Description The modular modular multiplicative inverse of an integer a modulo m is an integer x such that a-1≡x (mod m). This is equivalent toax≡1 (mod m). Input There are multiple test cases. The first line of input is an integer T ≍ 2000 indicating…
There are two ways of using the Jacobian matrix to solve kinematics. One is to use the transpose of the Jacobian JT. The other is to calculate the inverse of the Jacobian J-1. J is most likely redundant and non square,thus an ordinary inverse is not…
Given two integers n and k, find how many different arrays consist of numbers from 1 to n such that there are exactly k inverse pairs. We define an inverse pair as following: For ith and jthelement in the array, if i < j and a[i] > a[j] then it's an…
http://mathworld.wolfram.com/Moore-PenroseMatrixInverse.html 显然,埃尔米特矩阵主对角线上的元素都是实数的,其特征值也是实数.对于只包含实数元素的矩阵(实矩阵),如果它是对称阵,即所有元素关于主对角线对称,那么它也是埃尔米特矩阵.也就是说,实对称矩阵是埃尔米特矩阵的特例. https://en.wikipedia.org/wiki/Hermitian_matrix In mathematics, a Hermitian matrix (…
搞统计的线性代数和概率论必须精通,最好要能锻炼出直觉,再学机器学习才会事半功倍. 线性代数只推荐Prof. Gilbert Strang的MIT课程,有视频,有教材,有习题,有考试,一套学下来基本就入门了. 不多,一共10次课. 链接:https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/calendar/ SES # TOPICS KEY DATES 1 The geometry of linear e…
import numpy.matlib import numpy as np a = np.array([[1,2],[3,4]]) b = np.array([[11,12],[13,14]]) print(np.dot(a,b)) numpy.vdot() 函数是两个向量的点积. 如果第一个参数是复数,那么它的共轭复数会用于计算. 如果参数是多维数组,它会被展开. import numpy as np a = np.array([[1,2],[3,4]]) b = np.array([[11…
When performing inverse kinematics (IK) on a complicated bone chain, it can become too complex for an analytical solution. Cyclic Coordinate Descent (CCD) is an alternative that is both easy to implement and efficient to process.逆运动学问题一般采用解析法和基于Jacob…
The damped least squares method is also called the Levenberg-Marquardt method. Levenberg-Marquardt算法是最优化算法中的一种.它是使用最广泛的非线性最小二乘算法,具有梯度法和牛顿法的优点.当λ很小时,步长等于牛顿法步长,当λ很大时,步长约等于梯度下降法的步长. The damped least squares method can be theoretically justified as follo…
