matrices precalculus

Note: The article is translated from http://wgld.org/, the original author Sambonja 広 (doxas), the article if there is my additional instructions, I will add [Lufy:], in addition, The WEBGL research is not deep enough, some professional words, if the translation is wrong, you are welcome to correct. not to get you in front of the store .Lufy: You must be surprised, why call this topic, because the matrix in Japanese is called "the column", so the author makes a joke to the reader, I so direct tr

. The defect value is also counted in length.4.1.3 namingOne big feature of r vectors is the ability to name each element. In general, markup elements can make code more readable.x 4.1.4 Index VectorIn general, we only have to access parts or individual elements in the vector. This is the so-called index, which he implements with square brackets [].1. If you pass a positive number to a vector, it returns a vector element slice at this position. His first position was 1 (peer Python is 0)2. If yo

Matrix: A matrix is a mathematical model that is often used in numerical programming, which consists of a number of m rows and N columns (M=n is called a phalanx). In programs written in advanced languages, a two-dimensional array is usually used to represent the matrix, which enables each element in the matrix to find a corresponding storage location in a two-dimensional array. However, some high-order matrices with the following characteristics are

This article goes from a blog post.More detailed information can be downloaded from Baidu Cloud.For many sparse matrices with zero element, storing only non-0 elements makes the matrix operation more efficient. There are many ways to store sparse matrices, but most use the same basic technique, which is to store all non-0 elements of the matrix into a linear array, and provide auxiliary arrays to describe t

#include The result is:2 7 6 9 5 1 4 3 8 --------------------2 9 4 7 5 3 6 1 8 --------------------4 3 8 9 5 1 2 7 6 --------------------4 9 2 3 5 7 8 1 6 --------------------6 1 8 7 5 3 2 9 4 --------------------6 7 2 1 5 9 8 3 4 --------------------8 1 6 3 5 7 4 9 2 --------------------8 3 4 1 5

#include "stdafx.h" #include "stdio.h" #include "stdlib.h" #define max_vertex_num11 Maximum number of //vertices #defineinfinity32768 #define error0#defineok1typedef The type of enum{dg,dn,udg,udn}graphkind;//graph g represents a map, The DN indicates a NBSP;UDG, and the NBSP;UDN represents the non-direction network typedefcharvertexdata;typedefstructarcnode{ intadj;} arcnode;typedefstruct{vertexdatavexs[max_vertex_num]; //vertex Vector arcnodearcs[max_vertex_num][max_vertex_num];//adjacenc

]=null;}}void Main () {int row,col;//row and column numbercoutcin>>row>>col;Max (Row,col);}Results:Summary of Experience:The first is the failure to achieve the time complexity is O (n) requirements, design ideas are very important, with the idea can determine whether they can be done by code and how to complete, see the topic to have the overall solution of the idea, and on this basis, and constantly improve the idea, Rather than the idea of the world, but not the realization or implementation,

=* (* (array+k) +l); * (* (array+k) +l) = * (* (array+i) +l); * (* (array+i) +l) =temp; } Flag*=-1; b=1; Break; } } if(!b) {return 0; } I--; Continue; } for(; j1; j + +) { if(* (* (* (array+j+1) +i) = =0) Continue; Temp=-* (* (array+j+1) +i)/* (* (array+i) +i); for(k=i;k) * (* (array+j+1+K) + = * (* (array+i) +k) *temp; } } for(i=0; i) Sum*= * (* (array+i) +i); returnsum*Flag;}//Print ArrayvoidPrintfdoubl

) - if(ii+JJ) - for(intI=1; i+ (11) + for(intj=1; j+ (11) - { + if(ii) A { atDPMIN[I][J][II][JJ] = min (dpmin[i][j][ii-1][jj],dpmin[i+ (11))][j][ii-1][JJ]); -DPMAX[I][J][II][JJ] = max (dpmax[i][j][ii-1][jj],dpmax[i+ (11))][j][ii-1][JJ]); - } - Else - { -DPMIN[I][J][II][JJ] = min (dpmin[i][j][ii][jj-1],dpmin[i][j+ (11))][ii][jj-1]); inDPMAX[I][J][II][JJ] = max (dpmax[i][j][ii][jj-1],dpmax[i][j+ (11))][ii][jj-1]); - } to } + } -

diagonal as a single matrix: 1, using Np.diag two times, and then use mat conversion back to the matrix: >>> D = np.diag (Np.diag (m))>>> Darray ([[1, 0, 0], 5, 0], 9]])>>> D = Np.mat (d)>>> Dmatrix ([[1, 0, 0], 5, 0], 9]) 2, the use of the lower triangular matrix minus the next triangle matrix (that is, the lower triangular array under the diagonal): >>> D = Np.tril (m)- L>>> Darray ([[[1, 0, 0] ,5, 0] ,9 ]])>>> D = Np.mat (d)>>> Dmatrix ([[1,

Chatting with classmates about their own writing a calculator, or even the kind of high-end calculators that can perform matrix operations, but the current level is not enough, so think of the first practice to write a matrix of multiplication applet:Let's go over it. Matrix multiplication is as follows: Now the train of thought some block, come back first think carefully again to write?? 2017-11-07 20:35:22#filename:matmultiplyM= [[1,1],[2,2]]n= [[2,2],[1,1]]p=[[0,0],[0,0]]#p[0][0] = m[0][0] *

Ideas A helical matrix is a spiral matrix whose number starts with the first line to the right, and the downward becomes larger,The left is bigger, the upward is bigger, and so the loop goes.The helical matrices are represented by two-dimensional arrays, coordinates (X,Y), i.e. (x-axis, y-coordinate).The clockwise spiral direction is-> right, down, left, on, with a numerical value that is x plus 1 lattice (1,0), Y plus 1 lattice (0,1), X minus 1 latt

In general, the Matrix A two or three power after it becomes 0, this class can be used for (AE−A) n (ae-a) ^n, only need to follow the two-key expansion, calculate the first few items. A=αtαa = \alpha^t\alpha, you can use: An=αt (Tumi) .... (tumi) αa^n = \alpha^t (\alpha\alpha^t) .... (\alpha\alpha^t) \alpha is a simplification, the middle is a number. In addition, a similar diagonal array of matrices can be used to solve the power-times. Three dire