任意维度的向量vector都用粗体的小写字母表示:a,b,u,v,q,r 矩阵matrix都用大写的粗体字母表示A,B,M,R 其他作者可能会使用不同的标准。一个比较通用的标准是,在手写向量时在向量上方画一个箭头,比如a→ 数学中有一个专门研究向量和矩阵的分支,叫做线性代数linear algebra,其中就给出了前面的定义:向量就是...
defmatrix_dot_vector_unrolled(a,b):result=[]b_len=len(b)# 确保数组长度至少为1ifb_len<1:returnresultforrowina:dot=0i=0# 根据数组长度选择合适的展开方式ifb_len>=4:# 主循环每次处理4个元素foriinrange(0,b_len-3,4):dot+=(row[i]*b[i]+row[i+1]*b[i+1]+row[i+2]*b[i+2]+r...
二、数组array:多维的同一类型集合(字符型、数值型、逻辑型、复数型),R可以很容易地生成和处理数组,特别是矩阵matrix是一个二维数组。 1.可以通过定义dim(维度)将向量变成matrix。 a=c(1,3,4,5,6,7,8,9,3) > dim(a)=c(3,3) > a [,1] [,2] [,3] [1,] 1 5 8 [2,] 3 6 9 [3,] ...
A vector can be "scaled" off the unit vector. Here vector a is shown to be 2.5 times a unit vector. Notice they still point in the same direction:In 2 DimensionsUnit vectors can be used in 2 dimensions:Here we show that the vector a is made up of 2 "x" unit vectors and 1.3 "...
另外,维度属性(dim)可以让 atomic vector 转换为 matrix 或者 array 对象,有意思的是即使是List也可以通过增加dim属性转换成 list-matirx;增加class属性则会形成 S3 对象,关于 S3 对象我们后面会有推文专门详细讲解,最重要的几种 S3 对象包括:factor,date,times,data frame和tibble。下面两张示意图展示了向量和 ...
to handle cubic curves as well. This is significantly more complicated than the quadratic case, because of the procedural texture-coordinate-assignment phase. However, it should be possible to do this entirely on the GPU using DirectX 10-class hardware equipped with a geometry shader (Blythe 2...
或许可以这么理解，a,b和x,y之间的对偶，是因为它们处于更大的系统之中。跟着马同学，看图学数学，欢迎...
this stage, so we need to remove it.noTransViewMatrix.SetColumn(3,newVector4(0,0,0,1));}vargpuVPNoTrans=gpuNonJitteredProj*noTransViewMatrix;// A camera can be rendered multiple times in a single frame with different resolution/fov that would change the projection matrix// In this case...
We review the dimensional check problem of the high-level programming languages, discuss the existing solutions, and come up with a new solution suited for scientific and engineering computations. Then, we introduce Univec, our C++ library designed to make scalar, vector, and matrix operations using...
或许可以这么理解，a,b和x,y之间的对偶，是因为它们处于更大的系统之中。跟着马同学，看图学数学，欢迎...