{o}$ and moving towards the end point $x_{f}$.
The following simple necessary condition for optimality can be deduced readily from the definition of arc length:

Proposition $4.2$ Let $\Gamma^{}$ be an optimal admissible path for Problem 4.1, and $P^{\left(N^{}\right)}=$ $\left{x_{}^{(k)} \in \Gamma^{}, k=1, \ldots, N^{}\right}$ be a finite point set satisfying (4.16). Then, for any perturbed admissible path $\Gamma \in \overline{\mathcal{A}}{\bar{P}^{\left(N^{}\right)}}$ with finite point set $\left{x{}^{(1)}, \ldots, x_{}^{(k-1)}, x_{}^{(k)}+\right.$ $\left.\delta x, x_{}^{(k+1)}, \ldots, x_{}^{\left(N^{}\right)}\right}$ in which the point perturbation $\delta x$ about $x_{}^{(k)}$ satisfies $x_{}^{(k)}+$ $\delta x \in \Omega$, and condition (4.16) holds, the following inequality:

&\left|x_{}^{(k)}+\delta x-x_{}^{(k-1)}\right|+\left|x_{}^{(k+1)}-x_{}^{(k)}-\delta x\right| \geq\left|x_{}^{(k+1)}-x_{}^{(k)}\right| \
&\quad+\left|x_{}^{(k)}-x_{}^{(k-1)}\right|, \quad k=2, \ldots, N^{}-1, \end{aligned} $$ must be satisfied. For Problem 4.2, a necessary condition for optimality can be derived by considering local path perturbations. Let $I=[0,1]$. First, we parameterize an admissible path $\Gamma$ by the scalar parameter $\lambda \in I$, i.e. $$ \Gamma=\left{\left(x_{1}, x_{2}\right) \in \Omega: x_{1}=q_{1}(\lambda), x_{2}=q_{2}(\lambda), \lambda \in I\right} $$ where $q_{1}$ and $q_{2}$ are real-valued $C_{1}$-functions on $I$ satisfying $$ \left(q_{1}(0), q_{2}(0)\right)=\left(x_{o 1}, x_{o 2}\right) \text { and }\left(q_{1}(1), q_{2}(1)\right)=\left(x_{f 1}, x_{f 2}\right) $$ Let $\Gamma^{}$ and $\Gamma$ denote an optimal path and an admissible perturbed path specified by $q^{}(\lambda)=\left(q_{1}^{}(\lambda), q_{2}^{}(\lambda)\right)$ and $q^{}(\lambda)+\eta(\lambda)=\left(q_{1}^{}(\lambda)+\eta_{1}(\lambda), q_{2}^{}(\lambda)+\eta_{2}(\lambda)\right), \quad \lambda \in I$,
respectively, where $\eta=\left(\eta_{1}, \eta_{2}\right) \in \Sigma_{\Gamma^{}}$, the set of all admissible path perturbations about $\Gamma^{}$ defined by $\Sigma_{\Gamma^{}}=\left{\eta \in C_{1}\left(I ; \mathbb{R}^{2}\right): \eta(0)=(0,0), \eta(1)=(0,0) ; q^{}(\lambda)+\right.$ $\eta(\lambda) \in \Omega$ for all $\lambda \in I}$, with $C_{1}\left(I ; \mathbb{R}^{2}\right)$ being the normed linear space of all continuous functions defined on $I$ with their values in $\mathbb{R}^{2}$ and having continuous first derivatives on $I$, and normed by: $|\eta|_{m}=\sum_{i=1,2}\left(\max {\lambda \in I}\left|\eta{i}(\lambda)\right|+\max {\lambda \in I}\left|\eta{i}^{\prime}(\lambda)\right|\right)$, where $(\cdot)^{\prime}$ denotes differentiation with respect to $\lambda$.

robotics代写|寻路算法代写Path Planning Algorithms|Numerical Algorithms

To facilitate the development of numerical algorithms for the optimal path planning problems, a mesh on $\Omega$ using standard methods such as Delaunay triangulation is established. Then $G_{f}$ is approximated by a polyhedral surface $\hat{G}{f}$, in particular, a surface formed by triangular patches. In practical situations, the function $f=f(x)$ is usually given in the form of numerical data. An approximation of $G{f}$ can be obtained by interpolation of the given numerical data. Here, algorithms are developed for the approximate Problems $4.1$ and $4.2$ that make use of the numerical data directly.
For the Shortest Path Problem 4.1, consider the simplest case where the line segment $L$ joining the end points $x_{o}$ and $x_{f}$ lies in $\Omega$. Remark $4.4$ suggests that a possible approach to obtaining a solution to the approximate Problem $4.1$ is to seek first a finite number of points along $L$ having maximal visibility, and then introduce additional points close to $L$ to achieve total visibility. Finally, a Jordan-arc with minimal length passing through all the observation points is constructed.

Suppose that on $\Omega$, a mesh consisting of points $x^{(k)}, k=1, \ldots, M$ along with the approximate surface $\hat{G}{f}$ formed by triangular patches have been established. For convenience, let $x^{(1)}=x{o}$ and $x^{(M)}=x_{f}$. Let $\hat{\mathcal{G}}$ denote the set of all Jordan arcs connecting $x^{(1)}$ and $x^{(M)}$ formed by line segments corresponding to the edges of the triangles. The basic steps in our algorithm for determining an optimal path for the approximate Problem $4.1$ without assuming that the line segment $L$ joining $x_{o}$ and $x_{f}$ lies in $\Omega$ are as follows:

Step 3 Determine $\hat{\mathcal{G}}^{}=\left{\Gamma_{j}^{}, j=1, \ldots, K\right}$, the set of all Jordan arcs in $\hat{\mathcal{G}}$ having the shortest path length.
Step 4 Select a path in $\hat{\mathcal{G}}^{}$, say $\Gamma_{i}^{}$.
Step 5 Compute the visible set $\mathcal{V}\left(\left(x^{(k)}, f_{h_{v}}\left(x^{(k)}\right)\right)\right)$ corresponding to each point $x^{(k)}$ along the path $\Gamma_{i}^{}$ and its projection $\Pi_{\Omega} \mathcal{V}\left(\left(x^{(k)}, f_{h_{v}}\left(x^{(k)}\right)\right)\right)$. Step 6 Determine whether there exists a combination of points $x^{(k)}$ along $\Gamma_{i}^{}$ such that the union of their visible sets $\mathcal{V}\left(\left(x^{(k)}, f_{h_{v}}\left(x^{(k)}\right)\right)\right)$ is equal to $G_{f}$.
If YES, then $\Gamma_{i}^{}$ is an optimal path for the approximate Problem 4.1, STOP; if NO, select a neighboring path of $\Gamma_{i}^{}$ in the sense of arc length, and GO TO Step $5 .$

Remark $4.5$ In Steps 2 and 3, instead of considering triangles in $\Omega$, we may consider triangular patches associated with the polyhedral approximation of the surface $G_{f}$. Efficient algorithms for computing the shortest arc length such as those due to Sharir and Shorr [3], O’Rourke et al. [4], and Lawler [5] may be used.

Remark $4.6$ Step 5 involves the computation of visible sets $\mathcal{V}\left(\left(x^{(k)}, f_{h_{x}}\left(x^{(k)}\right)\right)\right)$ associated with points $x^{(k)}$ along the path $\Gamma_{i}^{*}$, an NP-hard problem in computational geometry. This task can be accomplished using a suitable algorithm developed recently by Balmes and Wang [1]. The complexity of that algorithm is $O\left(n p^{2}\right)$, where $n$ and $p$ are the number of observation points and the number of triangular patches respectively. This algorithm can be easily modified to take into account the limited aperture of cameras or sensors.

robotics代写|寻路算法代写Path Planning Algorithms|Visibility-Based Optimal Path Planning


robotics代写|寻路算法代写Path Planning Algorithms|Existence of Solutions

首先,我们考虑问题 4.1。以下结果确保了所有允许路径的集合Γ满足条件(1)是非空的。

命题 4.1 在定理 3.3 的条件下,存在一条允许路径Γ∈Ω满足条件(4.2)。

证明 4.I 来自定理3.3, 存在一个有限点集P^{(N)}=\left{x^{(k)}, k=\right.$ $1, \ldots, N} \subset \OmegaP^{(N)}=\left{x^{(k)}, k=\right.$ $1, \ldots, N} \subset \Omega满足总可见性约束 (1)。如果指定的端点X这和XF∈磷(ñ), 那么假设Ω是简单的连接,总是可以构造一个路径Γ在Ω对应于一条穿过所有点的 Jordan 弧磷(ñ). 特别是,如果连接任意一对点的线段磷(ñ)在于Ω,然后由连接连续点的直线段组成的若尔当弧磷(ñ)总是可以构建的。一个微不足道的情况是Ω是一个紧凸子集R2. 如果X这和/或XF∉磷(ñ),我们增加磷(ñ)通过这些点,继续构建约旦弧。最后,从构建的Γ, 对应路径Γ磷在磷可以从(X,G(X)):X∈Γ.

备注 4.3 命题4.1意味着存在一条通过有限观测点集的若尔当弧(X(ķ),FH在(X(ķ)))∈GFb和这样GF是完全可见的。一般来说,总能见度的观察点集合不是唯一的。此外,这个集合的基数取决于F.

备注 4.4 假设线段大号加入点X这和XF在于Ω, 和⋃X∈大号在((X,FH和(X)))=GF, 然后大号是一条最优路径。如果⋃X∈大号在((X,FH在(X)))⊂ GF, 那么对于某一类GF, 最优路径Γ∗接近大号在弧长的意义上。最少的游览大号可以引入使不可见的部分GF−⋃X∈大号在((X,FH在(X)))变得可见。

对于问题 4.1”,我们首先构造集合\波浪号{\Omega} \stackrel{\text { def }}{=}\left{x \in \Omega:|\nabla f(x)| \leq f_{\max }^{\prime}\right}\波浪号{\Omega} \stackrel{\text { def }}{=}\left{x \in \Omega:|\nabla f(x)| \leq f_{\max }^{\prime}\right},然后找到最短允许路径Γ⊂Ω¯这样⋃X∈Γ在((X,FH在(X)))= GF. 一般来说,有可能Ω¯由不相交的子集组成Ω, 中可能不存在允许的路径Ω¯(例如X这和XF位于两个不相交的子集中Ω由一条带隔开|∇F(X)|>F最大限度′对于所有点X在这个地带)。因此,问题 4.1″ 没有解决方案。还要注意线段大号加入X这和XF可能不在Ω¯.

自从F是一个C1-函数,集合Ω¯紧凑。假设存在一条允许路径Ω¯, 备注中给出的观察结果4.3和4.4也适用于本案。

robotics代写|寻路算法代写Path Planning Algorithms|Optimality Conditions

在这里,我们为问题开发最优条件4.1在存在解决方案的假设下。从定理3.3, 存在一个有限点集P^{(N)}=\left{x^{(k)}, k=\right.$ $1, \ldots, N} \subset \OmegaP^{(N)}=\left{x^{(k)}, k=\right.$ $1, \ldots, N} \subset \Omega和X(1)=X这和X(ñ)=XF这样
很满意。让磷表示所有此类的集合磷(ñ)与2≤ñ<∞. 基数磷一般是无限的。现在,对于给定的磷(ñ)⊂磷, 让一种~磷(ñ)表示所有允许路径的集合Γ由连接不同点对的线段形成磷(ñ). 基数一种¯磷(ñ)是≤(ñ−2)!. 因此,问题4.1减少到找到一个有限点集磷(ñ)⊂磷和可接受的路径Γ∈一种~磷(ñ)使得弧长Λ(Γ)=∑ķ=1ñ−1|X(ķ+1)−X(ķ)|

主张4.2让Γ是问题 4.1 的最优可接受路径,并且磷(ñ)= \left{x_{}^{(k)} \in \Gamma^{}, k=1, \ldots, N^{}\right}\left{x_{}^{(k)} \in \Gamma^{}, k=1, \ldots, N^{}\right}是满足(4.16)的有限点集。然后,对于任何扰动的允许路径Γ∈一种¯磷¯(ñ)有有限点集\left{x{}^{(1)}, \ldots, x_{}^{(k-1)}, x_{}^{(k)}+\right.$ $\left.\delta x, x_{}^{(k+1)}, \ldots, x_{}^{\left(N^{}\right)}\right}\left{x{}^{(1)}, \ldots, x_{}^{(k-1)}, x_{}^{(k)}+\right.$ $\left.\delta x, x_{}^{(k+1)}, \ldots, x_{}^{\left(N^{}\right)}\right}其中点扰动dX关于X(ķ)满足X(ķ)+ dX∈Ω, 并且条件 (4.16) 成立,以下不等式成立:|X(ķ)+dX−X(ķ−1)|+|X(ķ+1)−X(ķ)−dX|≥|X(ķ+1)−X(ķ)| +|X(ķ)−X(ķ−1)|,ķ=2,…,ñ−1,必须满足。对于问题 4.2,可以通过考虑局部路径扰动来推导出最优性的必要条件。让一世=[0,1]. 首先,我们参数化一个可接受的路径Γ通过标量参数λ∈一世, IE\Gamma=\left{\left(x_{1}, x_{2}\right) \in \Omega: x_{1}=q_{1}(\lambda), x_{2}=q_{2}( \lambda), \lambda \in I\right}\Gamma=\left{\left(x_{1}, x_{2}\right) \in \Omega: x_{1}=q_{1}(\lambda), x_{2}=q_{2}( \lambda), \lambda \in I\right}在哪里q1和q2是实值的C1- 功能开启一世令人满意的(q1(0),q2(0))=(X这1,X这2) 和 (q1(1),q2(1))=(XF1,XF2)让Γ和Γ表示最优路径和由下式指定的允许扰动路径q(λ)=(q1(λ),q2(λ))和q(λ)+这(λ)=(q1(λ)+这1(λ),q2(λ)+这2(λ)),λ∈一世,
分别在哪里这=(这1,这2)∈ΣΓ,所有允许的路径扰动的集合Γ被定义为\Sigma_{\Gamma^{}}=\left{\eta \in C_{1}\left(I ; \mathbb{R}^{2}\right): \eta(0)=(0,0) , \eta(1)=(0,0) ; q^{}(\lambda)+\right.$ $\eta(\lambda) \in \Omega$ 对于所有 $\lambda \in I}\Sigma_{\Gamma^{}}=\left{\eta \in C_{1}\left(I ; \mathbb{R}^{2}\right): \eta(0)=(0,0) , \eta(1)=(0,0) ; q^{}(\lambda)+\right.$ $\eta(\lambda) \in \Omega$ 对于所有 $\lambda \in I}, 和C1(一世;R2)是定义在上的所有连续函数的规范线性空间一世他们的价值观在R2并且有连续的一阶导数一世,并由以下规范:|这|米=∑一世=1,2(最大限度λ∈一世|这一世(λ)|+最大限度λ∈一世|这一世′(λ)|), 在哪里(⋅)′表示相对于λ.

robotics代写|寻路算法代写Path Planning Algorithms|Numerical Algorithms

为了促进最优路径规划问题的数值算法的开发,在Ω使用标准方法(例如 Delaunay 三角剖分)建立。然后GF由多面体表面近似G^F,特别是由三角形贴片形成的表面。在实际情况下,函数F=F(X)通常以数值数据的形式给出。一个近似值GF可以通过给定数值数据的插值获得。在这里,为近似问题开发了算法4.1和4.2直接使用数值数据。
对于最短路径问题 4.1,考虑线段的最简单情况大号连接端点X这和XF在于Ω. 评论4.4建议一种可能的方法来获得近似问题的解决方案4.1是首先寻找有限数量的点大号具有最大的能见度,然后引入接近的附加点大号以实现完全可见性。最后,构造一条通过所有观测点的长度最短的若尔当弧。

假设在Ω, 由点组成的网格X(ķ),ķ=1,…,米连同近似曲面G^F由三角形斑块形成。为方便起见,让X(1)=X这和X(米)=XF. 让G^表示连接的所有 Jordan 弧的集合X(1)和X(米)由对应于三角形边缘的线段组成。我们算法中用于确定近似问题的最佳路径的基本步骤4.1不假设线段大号加入X这和XF在于Ω如下面所述:

步骤 3 确定\hat{\mathcal{G}}^{}=\left{\Gamma_{j}^{}, j=1, \ldots, K\right}\hat{\mathcal{G}}^{}=\left{\Gamma_{j}^{}, j=1, \ldots, K\right}, 中所有 Jordan 弧的集合G^具有最短的路径长度。
步骤 4 选择路径G^, 说Γ一世.
步骤 5 计算可见集在((X(ķ),FH在(X(ķ))))对应每个点X(ķ)沿着路径Γ一世及其投影圆周率Ω在((X(ķ),FH在(X(ķ)))). Step 6 判断是否存在点组合X(ķ)沿着Γ一世这样它们的可见集的并集在((X(ķ),FH在(X(ķ))))等于GF.
如果是,那么Γ一世是近似问题 4.1,STOP 的最优路径;如果否,则选择相邻路径Γ一世在弧长的意义上,和 GO TO Step5.

评论4.5在步骤 2 和 3 中,而不是考虑三角形Ω,我们可以考虑与表面的多面体近似相关的三角形补丁GF. 用于计算最短弧长的有效算法,例如 Sharir 和 Shorr [3]、O’Rourke 等人的算法。[4] 和 Lawler [5] 可以使用。

评论4.6第 5 步涉及计算可见集在((X(ķ),FHX(X(ķ))))与点相关X(ķ)沿着路径Γ一世∗,计算几何中的一个 NP-hard 问题。这项任务可以使用 Balmes 和 Wang [1] 最近开发的合适算法来完成。该算法的复杂度是这(np2), 在哪里n和p分别是观察点的数量和三角形贴片的数量。该算法可以很容易地修改以考虑相机或传感器的有限孔径。

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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。



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