I am testing example of the Magnus Effect for OpenFoam-9
https://drive.google.com/file/d/1J2rKIRU8DAZadORyjUfd6OBBcfR-9rLo/view?usp=sharing
What I got from https://holzmann-cfd.com/community/training-cases/magnus-effect
And it works fine:
But when I change STL object with shifted a little position in STL file then simulation is breaking
snappyHexMeshDict:
geometry
{
cylinder_x01y0z0.stl
{
type triSurfaceMesh;
name cylinder;
}
};
Please help to understand why a little position shifting in STL file breaks simulation.
Thank you in advance.
Try to change the code in 0.orig/U for your cylinder boundary condition as follows (See the comments):
cylinder
{
type codedFixedValue;
value uniform (0 0 0);
name myBC;
code
#{
const scalar time = this->db().time().value();
const fvPatch& boundaryPatch = patch();
const vectorField& Cf = boundaryPatch.Cf();
vectorField rot(Cf.size(), vector(0,0,0));
const vector CENTER(0.1,0.0, 0.0); // <<<< Add this line and add it below
const scalar rotate_speed_max = 10.0;
const scalar rotate_time_start = 0.0;
scalar rotate_speed = 0.5 * (time - rotate_time_start) * (time - rotate_time_start);
rotate_speed = rotate_speed > rotate_speed_max ? rotate_speed_max : rotate_speed;
//- Start motion of the wall after 15s
if (time > rotate_time_start)
{
rot = rotate_speed * vector(0,0,1) ^ (Cf- CENTER); //<<<< Added here
// std::cout << __func__ << ":" << __LINE__ << " rotate_speed=" << rotate_speed <<std::endl;
}
operator==(rot);
#};
}
Related
I have created a custom double point-type for storing the point position in the PCD file. I required the double data type since my points are in global coordinates and have very large values (of order 10^6 to 10^7) and require good precision. Since the values are large and the default FLOAT32 precision is limited, there is considerable data approximation which is also visible during visualization.
I created this PCD by transforming the raw pointcloud with the initial global reference coordinate from GPS in the data bag that I have. I am using a 15 point precision.
I created a separate script for visualizing this custom point-type PCD. But by visually comparing, I cannot see any considerable difference between the FLOAT32 and double data-type PCD's.
Raw_float_pcd_visualization
Transformed_float_pcd_visualization
Transformed_double_pcd_visualization
You can see that the transformed_double and transformed_float PCD's are quite similar and approximated. While the raw_float PCD is quite good as compared to these two.
I am attaching the PCD files for reference:
raw_float
transformed_float
transformed_double
I think that I am skipping some things while loading the pointcloud and there are some more changes that need to be done in order to visualize the points with double point precision.
I used "pcl_viewer" from pcl_tools for visualizing FLOAT type PCD's.
Code for visualizaing custom DOUBLE point-structure PCD:
#define PCL_NO_PRECOMPILE
#include <iostream>
// #include "double_viz/pcl_double.h"
#include <pcl-1.7/pcl/common/common.h>
#include <pcl-1.7/pcl/io/pcd_io.h>
#include <pcl-1.7/pcl/visualization/pcl_visualizer.h>
#include <pcl-1.7/pcl/console/parse.h>
#include <pcl-1.7/pcl/point_cloud.h>
#include <pcl-1.7/pcl/point_types.h>
namespace pcl
{
#define PCL_ADD_UNION_POINT4D_DOUBLE \
union EIGEN_ALIGN16 { \
double data[4]; \
struct { \
double x; \
double y; \
double z; \
}; \
};
struct _PointXYZDouble
{
PCL_ADD_UNION_POINT4D_DOUBLE; // This adds the members x,y,z which can also be accessed using the point (which is float[4])
EIGEN_MAKE_ALIGNED_OPERATOR_NEW
};
struct EIGEN_ALIGN16 PointXYZDouble : public _PointXYZDouble
{
inline PointXYZDouble (const _PointXYZDouble &p)
{
x = p.x; y = p.y; z = p.z; data[3] = 1.0;
}
inline PointXYZDouble ()
{
x = y = z = 0.0;
data[3] = 1.0;
}
inline PointXYZDouble (double _x, double _y, double _z)
{
x = _x; y = _y; z = _z;
data[3] = 1.0;
}
EIGEN_MAKE_ALIGNED_OPERATOR_NEW
};
}
POINT_CLOUD_REGISTER_POINT_STRUCT (pcl::_PointXYZDouble,
(double, x, x)
(double, y, y)
(double, z, z)
)
POINT_CLOUD_REGISTER_POINT_WRAPPER(pcl::PointXYZDouble, pcl::_PointXYZDouble)
// This function displays the help
void
showHelp(char * program_name)
{
std::cout << std::endl;
std::cout << "Usage: " << program_name << " cloud_filename.[pcd]" << std::endl;
std::cout << "-h: Show this help." << std::endl;
}
// This is the main function
int
main (int argc, char** argv)
{
// Show help
if (pcl::console::find_switch (argc, argv, "-h") || pcl::console::find_switch (argc, argv, "--help"))
{
showHelp (argv[0]);
return 0;
}
// Fetch point cloud filename in arguments | Works with PCD
std::vector<int> filenames;
if (filenames.size () != 1)
{
filenames = pcl::console::parse_file_extension_argument (argc, argv, ".pcd");
if (filenames.size () != 1)
{
showHelp (argv[0]);
return -1;
}
}
// Load file | Works with PCD and PLY files
pcl::PointCloud<pcl::PointXYZDouble>::Ptr source_cloud (new pcl::PointCloud<pcl::PointXYZDouble> ());
if (pcl::io::loadPCDFile (argv[filenames[0]], *source_cloud) < 0)
{
std::cout << "Error loading point cloud " << argv[filenames[0]] << std::endl << std::endl;
showHelp (argv[0]);
return -1;
}
// Visualization
// printf( "\nPoint cloud colors : white = original point cloud\n"
// " red = transformed point cloud\n");
pcl::visualization::PCLVisualizer viewer ("Visualize double PCL");
// Define R,G,B colors for the point cloud
pcl::visualization::PointCloudColorHandlerCustom<pcl::PointXYZDouble> source_cloud_color_handler (source_cloud, 100, 100, 100);
// We add the point cloud to the viewer and pass the color handler
viewer.addPointCloud (source_cloud, source_cloud_color_handler, "original_cloud");
viewer.addCoordinateSystem (1.0, "cloud", 0);
viewer.setBackgroundColor(0.05, 0.05, 0.05, 0); // Setting background to a dark grey
viewer.setPointCloudRenderingProperties (pcl::visualization::PCL_VISUALIZER_OPACITY, 1, "original_cloud");
viewer.setPointCloudRenderingProperties (pcl::visualization::PCL_VISUALIZER_POINT_SIZE, 1, "original_cloud");
viewer.setPointCloudRenderingProperties (pcl::visualization::PCL_VISUALIZER_LINE_WIDTH, 1, "original_cloud");
//viewer.setPosition(800, 400); // Setting visualiser window position
while (!viewer.wasStopped ()) // Display the visualiser until 'q' key is pressed
{
viewer.spinOnce ();
}
return 0;
}
In the raw_float file, the size field has been defined as 4 bytes each: SIZE 4 4 4 4,
to be read as double it should be SIZE 8 8 8 8.
With your current implementation each field is being read as Float32
I am implementing this neural network for some classification problem. I initially tried back propagation but it takes longer to converge. So I though of using RPROP. In my test setup RPROP works fine for AND gate simulation but never converges for OR and XOR gate simulation.
How and when should I update bias for RPROP?
Here my weight update logic:
for(int l_index = 1; l_index < _total_layers; l_index++){
Layer* curr_layer = get_layer_at(l_index);
//iterate through each neuron
for (unsigned int n_index = 0; n_index < curr_layer->get_number_of_neurons(); n_index++) {
Neuron* jth_neuron = curr_layer->get_neuron_at(n_index);
double change = jth_neuron->get_change();
double curr_gradient = jth_neuron->get_gradient();
double last_gradient = jth_neuron->get_last_gradient();
int grad_sign = sign(curr_gradient * last_gradient);
//iterate through each weight of the neuron
for(int w_index = 0; w_index < jth_neuron->get_number_of_weights(); w_index++){
double current_weight = jth_neuron->give_weight_at(w_index);
double last_update_value = jth_neuron->give_update_value_at(w_index);
double new_update_value = last_update_value;
if(grad_sign > 0){
new_update_value = min(last_update_value*1.2, 50.0);
change = sign(curr_gradient) * new_update_value;
}else if(grad_sign < 0){
new_update_value = max(last_update_value*0.5, 1e-6);
change = -change;
curr_gradient = 0.0;
}else if(grad_sign == 0){
change = sign(curr_gradient) * new_update_value;
}
//Update neuron values
jth_neuron->set_change(change);
jth_neuron->update_weight_at((current_weight + change), w_index);
jth_neuron->set_last_gradient(curr_gradient);
jth_neuron->update_update_value_at(new_update_value, w_index);
double current_bias = jth_neuron->get_bias();
jth_neuron->set_bias(current_bias + _learning_rate * jth_neuron->get_delta());
}
}
}
In principal you don't treat the bias differently than before when you did backpropagation. It's learning_rate * delta which you seem to be doing.
One source of error may be that the sign of the weight change depends on how you calculate your error. There's different conventions and (t_i-y_i) instead of (y_i - t_i) should result in returning (new_update_value * sgn(grad)) instead of -(new_update_value * sign(grad)) so try switching the sign. I'm also unsure about how you specifically implemented everything since a lot is not shown here. But here's a snippet of mine in a Java implementation that might be of help:
// gradient didn't change sign:
if(weight.previousErrorGradient * errorGradient > 0)
weight.lastUpdateValue = Math.min(weight.lastUpdateValue * step_pos, update_max);
// changed sign:
else if(weight.previousErrorGradient * errorGradient < 0)
{
weight.lastUpdateValue = Math.max(weight.lastUpdateValue * step_neg, update_min);
}
else
weight.lastUpdateValue = weight.lastUpdateValue; // no change
// Depending on language, you should check for NaN here.
// multiply this with -1 depending on your error signal's sign:
return ( weight.lastUpdateValue * Math.signum(errorGradient) );
Also, keep in mind that 50.0, 1e-6 and especially 0.5, 1.2 are empirically gathered values so they might need to be adjusted. You should definitely print out the gradients and weight changes to see if there's something weird going on (e.g. exploding gradients->NaN although you're only testing AND/XOR). Your last_gradient value should also be initialized to 0 at the first timestep.
For my doctoral thesis I am building a 3D printer based loosely off of one from the University of Twente:
http://pwdr.github.io/
So far, everything has gone relatively smoothly. The hardware part took longer than expected, but the electronics frighten me a little bit. I can sucessfully jog all the motors and, mechanically, everything does what is supposed to do.
However, now that I am working on the software side, I am getting headaches.
The Pwder people wrote a code that uses Processing to take an .STL file and slice it into layers. Upon running the code, a Processing GUI opens where I can load a model. The model loads fine (I'm using the Utah Teapot) and shows that it will take 149 layers.
Upon hitting "convert" the program is supposed to take the .STL file and slice it into layers, followed by writing a text file that I can then upload to an SD card. The printer will then print directly from the SD card.
However, when I hit "convert" I get an "Array Index Out of Bounds" error. I'm not quite sure what this means.. can anyone enlighten me?
The code can be found below, along with a picture of the error.
Thank you.
// Convert the graphical output of the sliced STL into a printable binary format.
// The bytes are read by the Arduino firmware
PrintWriter output, outputUpper;
int loc;
int LTR = 0;
int lowernozzles = 8;
int uppernozzles = 4;
int nozzles = lowernozzles+uppernozzles;
int printXcoordinate = 120+280; // Left margin 120
int printYcoordinate = 30+190; // Top margin 30
int printWidth = 120; // Total image width 650
int printHeight = 120; // Total image height 480
int layer_size = printWidth * printHeight/nozzles * 2;
void convertModel() {
// Create config file for the printer, trailing comma for convenience
output = createWriter("PWDR/PWDRCONF.TXT"); output.print(printWidth+","+printHeight/nozzles+","+maxSlices+","+inkSaturation+ ",");
output.flush();
output.close();
int index = 0;
byte[] print_data = new byte[layer_size * 2];
// Steps of 12 nozzles in Y direction
for (int y = printYcoordinate; y < printYcoordinate+printHeight; y=y+nozzles ) {
// Set a variable to know wheter we're moving LTR of RTL
LTR++;
// Step in X direction
for (int x = 0; x < printWidth; x++) {
// Clear the temp strings
String[] LowerStr = {""};
String LowerStr2 = "";
String[] UpperStr = {""};
String UpperStr2 = "";
// For every step in Y direction, sample the 12 nozzles
for ( int i=0; i<nozzles; i++) {
// Calculate the location in the pixel array, use total window width!
// Use the LTR to determine the direction
if (LTR % 2 == 1){
loc = printXcoordinate + printWidth - x + (y+i) * width;
} else {
loc = printXcoordinate + x + (y+i) * width;
}
if (brightness(pixels[loc]) < 100) {
// Write a zero when the pixel is white (or should be white, as the preview is inverted)
if (i<uppernozzles) {
UpperStr = append(UpperStr, "0");
} else {
LowerStr = append(LowerStr, "0");
}
} else {
// Write a one when the pixel is black
if (i<uppernozzles) {
UpperStr = append(UpperStr, "1");
} else {
LowerStr = append(LowerStr, "1");
}
}
}
LowerStr2 = join(LowerStr, "");
print_data[index] = byte(unbinary(LowerStr2));
index++;
UpperStr2 = join(UpperStr, "");
print_data[index] = byte(unbinary(UpperStr2));
index++;
}
}
if (sliceNumber >= 1 && sliceNumber < 10){
String DEST_FILE = "PWDR/PWDR000"+sliceNumber+".DAT";
File dataFile = sketchFile(DEST_FILE);
if (dataFile.exists()){
dataFile.delete();
}
saveBytes(DEST_FILE, print_data); // Savebytes directly causes bug under Windows
} else if (sliceNumber >= 10 && sliceNumber < 100){
String DEST_FILE = "PWDR/PWDR00"+sliceNumber+".DAT";
File dataFile = sketchFile(DEST_FILE);
if (dataFile.exists()){
dataFile.delete();
}
saveBytes(DEST_FILE, print_data); // Savebytes directly causes bug under Windows
} else if (sliceNumber >= 100 && sliceNumber < 1000){
String DEST_FILE = "PWDR/PWDR0"+sliceNumber+".DAT";
File dataFile = sketchFile(DEST_FILE);
if (dataFile.exists()){
dataFile.delete();
}
saveBytes(DEST_FILE, print_data); // Savebytes directly causes bug under Windows
} else if (sliceNumber >= 1000) {
String DEST_FILE = "PWDR/PWDR"+sliceNumber+".DAT";
File dataFile = sketchFile(DEST_FILE);
if (dataFile.exists()){
dataFile.delete();
}
saveBytes(DEST_FILE, print_data); // Savebytes directly causes bug under Windows
}
sliceNumber++;
println(sliceNumber);
}
What's happening is that print_data is smaller than index. (For example, if index is 123, but print_data only has 122 elements.)
Size of print_data is layer_size * 2 or printWidth * printHeight/nozzles * 4 or 4800
Max size of index is printHeight/nozzles * 2 * printWidth or 20*120 or 2400.
This seems alright, so I probably missed something, and it appears to be placing data in element 4800, which is weird. I suggest a bunch of print statements to get the size of print_data and the index.
I am working on some fairly simple linear attenuation and absorption calculations and from high school math I seem to remember that there is an approximation of:
1-exp(-mu*t)
When
mu*t << 1
Does this approximation exist? I thought it was a taylor series expansion but could not convince myself after looking through old math textbooks.
Any help or direction is greatly appreciated.
mu*t plus O((mu*t)^2)
To see why, try rewriting this as f(u) = 1-exp(-u), and taking a Taylor series expansion at the point u=0.
If you are using C++11, for example, it has this function as part of the standard library: expm1.
In your case, you would call it as -expm1(-mu*t).
Otherwise, you can derive the Maclaurin series for expm1 easily from the Maclaurin series for exp(x) by simply dropping the first 1. One implementation is given below in expm1_maclaurin.
Comparing this with the built-in expm1:
#include <cmath>
#include <iostream>
#include <limits>
using namespace std;
double expm1_maclaurin( double x )
{
const double order = 10;
double retval = 1.0;
for( int i = order ; 1 < i ; --i ) retval = 1.0 + x*retval/i;
return x*retval;
}
int main()
{
cout.precision(numeric_limits<double>::digits10);
for( int i = 0 ; i <= 32 ; ++i )
{
double x = i < 0 ? 1.0 * (1u<<-i) : i < 32 ? 1.0 / (1u<<i) : 0;
cout << "x=" << x << ' '
<< expm1(x) << ' '
<< expm1_maclaurin(x) << ' '
<< ( expm1(x) == expm1_maclaurin(x) ) << endl;
}
return 0;
}
Output:
x=1 1.71828182845905 1.71828180114638 0
x=0.5 0.648721270700128 0.648721270687366 0
x=0.25 0.284025416687742 0.284025416687735 0
x=0.125 0.133148453066826 0.133148453066826 1
x=0.0625 0.0644944589178594 0.0644944589178594 1
x=0.03125 0.0317434074991027 0.0317434074991027 1
...
For all positive x <= 1/8 the result is equal to full double precision of expm1.
This is an interview question I saw on some site.
It was mentioned that the answer involves forming a recurrence of log2() as follows:
double log2(double x )
{
if ( x<=2 ) return 1;
if ( IsSqureNum(x) )
return log2(sqrt(x) ) * 2;
return log2( sqrt(x) ) * 2 + 1; // Why the plus one here.
}
as for the recurrence, clearly the +1 is wrong. Also, the base case is also erroneous.
Does anyone know a better answer?
How is log() and log10() actually implemented in C.
Perhaps I have found the exact answers the interviewers were looking for. From my part, I would say it's little bit difficult to derive this under interview pressure. The idea is, say you want to find log2(13), you can know that it lies between 3 to 4. Also 3 = log2(8) and 4 = log2(16),
from properties of logarithm, we know that log( sqrt( (8*16) ) = (log(8) + log(16))/2 = (3+4)/2 = 3.5
Now, sqrt(8*16) = 11.3137 and log2(11.3137) = 3.5. Since 11.3137<13, we know that our desired log2(13) would lie between 3.5 and 4 and we proceed to locate that. It is easy to notice that this has a Binary Search solution and we iterate up to a point when our value converges to the value whose log2() we wish to find. Code is given below:
double Log2(double val)
{
int lox,hix;
double rval, lval;
hix = 0;
while((1<<hix)<val)
hix++;
lox =hix-1;
lval = (1<<lox) ;
rval = (1<<hix);
double lo=lox,hi=hix;
// cout<<lox<<" "<<hix<<endl;
//cout<<lval<<" "<<rval;
while( fabs(lval-val)>1e-7)
{
double mid = (lo+hi)/2;
double midValue = sqrt(lval*rval);
if ( midValue > val)
{
hi = mid;
rval = midValue;
}
else{
lo=mid;
lval = midValue;
}
}
return lo;
}
It's been a long time since I've written pure C, so here it is in C++ (I think the only difference is the output function, so you should be able to follow it):
#include <iostream>
using namespace std;
const static double CUTOFF = 1e-10;
double log2_aux(double x, double power, double twoToTheMinusN, unsigned int accumulator) {
if (twoToTheMinusN < CUTOFF)
return accumulator * twoToTheMinusN * 2;
else {
int thisBit;
if (x > power) {
thisBit = 1;
x /= power;
}
else
thisBit = 0;
accumulator = (accumulator << 1) + thisBit;
return log2_aux(x, sqrt(power), twoToTheMinusN / 2.0, accumulator);
}
}
double mylog2(double x) {
if (x < 1)
return -mylog2(1.0/x);
else if (x == 1)
return 0;
else if (x > 2.0)
return mylog2(x / 2.0) + 1;
else
return log2_aux(x, 2.0, 1.0, 0);
}
int main() {
cout << "5 " << mylog2(5) << "\n";
cout << "1.25 " << mylog2(1.25) << "\n";
return 0;
}
The function 'mylog2' does some simple log trickery to get a related number which is between 1 and 2, then call log2_aux with that number.
The log2_aux more or less follows the algorithm that Scorpi0 linked to above. At each step, you get 1 bit of the result. When you have enough bits, stop.
If you can get a hold of a copy, the Feynman Lectures on Physics, number 23, starts off with a great explanation of logs and more or less how to do this conversion. Vastly superior to the Wikipedia article.