Finding the recurrence equations of a function - recurrence

I have to find the recurrence equations of the following function:
static int f(int[] a, int inf, int sup) {
if(sup == inf)
return a[inf];
if(sup == inf+1)
return a[inf] + a[sup];
else {
int thrd = (sup - inf + 1)/3;
int i = inf + thrd;
int j = i + thrd;
int sum = 0;
for(int k = i; k < j; k++)
sum += a[k];
return f(a, inf, i-1) + f(a, j, sup) + sum;
}
}
The base case is T(1) = 1 (from if(sup == inf) to sum += a[k];).
Instead the recursive case what is? I would say T(n) = 2T(n/3) + 1 but I'm not sure..
Thanks

Below is the cost for each line of your recursive case
static int f(int[] a, int inf, int sup) {
if(sup == inf)
return a[inf];
if(sup == inf+1)
return a[inf] + a[sup];
else {
int thrd = (sup - inf + 1)/3; //O(1)
int i = inf + thrd; //O(1)
int j = i + thrd; //O(1)
int sum = 0; //O(1)
for(int k = i; k < j; k++) sum += a[k]; //O(n/3)
return f(a, inf, i-1) + f(a, j, sup) + sum; //2 * T(n/3)
}
}
The O(n/3) comes from the fact that your for loop is iterating over one third of your input size, and the 2 * T(n/3) term comes from the fact that we are recursing on one third of the input size twice. This gives us
T(n) = O(1) + O(1) + O(1) + O(1) + O(n/3) + 2 * T(n/3)
Since O(1) + O(1) is still O(1), the first 4 O(1)'s collapse into a single term, and O(n/3) is the same as O(n), we are left with
T(n) = 2T(n/3) + O(n) + O(1)

Related

How to transform DCT block back to color values?

So I am trying to use this
https://www.nayuki.io/res/fast-discrete-cosine-transform-algorithms/NaiveDct.cs
in my image processing assignment, in which we are supposed to apply DCT on an a picture. (8x8 block)
static public double[,] Dct(double[,] array)
{
double[,] dct = new double[N, M];
double factor = Math.PI / (N * M);
//dct
for (int i = 0; i < M; i++)
{
for (int j = 0; j < N; j++)
{
double sum = 0;
for (int k = 0; k < M; k++)
{
for (int l = 0; l < N; l++)
{
sum += array[k, l] * Math.Cos((k * M + l + 0.5) * (i * M + j) * factor);
}
}
dct[i, j] = (int) sum;
}
}
return dct;
}
This is the method I use for the forward transformation.
Results on an 8x8 block look like this
But trying to restore the "color block" (in this case it was used on the "blue" values of an rgb color).
With this code:
static public double[,] inverseDct(double[,] array)
{
double[,] colorBlock = new double[N, M];
double factor = Math.PI / (N * M);
//dct
for (int i = 0; i < M; i++)
{
for (int j = 0; j < N; j++)
{
double sum = array[0, 0] / 2;
for (int k = 0; k < M; k++)
{
int l = 0;
if (k == 0) l = 1;
for (; l < N; l++)
{
sum += array[k, l] * Math.Cos((k * M + l) * ((i * M + j) + 0.5) * factor);
}
}
colorBlock[i, j] = (int) sum;
}
}
return colorBlock;
}
It doesn't seem to work properly because the output of (the blue color value block in the picture above) now says this:
I posted my entire code here:
https://pastebin.com/XbCE3kBK
How do I get back my "color" values from the DCT Block? (doing the reverse transformation?)

Implementation of LASSO in C

I am trying to understand the LASSO algorithm for linear regression. I have implemented the algorithm using naive coordinate descent method for optimization. However the coefficients that I obtained from my code, wasn't matching with those obtained from the 'glmnet'package for LASSO in R. I wanted to understand how I could make the algorithm more accurate, so that the coefficients match with those obtained from R. I think they use coordinate descent as well.
Note: I have generated some toy data with 11 observations, and 6
features(x,x^2 ,x^3,...,x^6). The last column contains the y values
generated from a dummy function (e^(-x^2)). I wanted to use LASSO to
estimate this function. Also, I have randomly picked the initial
weight vector, multiple times to crosscheck my results.
Here is my code:
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<time.h>
int num_dim = 6;
int num_obs = 11;
/*Computes the normalization factor*/
float norm_feature(int j,double arr[][7],int n){
float sum = 0.0;
int i;
for(i=0;i<n;i++){
sum = sum + pow(arr[i][j],2);
}
return sum;
}
/*Computes the partial sum*/
float approx(int dim,int d_ignore,float weights[],double arr[][7],int
i){
int flag = 1;
if(d_ignore == -1)
flag = 0;
int j;
float sum = 0.0;
for(j=0;j<dim;j++){
if(j != d_ignore)
sum = sum + weights[j]*arr[i][j];
else
continue;
}
return sum;
}
/* Computes rho-j */
float rho_j(double arr[][7],int n,int j,float weights[7]){
float sum = 0.0;
int i;
float partial_sum ;
for(i=0;i<n;i++){
partial_sum = approx(num_dim,j,weights,arr,i);
sum = sum + arr[i][j]*(arr[i][num_dim]-partial_sum);
}
return sum;
}
float intercept(float arr1[7],double arr[][7],int dim) {
int i;
float sum =0.0;
for (i = 0; i < num_obs; i++) {
sum = sum + pow((arr[i][num_dim]) - approx(num_dim, -1, arr1, arr,
i), 1);
}
return sum;
}
int main(){
double data[num_obs][7];
int i=0,j=0;
float a = 1.0;
float lambda = 0.1; //Setting lambda
float weights[7]; //weights[6] contains the intercept
srand((unsigned int) time(NULL));
/*Generating the data matrix */
for(i=0;i<11;i++)
data[i][0] = ((float)rand()/(float)(RAND_MAX)) * a;
for(i=0;i<11;i++)
for(j=1;j<6;j++)
data[i][j] = pow(data[i][0],j+1);
for(i=0;i<11;i++)
data[i][6] = exp(-pow(data[i][0],2)); // the last column in the
datamatrix contains the y values generated by the dummy function
/*Printing the data matrix */
printf("Data Matrix:\n");
for(i=0;i<11;i++){
for(j=0;j<7;j++){
printf("%lf ",data[i][j]);}
printf("\n");}
printf("\n");
int seed =0;
while(seed<20) {
//Initializing the weight vector
for (i = 0; i < 7; i++)
weights[i] = ((float) rand() / (float) (RAND_MAX)) * a;
int iter = 500;
int t = 0;
int r, l;
double rho[num_dim];
for (i = 0; i < 6; i++) {
rho[i] = rho_j(data, num_obs, r, weights);
}
// Intercept initialization
weights[num_dim] = intercept(weights,data,num_dim);
printf("Weights initialization: ");
for (i = 0; i < (num_dim+1); i++)
printf("%f ", weights[i]);
printf("\n");
while (t < iter) {
for (r = 0; r < num_dim; r++) {
rho[r] = rho_j(data, num_obs, r, weights);
//printf("rho %d:%f ",r,rho[r]);
if (rho[r] < -lambda / 2)
weights[r] = (rho[r] + lambda / 2) / norm_feature(r,
data, num_obs);
else if (rho[r] > lambda / 2)
weights[r] = (rho[r] - lambda / 2) / norm_feature(r,
data, num_obs);
else
weights[r] = 0;
weights[num_dim] = intercept(weights, data, num_dim);
}
/* printf("Iter(%d): ", t);
for (l = 0; l < 7; l++)
printf("%f ", weights[l]);
printf("\n");*/
t++;
}
//printf("\n");
printf("Final Weights: ");
for (i = 0; i < 7; i++)
printf("%f ", weights[i]);
printf("\n");
printf("\n");
seed++;
}
return 0;
}
PseudoCode:

Accessing global memory in CUDA is slow

I have a CUDA kernel doing some computation on a local variable (in register), and after it gets computed, its value gets written into a global array p:
__global__ void dd( float* p, int dimX, int dimY, int dimZ )
{
int
i = blockIdx.x*blockDim.x + threadIdx.x,
j = blockIdx.y*blockDim.y + threadIdx.y,
k = blockIdx.z*blockDim.z + threadIdx.z,
idx = j*dimX*dimY + j*dimX +i;
if (i >= dimX || j >= dimY || k >= dimZ)
{
return;
}
float val = 0;
val = SomeComputationOnVal();
p[idx ]= val;
__syncthreads();
}
Unfortunately, this function executes very slow.
However, it runs very fast if I do this:
__global__ void dd( float* p, int dimX, int dimY, int dimZ )
{
int
i = blockIdx.x*blockDim.x + threadIdx.x,
j = blockIdx.y*blockDim.y + threadIdx.y,
k = blockIdx.z*blockDim.z + threadIdx.z,
idx = j*dimX*dimY + j*dimX +i;
if (i >= dimX || j >= dimY || k >= dimZ)
{
return;
}
float val = 0;
//val = SomeComputationOnVal();
p[idx ]= val;
__syncthreads();
}
It also runs very fast if I do this:
__global__ void dd( float* p, int dimX, int dimY, int dimZ )
{
int
i = blockIdx.x*blockDim.x + threadIdx.x,
j = blockIdx.y*blockDim.y + threadIdx.y,
k = blockIdx.z*blockDim.z + threadIdx.z,
idx = j*dimX*dimY + j*dimX +i;
if (i >= dimX || j >= dimY || k >= dimZ)
{
return;
}
float val = 0;
val = SomeComputationOnVal();
// p[idx ]= val;
__syncthreads();
}
So I am confused, and have no idea how to solve this problem. I have used NSight step in, and did not find access violations.
Here is how I launch the kernel (dimX:924; dimY: 16: dimZ: 1120):
dim3
blockSize(8,16,2),
gridSize(dimX/blockSize.x+1,dimY/blockSize.y, dimZ/blockSize.z);
float* dev_p; cudaMalloc((void**)&dev_p, dimX*dimY*dimZ*sizeof(float));
dd<<<gridSize, blockSize>>>( dev_p,dimX,dimY,dimZ);
Could anyone please gives some pointers? Because it does not make much sense to me. All computation of val is fast, and the final step is to move val into p. p never gets involved in the computation, and it only shows up once. So why is it so slow?
The computations are basically a loop over a 512 X 512 matrix. It is pretty fair amount of computation I'd say.
The computations you perform in the SomeComputationOnVal are extremely expensive. Each thread reads at least 1MB of data which is off cache (or in L2 at best for a small part should k vary in a small range) which totals for your run about 16 TB of data. Even on a high end gpu, it would take about 2 minutes to run, at the minimum. Not to mention everything that could slow this down.
Your function does not write any data in global memory and has no boundary effect. The compiler may decide to optimize out the method call should you not use the output.
Hence cases two and three not doing calculation are very fast. Writing 64 MB on gpu memory, with coesced threads is very fast (milliseconds range).
You can verify the generated ptx to see if code gets optimized out. Use the --keep option in nvcc and search for ptx files.

Multi otsu(multi-thresholding) with openCV

I am trying to carry out multi-thresholding with otsu. The method I am using currently is actually via maximising the between class variance, I have managed to get the same threshold value given as that by the OpenCV library. However, that is just via running otsu method once.
Documentation on how to do multi-level thresholding or rather recursive thresholding is rather limited. Where do I do after obtaining the original otsu's value? Would appreciate some hints, I been playing around with the code, adding one external for loop, but the next value calculated is always 254 for any given image:(
My code if need be:
//compute histogram first
cv::Mat imageh; //image edited to grayscale for histogram purpose
//imageh=image; //to delete and uncomment below;
cv::cvtColor(image, imageh, CV_BGR2GRAY);
int histSize[1] = {256}; // number of bins
float hranges[2] = {0.0, 256.0}; // min andax pixel value
const float* ranges[1] = {hranges};
int channels[1] = {0}; // only 1 channel used
cv::MatND hist;
// Compute histogram
calcHist(&imageh, 1, channels, cv::Mat(), hist, 1, histSize, ranges);
IplImage* im = new IplImage(imageh);//assign the image to an IplImage pointer
IplImage* finalIm = cvCreateImage(cvSize(im->width, im->height), IPL_DEPTH_8U, 1);
double otsuThreshold= cvThreshold(im, finalIm, 0, 255, cv::THRESH_BINARY | cv::THRESH_OTSU );
cout<<"opencv otsu gives "<<otsuThreshold<<endl;
int totalNumberOfPixels= imageh.total();
cout<<"total number of Pixels is " <<totalNumberOfPixels<< endl;
float sum = 0;
for (int t=0 ; t<256 ; t++)
{
sum += t * hist.at<float>(t);
}
cout<<"sum is "<<sum<<endl;
float sumB = 0; //sum of background
int wB = 0; // weight of background
int wF = 0; //weight of foreground
float varMax = 0;
int threshold = 0;
//run an iteration to find the maximum value of the between class variance(as between class variance shld be maximise)
for (int t=0 ; t<256 ; t++)
{
wB += hist.at<float>(t); // Weight Background
if (wB == 0) continue;
wF = totalNumberOfPixels - wB; // Weight Foreground
if (wF == 0) break;
sumB += (float) (t * hist.at<float>(t));
float mB = sumB / wB; // Mean Background
float mF = (sum - sumB) / wF; // Mean Foreground
// Calculate Between Class Variance
float varBetween = (float)wB * (float)wF * (mB - mF) * (mB - mF);
// Check if new maximum found
if (varBetween > varMax) {
varMax = varBetween;
threshold = t;
}
}
cout<<"threshold value is: "<<threshold;
To extend Otsu's thresholding method to multi-level thresholding the between class variance equation becomes:
Please check out Deng-Yuan Huang, Ta-Wei Lin, Wu-Chih Hu, Automatic
Multilevel Thresholding Based on Two-Stage Otsu's Method with Cluster
Determination by Valley Estimation, Int. Journal of Innovative
Computing, 2011, 7:5631-5644 for more information.
http://www.ijicic.org/ijicic-10-05033.pdf
Here is my C# implementation of Otsu Multi for 2 thresholds:
/* Otsu (1979) - multi */
Tuple < int, int > otsuMulti(object sender, EventArgs e) {
//image histogram
int[] histogram = new int[256];
//total number of pixels
int N = 0;
//accumulate image histogram and total number of pixels
foreach(int intensity in image.Data) {
if (intensity != 0) {
histogram[intensity] += 1;
N++;
}
}
double W0K, W1K, W2K, M0, M1, M2, currVarB, optimalThresh1, optimalThresh2, maxBetweenVar, M0K, M1K, M2K, MT;
optimalThresh1 = 0;
optimalThresh2 = 0;
W0K = 0;
W1K = 0;
M0K = 0;
M1K = 0;
MT = 0;
maxBetweenVar = 0;
for (int k = 0; k <= 255; k++) {
MT += k * (histogram[k] / (double) N);
}
for (int t1 = 0; t1 <= 255; t1++) {
W0K += histogram[t1] / (double) N; //Pi
M0K += t1 * (histogram[t1] / (double) N); //i * Pi
M0 = M0K / W0K; //(i * Pi)/Pi
W1K = 0;
M1K = 0;
for (int t2 = t1 + 1; t2 <= 255; t2++) {
W1K += histogram[t2] / (double) N; //Pi
M1K += t2 * (histogram[t2] / (double) N); //i * Pi
M1 = M1K / W1K; //(i * Pi)/Pi
W2K = 1 - (W0K + W1K);
M2K = MT - (M0K + M1K);
if (W2K <= 0) break;
M2 = M2K / W2K;
currVarB = W0K * (M0 - MT) * (M0 - MT) + W1K * (M1 - MT) * (M1 - MT) + W2K * (M2 - MT) * (M2 - MT);
if (maxBetweenVar < currVarB) {
maxBetweenVar = currVarB;
optimalThresh1 = t1;
optimalThresh2 = t2;
}
}
}
return new Tuple(optimalThresh1, optimalThresh2);
}
And this is the result I got by thresholding an image scan of soil with the above code:
(T1 = 110, T2 = 147).
Otsu's original paper: "Nobuyuki Otsu, A Threshold Selection Method
from Gray-Level Histogram, IEEE Transactions on Systems, Man, and
Cybernetics, 1979, 9:62-66" also briefly mentions the extension to
Multithresholding.
https://engineering.purdue.edu/kak/computervision/ECE661.08/OTSU_paper.pdf
Hope this helps.
Here is a simple general approach for 'n' thresholds in python (>3.0) :
# developed by- SUJOY KUMAR GOSWAMI
# source paper- https://people.ece.cornell.edu/acharya/papers/mlt_thr_img.pdf
import cv2
import numpy as np
import math
img = cv2.imread('path-to-image')
img = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
a = 0
b = 255
n = 6 # number of thresholds (better choose even value)
k = 0.7 # free variable to take any positive value
T = [] # list which will contain 'n' thresholds
def sujoy(img, a, b):
if a>b:
s=-1
m=-1
return m,s
img = np.array(img)
t1 = (img>=a)
t2 = (img<=b)
X = np.multiply(t1,t2)
Y = np.multiply(img,X)
s = np.sum(X)
m = np.sum(Y)/s
return m,s
for i in range(int(n/2-1)):
img = np.array(img)
t1 = (img>=a)
t2 = (img<=b)
X = np.multiply(t1,t2)
Y = np.multiply(img,X)
mu = np.sum(Y)/np.sum(X)
Z = Y - mu
Z = np.multiply(Z,X)
W = np.multiply(Z,Z)
sigma = math.sqrt(np.sum(W)/np.sum(X))
T1 = mu - k*sigma
T2 = mu + k*sigma
x, y = sujoy(img, a, T1)
w, z = sujoy(img, T2, b)
T.append(x)
T.append(w)
a = T1+1
b = T2-1
k = k*(i+1)
T1 = mu
T2 = mu+1
x, y = sujoy(img, a, T1)
w, z = sujoy(img, T2, b)
T.append(x)
T.append(w)
T.sort()
print(T)
For full paper and more informations visit this link.
I've written an example on how otsu thresholding work in python before. You can see the source code here: https://github.com/subokita/Sandbox/blob/master/otsu.py
In the example there's 2 variants, otsu2() which is the optimised version, as seen on Wikipedia page, and otsu() which is more naive implementation based on the algorithm description itself.
If you are okay in reading python codes (in this case, they are pretty simple, almost pseudo code like), you might want to look at otsu() in the example and modify it. Porting it to C++ code is not hard either.
#Antoni4 gives the best answer in my opinion and it's very straight forward to increase the number of levels.
This is for three-level thresholding:
#include "Shadow01-1.cuh"
void multiThresh(double &optimalThresh1, double &optimalThresh2, double &optimalThresh3, cv::Mat &imgHist, cv::Mat &src)
{
double W0K, W1K, W2K, W3K, M0, M1, M2, M3, currVarB, maxBetweenVar, M0K, M1K, M2K, M3K, MT;
unsigned char *histogram = (unsigned char*)(imgHist.data);
int N = src.rows*src.cols;
W0K = 0;
W1K = 0;
M0K = 0;
M1K = 0;
MT = 0;
maxBetweenVar = 0;
for (int k = 0; k <= 255; k++) {
MT += k * (histogram[k] / (double) N);
}
for (int t1 = 0; t1 <= 255; t1++)
{
W0K += histogram[t1] / (double) N; //Pi
M0K += t1 * (histogram[t1] / (double) N); //i * Pi
M0 = M0K / W0K; //(i * Pi)/Pi
W1K = 0;
M1K = 0;
for (int t2 = t1 + 1; t2 <= 255; t2++)
{
W1K += histogram[t2] / (double) N; //Pi
M1K += t2 * (histogram[t2] / (double) N); //i * Pi
M1 = M1K / W1K; //(i * Pi)/Pi
W2K = 1 - (W0K + W1K);
M2K = MT - (M0K + M1K);
if (W2K <= 0) break;
M2 = M2K / W2K;
W3K = 0;
M3K = 0;
for (int t3 = t2 + 1; t3 <= 255; t3++)
{
W2K += histogram[t3] / (double) N; //Pi
M2K += t3 * (histogram[t3] / (double) N); // i*Pi
M2 = M2K / W2K; //(i*Pi)/Pi
W3K = 1 - (W1K + W2K);
M3K = MT - (M1K + M2K);
M3 = M3K / W3K;
currVarB = W0K * (M0 - MT) * (M0 - MT) + W1K * (M1 - MT) * (M1 - MT) + W2K * (M2 - MT) * (M2 - MT) + W3K * (M3 - MT) * (M3 - MT);
if (maxBetweenVar < currVarB)
{
maxBetweenVar = currVarB;
optimalThresh1 = t1;
optimalThresh2 = t2;
optimalThresh3 = t3;
}
}
}
}
}
#Guilherme Silva
Your code has a BUG
You Must Replace:
W3K = 0;
M3K = 0;
with
W2K = 0;
M2K = 0;
and
W3K = 1 - (W1K + W2K);
M3K = MT - (M1K + M2K);
with
W3K = 1 - (W0K + W1K + W2K);
M3K = MT - (M0K + M1K + M2K);
;-)
Regards
EDIT(1): [Toby Speight]
I discovered this bug by applying the effect to the same picture at different resoultions(Sizes) and seeing that the output results were to much different from each others (Even changing resolution a little bit)
W3K and M3K must be the totals minus the Previous WKs and MKs.
(I thought about this for Code-similarity with the one with one level less)
At the moment due to my lacks of English I cannot explain Better How and Why
To be honest I'm still not 100% sure that this way is correct, even thought from my outputs I could tell that it gives better results. (Even with 1 Level more (5 shades of gray))
You could try yourself ;-)
Sorry
My Outputs:
3 Thresholds
4 Thresholds
I found a useful piece of code in this thread. I was looking for a multi-level Otsu implementation for double/float images. So, I tried to generalize example for N-levels with double/float matrix as input. In my code below I am using armadillo library as dependency. But this code can be easily adapted for standard C++ arrays, just replace vec, uvec objects with single dimensional double and integer arrays, mat and umat with two-dimensional. Two other functions from armadillo used here are: vectorise and hist.
// Input parameters:
// map - input image (double matrix)
// mask - region of interest to be thresholded
// nBins - number of bins
// nLevels - number of Otsu thresholds
#include <armadillo>
#include <algorithm>
#include <vector>
mat OtsuFilterMulti(mat map, int nBins, int nLevels) {
mat mapr; // output thresholded image
mapr = zeros<mat>(map.n_rows, map.n_cols);
unsigned int numElem = 0;
vec threshold = zeros<vec>(nLevels);
vec q = zeros<vec>(nLevels + 1);
vec mu = zeros<vec>(nLevels + 1);
vec muk = zeros<vec>(nLevels + 1);
uvec binv = zeros<uvec>(nLevels);
if (nLevels <= 1) return mapr;
numElem = map.n_rows*map.n_cols;
uvec histogram = hist(vectorise(map), nBins);
double maxval = map.max();
double minval = map.min();
double odelta = (maxval - abs(minval)) / nBins; // distance between histogram bins
vec oval = zeros<vec>(nBins);
double mt = 0, variance = 0.0, bestVariance = 0.0;
for (int ii = 0; ii < nBins; ii++) {
oval(ii) = (double)odelta*ii + (double)odelta*0.5; // centers of histogram bins
mt += (double)ii*((double)histogram(ii)) / (double)numElem;
}
for (int ii = 0; ii < nLevels; ii++) {
binv(ii) = ii;
}
double sq, smuk;
int nComb;
nComb = nCombinations(nBins,nLevels);
std::vector<bool> v(nBins);
std::fill(v.begin(), v.begin() + nLevels, true);
umat ibin = zeros<umat>(nComb, nLevels); // indices from combinations will be stored here
int cc = 0;
int ci = 0;
do {
for (int i = 0; i < nBins; ++i) {
if(ci==nLevels) ci=0;
if (v[i]) {
ibin(cc,ci) = i;
ci++;
}
}
cc++;
} while (std::prev_permutation(v.begin(), v.end()));
uvec lastIndex = zeros<uvec>(nLevels);
// Perform operations on pre-calculated indices
for (int ii = 0; ii < nComb; ii++) {
for (int jj = 0; jj < nLevels; jj++) {
smuk = 0;
sq = 0;
if (lastIndex(jj) != ibin(ii, jj) || ii == 0) {
q(jj) += double(histogram(ibin(ii, jj))) / (double)numElem;
muk(jj) += ibin(ii, jj)*(double(histogram(ibin(ii, jj)))) / (double)numElem;
mu(jj) = muk(jj) / q(jj);
q(jj + 1) = 0.0;
muk(jj + 1) = 0.0;
if (jj>0) {
for (int kk = 0; kk <= jj; kk++) {
sq += q(kk);
smuk += muk(kk);
}
q(jj + 1) = 1 - sq;
muk(jj + 1) = mt - smuk;
mu(jj + 1) = muk(jj + 1) / q(jj + 1);
}
if (jj>0 && jj<(nLevels - 1)) {
q(jj + 1) = 0.0;
muk(jj + 1) = 0.0;
}
lastIndex(jj) = ibin(ii, jj);
}
}
variance = 0.0;
for (int jj = 0; jj <= nLevels; jj++) {
variance += q(jj)*(mu(jj) - mt)*(mu(jj) - mt);
}
if (variance > bestVariance) {
bestVariance = variance;
for (int jj = 0; jj<nLevels; jj++) {
threshold(jj) = oval(ibin(ii, jj));
}
}
}
cout << "Optimized thresholds: ";
for (int jj = 0; jj<nLevels; jj++) {
cout << threshold(jj) << " ";
}
cout << endl;
for (unsigned int jj = 0; jj<map.n_rows; jj++) {
for (unsigned int kk = 0; kk<map.n_cols; kk++) {
for (int ll = 0; ll<nLevels; ll++) {
if (map(jj, kk) >= threshold(ll)) {
mapr(jj, kk) = ll+1;
}
}
}
}
return mapr;
}
int nCombinations(int n, int r) {
if (r>n) return 0;
if (r*2 > n) r = n-r;
if (r == 0) return 1;
int ret = n;
for( int i = 2; i <= r; ++i ) {
ret *= (n-i+1);
ret /= i;
}
return ret;
}

text parsing to XML using JDOM

I an newbee need you your help.
I am converting a text in to XML (with some extra attributes)
my text is
SPLINE(N, -1.151,1.002, -0.161,0.997, 0.840,-0.004, OUTLINED)
i need to have in XML using JDOM like following
<SPLINE n="3" x1="0.840" y1="-1.004" x2 ="-0.161" y2 ="0.997" x3 ="0.840" y3"-0.004" prim_style="OUTLINED" />
I can convert simply if N is fixed , in the above example N= 3 , so therefore has 3 x and 3 y coordinates. But If I am using for loop as below the result is not as excepted . any help will be great
root.addContent(child);
document.setContent(root);
int i = Integer.parseInt(temp_token[2]);
int count = i * 2 + i + 4;
for (int j = 0; j <= count - 5; j = j + 3) {
String x = null;
String y = null;
Element SPLINE = new Element("SPLINE")
.setAttribute("n", temp_token[2])
.setAttribute("x", temp_token[j + 4])
.setAttribute("y", temp_token[j + 5])
.setAttribute("prim_style",
temp_token[count]);
child.addContent(SPLINE);
From the above code
You should not be creating the SPLINE element inside the loop, it should be outside... (and variable names should be lowercase)
root.addContent(child);
document.setContent(root);
int i = Integer.parseInt(temp_token[2]);
int count = i * 2 + i + 4;
Element spline = new Element("SPLINE");
child.addContent(SPLINE);
spline.setAttribute("n", temp_token[2]);
int pair = 0;
for (int j = 0; j <= count - 5; j = j + 3) {
pair++;
spline.setAttribute("x" + pair, temp_token[j + 4]);
spline.setAttribute("y" + pair, temp_token[j + 5]);
}
spline.setAttribute("prim_style",temp_token[count]);

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