SRSS 4.2 readMessage::socket looping limited exceeded
I have 1 user out of 45 Sun Rays that keeps getting rebooted.
The Sun Ray session terminates, the /var/opt/SUNWut/log/messages says:
sunray-servers utauthd: [ID XXXXXX user.info] Worker1 NOTICE: readMessage::socket looping limit exceeded. Close it.
The unit power cycles then reconnects to the RDP session and with less then 1 minute it reboots again.
The user can take her smart card to another Sun Ray terminal and work without any issue. I replaced the Sun Ray2 unit with a new one, same result. I switched the network jack on the wall, and I switched the network port on the switch, still same result.
HELP!
More information:
Now the user tried to use her smartcard at another Sun Ray and now that Sun Ray is rebooting. I tried a spare smart card and same issue.
sunray-servers autauthd: [ID 715479 user.info] Worker7 UNEXPECTED: during send to: java.net.SocketOuputStream@xxxxxx error=java.net.SocketException: Broken pipe
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Client wants to block the order if customer's credit Limits exceeds.
Dear All,
Client wants to block the order if customer's credit Limits exceeds. But Sales order no. is to be generated.Later on that blocked order is to be released by Authority.
I did all the configurations. Order is blocked if the customer credits exceeds, but order no is not get generated. Without order no, Authority can not release.
Kindly guide me where i have gone wrong.
Awaiting for your quick reply
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Please do not put a credit block in the Credit Management settings. Instead check in the CMR and the VOV8 sales order setting. Also if possible maintain an incompletion procedure wherein SO number would created but the document would be blocked for delivery creation.
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Non-blocking socket concurrent limitation?
I have 2 socket program,one is server side used nio package with JDK1.4.1,the other is client used traditional socket,the client will initialize about 50
threads trying to connect with server when starting,but only about 15
can be accepted,these 2 program are runnning in the same computer which
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the followd is these code:
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server:
package nio_select_demo;
import java.io.*;
import java.net.*;
import java.nio.*;
import java.nio.channels.*;
import java.util.*;
import java.nio.charset.Charset;
import java.nio.charset.CharsetDecoder;
public class Server implements Runnable
// The port we will listen on
private int port;
// A pre-allocated buffer for processing data
private final ByteBuffer buffer = ByteBuffer.allocate( 16384 );
private ByteBuffer resBuf = ByteBuffer.allocate( 128 );
Selector selector;
AddInfo test ;
public Server( int port ) {
this.port = port;
// for (int i=0; i<threadnum; ++i) {
new Thread( this ).start();
test = new AddInfo();
test.start();
public void run() {
try {
// create a ServerSocketChannel
ServerSocketChannel ssc1 = ServerSocketChannel.open();
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ssc1.configureBlocking( false );
// Get the Socket connected to this channel, and bind it
// to the listening port
ServerSocket ss = ssc1.socket();
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ss.bind( isa , 60 );
// Create a new Selector for selecting
selector = Selector.open();
// Register the ServerSocketChannel, so we can
// listen for incoming connections
ssc1.register( selector, SelectionKey.OP_ACCEPT );
System.out.println( "Listening on port "+port );
int n = 0;
while (true) {
// See if we've had any activity -- either
// an incoming connection, or incoming data on an
// existing connection
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// If we don't have any activity, loop around and wait
// again
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// It's an incoming connection.
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// use a selector on it.
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//ssc.register(selector , SelectionKey.OP_READ);
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try {
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Socket s1 = sc.socket();
s1.setTcpNoDelay(true);
System.out.println( "enter processing data" );
boolean ok = processInput( key );
synchronized (selector) {
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try {
s = sc.socket();
s.close();
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System.out.println("Enter Writing");
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if((response=this.test.getInfo())!=null){
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SocketChannel sc = (SocketChannel)key.channel();
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sc.write( resBuf );
synchronized (selector) {
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} catch( IOException ie ) {
System.err.println( ie );
private boolean processInput( SelectionKey key ) throws IOException {
buffer.clear();
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Charset charset=Charset.forName("ISO-8859-1");
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return true;
static public void main( String args[] ) throws Exception {
int port = Integer.parseInt( args[0] );
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cilent:
import java.io.*;
import java.net.*;
import java.util.*;
public class Client implements Runnable
private String host;
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//the size of buffer on how much we write and read per cycle
private static final int maxWriteSize = 128;
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for(int i =0;i<50;i++){//initialize 50 client threads
new Thread(this).start();
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byte buffer[] = new byte[maxWriteSize];
byte buffer2[] = new byte[maxWriteSize];
try {
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InetSocketAddress sa = new InetSocketAddress(host,this.port);
s.connect(sa);
System.out.println(s);
s.setTcpNoDelay(true);
InputStream in = s.getInputStream();
OutputStream out = s.getOutputStream();
for (int i=0; i<maxWriteSize; ++i) {
buffer[i] = (byte)'a';
out.write( buffer, 0, maxWriteSize );
int pause = 500;
in.read( buffer , 0 , maxWriteSize );
System.out.println( Thread.currentThread()+" wrote "+maxWriteSize);
String res = new String ( buffer );
String res2 = new String ( buffer2 );
System.out.println( res );
try { Thread.sleep( pause ); } catch( InterruptedException ie ) {}
} catch( Exception ie ) {
ie.printStackTrace();
System.err.println(ie.getMessage());
static public void main( String args[] ) throws Exception {
String host = "127.0.0.1";
int port = Integer.parseInt( args[0] );
int numThreads = Integer.parseInt( args[1] );
new Client( host, port, numThreads );I have found the reason!!!
because of system resource limitation,windows can't afford to maintain
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I modified the client side code,adding thes segments to client instantialize
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Java Swing App hangs on socket loop
H}ello everyone i've run into a bit of a snag with my application, its a simple chat bot right now but will evolve into a chat client soon. I can't do that however since my app hangs when i look through the readLine() function to receive data and i dont know how to fix this error. The code is below.
The doSocket() function is where the while loop is if anyone can help me with this i'd be very greatful.
* GuiFrame.java
* Created on August 13, 2008, 9:36 PM
import java.net.*;
import java.io.*;
import java.util.logging.Level;
import java.util.logging.Logger;
* @author brian
public class GuiFrame extends javax.swing.JFrame {
/** Creates new form GuiFrame */
public GuiFrame() {
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Socket client_sock = null;
PrintWriter out = null;
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@SuppressWarnings("unchecked")
// <editor-fold defaultstate="collapsed" desc="Generated Code">
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.addContainerGap(26, Short.MAX_VALUE))
pack();
}// </editor-fold>
private void convertButtonActionPerformed(java.awt.event.ActionEvent evt) {
if (convertButton.getText()=="Connect") {
String old;
try {
client_sock = new Socket("www.spinchat.com", 3001);
out = new PrintWriter(client_sock.getOutputStream(), true);
in = new BufferedReader(new InputStreamReader(client_sock.getInputStream()));
} catch (UnknownHostException e) {
} catch (IOException e) {
try {
doSocket();
} catch (IOException ex) {
Logger.getLogger(GuiFrame.class.getName()).log(Level.SEVERE, null, ex);
} else if (convertButton.getText()=="Disconnect") {
out.println("e");
out.close();
try {
client_sock.close();
in.close();
} catch (IOException ex) {
Logger.getLogger(GuiFrame.class.getName()).log(Level.SEVERE, null, ex);
private void doSocket() throws IOException {
BufferedReader stdIn = new BufferedReader(new InputStreamReader(System.in));
String userInput;
String old;
while ((userInput = stdIn.readLine()) != null) {
old = userInput;
if (userInput != old) {
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if (proto == ":") {
out.println("{2");
out.println("BI'm a bot.");
out.println("aNICKHERE");
out.println("bPASSHERE");
} else if (proto == "a") {
convertButton.setText("Disconnect");
out.println("JoinCHannel");
* @param args the command line arguments
public static void main(String args[]) {
java.awt.EventQueue.invokeLater(new Runnable() {
public void run() {
new GuiFrame().setVisible(true);
// Variables declaration - do not modify
private javax.swing.JButton convertButton;
// End of variables declaration
}Edited by: briansykes on Aug 13, 2008 9:55 PM
Edited by: briansykes on Aug 13, 2008 9:56 PM>
..i've run into a bit of a snag with my application, its a simple chat bot right now but will evolve into a chat client soon. >Is this intended as a GUId app? If so, I would stick to using a GUI for input, rather than reading from the command line (which when I run it, is the DOS window that jumps up in the BG - quite counterintuitive). On the other hand, if it is intended as a non-GUId or headless app., it might be better to avoid any use of JComponents at all.
My edits stick to using a GUI.
Other notes:
- String comparison should be done as
s1.equals(s2)..rather than..
s1 == s2- Never [swallow exceptions|http://pscode.org/javafaq.html#stacktrace] in code that does not work.
- Some basic debugging skills are well called for here, to find where the program is getting stuck. When in doubt, print out!
- What made you think that
a) a test of equality on a member against which you had just set the value to the comparator, would logically lead to 'false'?
old = userInput;
if (userInput != old) ..b) A substring from indices '0 thru 0' would provide 1 character?
String proto = userInput.substring(0, 0);
if (proto == ":") ..
>
..if anyone can help me with this i'd be very greatful.>Gratitude is often best expressed through the offering of [Duke Stars|http://wikis.sun.com/display/SunForums/Duke+Stars+Program+Overview].
* GuiFrame.java
* Created on August 13, 2008, 9:36 PM
import java.net.*;
import java.io.*;
import java.util.logging.Level;
import java.util.logging.Logger;
import javax.swing.*;
* @author brian
public class GuiFrame extends JFrame {
/** Creates new form GuiFrame */
public GuiFrame() {
initComponents();
Socket client_sock = null;
PrintWriter out = null;
BufferedReader in = null;
@SuppressWarnings("unchecked")
// <editor-fold defaultstate="collapsed" desc="Generated Code">
private void initComponents() {
convertButton = new JButton();
setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE);
setTitle("Test Bot");
convertButton.setText("Connect");
convertButton.addActionListener(new java.awt.event.ActionListener() {
public void actionPerformed(java.awt.event.ActionEvent evt) {
convertButtonActionPerformed(evt);
GroupLayout layout = new GroupLayout(getContentPane());
getContentPane().setLayout(layout);
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layout.createParallelGroup(GroupLayout.Alignment.LEADING)
.addGroup(layout.createSequentialGroup()
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layout.setVerticalGroup(
layout.createParallelGroup(GroupLayout.Alignment.LEADING)
.addGroup(layout.createSequentialGroup()
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pack();
setLocationByPlatform(true);
}// </editor-fold>
private void convertButtonActionPerformed(java.awt.event.ActionEvent evt) {
if (convertButton.getText()=="Connect") {
String old;
try {
System.out.println( "Connect start.." );
client_sock = new Socket("www.spinchat.com", 3001);
out = new PrintWriter(client_sock.getOutputStream(), true);
in = new BufferedReader(new InputStreamReader(client_sock.getInputStream()));
System.out.println( "Connect end.." );
} catch (UnknownHostException e) {
e.printStackTrace();
} catch (IOException e) {
e.printStackTrace();
try {
doSocket();
} catch (IOException ex) {
Logger.getLogger(GuiFrame.class.getName()).log(Level.SEVERE, null, ex);
} else if (convertButton.getText()=="Disconnect") {
out.println("e");
out.close();
try {
client_sock.close();
in.close();
} catch (IOException ex) {
Logger.getLogger(GuiFrame.class.getName()).log(Level.SEVERE, null, ex);
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System.out.println( "doSocket start.." );
String userInput;
String old;
userInput = JOptionPane.showInputDialog(this, "Send..");
while(userInput!=null && userInput.trim().length()>0) {
System.out.println( "doSocket loop 1.." );
String proto = userInput.substring(0, 1);
System.out.println("proto: '" + proto + "'");
if (proto.equals(":")) {
System.out.println("Sending data..");
out.println("{2");
out.println("BI'm a bot.");
out.println("aNICKHERE");
out.println("bPASSHERE");
} else if (proto.equals("a")) {
convertButton.setText("Disconnect");
out.println("JoinCHannel");
userInput = JOptionPane.showInputDialog(this, "Send..");
System.out.println( "doSocket end.." );
* @param args the command line arguments
public static void main(String args[]) {
java.awt.EventQueue.invokeLater(new Runnable() {
public void run() {
new GuiFrame().setVisible(true);
// Variables declaration - do not modify
private JButton convertButton;
// End of variables declaration
} -
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Unix man pages are your friend.
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in a shell prompt
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Aloha,
When I attempted to send my first Mail-originated e-mail this morning, I received the message:
The sender address [email protected] was rejected by the server p13-smtp.mail.me.com.
The server response was: [email protected]: You have exceeded your daily sending limits. See http://support.apple.com/kb/ht4863
I tried to send from both my iPhone and MacBook and received identical messages.
As I hadn't sent a single e-mail, how can this be?
Following somewhat old thoughts here in Apple Discussions, I called my Service Provider to see if the problem was at their end.
After a delightful 1/2 hour it became abundantly clear the problem was not with the Service Provider.
Following other somewhat old thoughts there in Apple Discussions, I tried sending e-mail from my iCloud account as accessed through a browser.
Again, cannot send e-mail. The response:
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Recipient address: (my school e-mail address)
Reason: Server rejected MAIL FROM address.
Diagnostic code: smtp;550 5.7.1 [email protected]: You have exceeded your daily sending limits. See http://support.apple.com/kb/ht4863
Remote system: dns;p13-asmtpout.me.com (TCP|17.164.56.16|42392|17.164.60.196|25)
This problem has persisted all day.
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Hello experts,
I have a little problem using integration events: I use JDeveloper for creating necessary proxy classes automatically for wsdl-files. It works fine for almost every wsdl provided by SoD. But for the IntegrationEvent.wsdl this procedere fails: JDeveloper creates some methods which exceeds the JVM limit of 64KB per method. The compiler aborts.
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After spending almost all my friday to try to fix this problem, I finally find the solution today morning.
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Hi again..
I´d like to know if any of you know why the code below returns this error:
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It seems that the FOR-LOOP variable which in this case is represented by I doesn´t hold as much data as a NUMBER variable. How much data does this internal variable hold?
DECLARE
NUM1 NUMBER := 59171108702;
NUM2 NUMBER := 59171108702;
BEGIN
FOR I IN NUM1 .. NUM2 LOOP
DBMS_OUTPUT.PUT_LINE ('NUM: ' || I);
END LOOP;
EXCEPTION
WHEN OTHERS THEN
DBMS_OUTPUT.PUT_LINE (SQLERRM);
END;Ohh, I´d also like to know how I can post code here.
Chears,
Bruno
Edited by: brunosdiniz on 20/01/2009 03:33The following shows with the limit of the PLS_INTEGER...
SQL> ed
Wrote file afiedt.buf
1 DECLARE
2 NUM1 NUMBER := 2147483647; --59171108702;
3 NUM2 NUMBER := 2147483647; --59171108702;
4 BEGIN
5 FOR I IN NUM1 .. NUM2 LOOP
6 DBMS_OUTPUT.PUT_LINE ('NUM: ' || I);
7 END LOOP;
8* END;
SQL> /
NUM: 2147483647
PL/SQL procedure successfully completed.
SQL> ed
Wrote file afiedt.buf
1 DECLARE
2 NUM1 NUMBER := 2147483648; --59171108702;
3 NUM2 NUMBER := 2147483648; --59171108702;
4 BEGIN
5 FOR I IN NUM1 .. NUM2 LOOP
6 DBMS_OUTPUT.PUT_LINE ('NUM: ' || I);
7 END LOOP;
8* END;
SQL> /
DECLARE
ERROR at line 1:
ORA-01426: numeric overflow
ORA-06512: at line 5
SQL>The latter example being 1 too much for PLS_INTEGER. -
I have reached the authorization limit for my account in Adobe Digital Editions because I had to authorize/deauthorize/reauthorize devices. Could you please reset the authorization limit for me?
Sorry this is not right forum for your query.
Please go to security forum.
SAP Community Network Forums » SAP NetWeaver » Security
Regards,
Surpreet -
Hi,
I have "Integration Process" which reads data items from DB table and sends it to webserive.
Webservice accepts only 1 item of data, so I have loop in bpm interating through every data item and calling webservice.
The process works fine with no errors, but if number of loop iterations exceeds some number (like 100 or somthing close to that) the process cannot go to "completed" status. It goes through all iterations, sends all data and just hanging in system with status=started. When i'm trying to delete it with SWWL transaction i got dump. I also see same dump from user WF-BATCH occuered exactly the same time the process excpected to go to completed state.
Error analysis
Short text of the error message:
"Exception CX_SY_NO_HANDLER triggered by CL_SWF_XI_INSTANCE============CP in
line 1 with text: An exception with the type CX_SY_OPEN_SQL_DB occurred, but
was neither handled locally, nor declared in a RAISING clause"
Any ideas how to resolve this problem?
Regards,
Ilya.
Edited by: Ilya Karnauhov on Oct 1, 2009 9:29 AMhi,
>>an error code with 99
check cache refesh and tell me if it gives any error!?
regards,
Felix -
Well, this is not a problem, but I just had to mention that I could not believe that Java would actually process 106 nested for next loops. I had an hour of free time yesterday and we needed to run an exhaustive branch test of an application that we have, to do so we needed to have 104 data elements generated with all possible cases. I thought, what the heck, and tried it in Java--our old language wouldn't do that on it's best day and in our dreams! Java did it, it not only did it, but it left a clean environment after it was done!
well, here is more the thing that comes to mind with i think about loop limits: in VB when you get a dozen or so pending closing parentesis, things start to go funny in memory and in some cases, the formula/routine becomes too complicated to interpret. Just how many pending closing parentesis will be accepted before things go bonkers.
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Almost all my songs are marked 'Exceeded limit' when i only have 13k songs. what does this mean?
I only have 13,ooo songs. only about 40 matched. most say Exceeded Limit and have a little dotted cloud.
does this mean they're not in the could? i have the song title listed in my phone with match on, but there is no cloud there to download it.
how do i get these songs to upload and or match?Hi,
Try signing out of iTunes Store / match. Close iTunes. Reboot computer. Open iTunes, sign into iTunes Store the match. You will be asked to add this computer. Select this and let match go through the complete match process.
If this does not work, close iTunes and find cookie for iTunes which you will find it in safari's cookie. Delete this cookie and close safari. Reopen iTunes and turn on / update matched. You will be asked to sign in.
If this does not work, try creating a new library by holding ctrl key whilst launching iTunes. You will get a pop up box - select create new library. This will be blank. Sign into iTunes Store then match, you will be asked to add this computer.
This will now display all your music in the cloud. If you see any track with cloud status limited exceeded, delete tracks.
Now sign out and try step one again.
Jim -
Hi,
I've been asked to see if I can fix a C program so that it will run on a mac. It currently compiles and runs perfectly on a linux machine, but as soon as you run it on a mac, it will compile, but quit with a bus error very early on. The full code is here:
// Program for the construction of cartograms (density-equalizing map
// projections) using the Gastner-Newman technique. The program needs polygon
// coordinates and a count of cases in each region as input, calculates the new
// coordinates, and writes these to a file. Postscript images of the original
// map and the cartogram are created.
// WRITTEN BY MICHAEL GASTNER, September 20, 2004.
// If you use output created by this program please acknowledge the use of this
// code and its first publication in:
// "Generating population density-equalizing maps", Michael T. Gastner and
// M. E. J. Newman, Proceedings of the National Academy of Sciences of the
// United States of America, vol. 101, pp. 7499-7504, 2004.
// The input coordinates in MAPGENFILE must be in ArcInfo "generate" format of
// the type:
// 1
// 0.3248690E+06 0.8558454E+06
// 0.3248376E+06 0.8557575E+06
// 0.3248171E+06 0.8556783E+06
// 0.3247582E+06 0.8556348E+06
// 0.3246944E+06 0.8555792E+06
// 0.3246167E+06 0.8555253E+06
// 0.3250221E+06 0.8557324E+06
// 0.3249436E+06 0.8557322E+06
// 0.3248690E+06 0.8558454E+06
// END
// 1
// 0.3248690E+06 0.8558454E+06
// 0.3249651E+06 0.8558901E+06
// 0.3250519E+06 0.8559769E+06
// 0.3250691E+06 0.8561246E+06
// 0.3249678E+06 0.8560541E+06
// 0.3249003E+06 0.8560088E+06
// 0.3076424E+06 0.8477603E+06
// 0.3075691E+06 0.8477461E+06
// 0.3075595E+06 0.8476719E+06
// END
// 2
// 0.6233591E+06 0.6056502E+06
// 0.6235193E+06 0.6056467E+06
// 0.6235054E+06 0.6055372E+06
// 0.7384296E+06 0.2334260E+06
// 0.7383532E+06 0.2345770E+06
// END
// END
// The number of cases in CENSUSFILE must be given in the form
// region #cases (optional comment), e. g:
// 43 0.9 Alabama
// 51 0.3 Alaska
// 37 0.8 Arizona
// 47 0.6 Arkansas
// 25 5.4 California
// 32 0.8 Colorado
// 19 0.8 Connecticut
// 29 0.3 Delaware
// 28 0.3 District of Columbia
// 49 2.5 Florida
// 45 1.3 Georgia
// 1 0.4 Hawaii
// The output coordinates are written to CARTGENFILE in ArcInfo "generate"
// format. A postscript image of the original input is prepared as MAP2PS,
// an image of the cartogram as CART2PS.
// Modified on Oct 29, 2004. The number of divisions in each dimension lx, ly
// will now be determined from the input map. Also fixed array bound
// violations in intpol and newt2, and centered the ps-files.
// Modified on Dec 3, 2004. Introduced pointers bbmaxx,bbmaxy,bbminx,bbminy -
// the bounding box coordinates for each polygon - to reduce calculations in
// crnmbr. Thanks to Chris Brunsdon for the suggestion.
// Program now terminates with error message if there is no density specified
// in CENSUSFILE for a region on the map.
// "Donut" polygons are now handled properly. Polygons oriented clockwise will
// be considered exterior boundaries. If they are oriented anti-clockwise they
// are holes inside an enclosing polygon. (Unconventional for mathematicians,
// but this is ArcGIS standard.) The identifier is either that of the enclosing
// polygon, or -99999 in which case it is a hole in the preceding polygon.
// The population can now be a floating-point number.
// If a region contains exactly zero population, it will be replaced by
// MINPOPFAC times the smallest positive population in any region.
// Obviously, MINPOPFAC should be <1, I will set it to 0.1 by default. This
// should reduce the value of sigma necessary for the integrator to finish
// properly.
// Modified on March 31, 2005. Initialized maxchange in nonlinvoltra() as
// INFTY. Replaced crnmbr() by a similar, but faster routine interior().
// Many thanks to Stuart Anderson for pointing out this shortcut.
// TO DO LIST:
// - Do Gaussian blur within nonlinvoltra as a simple call to calcv and
// eliminate gaussianblur().
// - Modify the NR code for the FFTs to deal more naturally with the fencepost
// issue. No more copying of arrays in sinft and cosft.
// - Write truly two-dimensional versions of coscosft, cossinft, and sincosft.
// See Chan and Ho: A new two-dimensional fast cosine transform algorithm,
// IEEE Transactions on Signal Processing, 39, 481ff. (1991).
// - Read polygon data directly from shapefile instead of generate file.
// - Reorganize data structures. It is currently quite a mess to read.
// Inclusions
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
// Definitions
#define CART2PS "./cart.ps","w" // Cartogram image.
#define CARTGENFILE "./cartogram.gen" // Cartogram generate file.
#define CENSUSFILE "./census.dat","r" // Input.
#define CONVERGENCE 1e-100 // Convergence criterion for integrator.
// #define DISPLFILE "./displ.dat","w"
#define FALSE 0
#define HINITIAL 1e-4 // Initial time step size in nonlinvoltra.
#define IMAX 50 // Maximum number of iterations in Newton-Raphson routine.
#define INFTY 1e100
#define LINELENGTH 1000
#define MAP2PS "map.ps","w" // Map image.
#define MAPGENFILE "./map.gen","r" // Input coordinates.
#define MAX(a,b) ((b>a)?(b):(a))
#define MAXINTSTEPS 3000 // Maximum number of time steps in nonlinvoltra.
#define MAXNSQLOG 18 // The number of sample points for rho_0 is <~2^MAXNSQLOG.
#define MIN(a,b) ((b<a)?(b):(a))
#define MINH 1e-5 // Smallest permitted time step in the integrator.
#define MINPOPFAC 0.1 // Replace 0 population by a fraction of the minimum.
#define NR_END 1
#define NSUBDIV 1 // Number of linear subdivisions for digitizing the density.
#define PADDING 1.5 // Determines space between map and boundary.
#define PI 3.141592653589793
#define SIGMA 0.1 // Initial width of Gaussian blur.
#define SIGMAFAC 1.2 // Increase sigma by this factor. Must be > 1.
#define SWAP(a,b) tempr=(a);(a)=(b);(b)=tempr;
#define TIMELIMIT 1e8 // Maximum time allowed in integrator.
#define TOLF 1e-3 // Sensitivity w. r. t. function value in newt2.
#define TOLINT 1e-3 // Sensitivity of the integrator.
#define TOLX 1e-3 // Sensitivity w. r. t. independent variables in newt2.
#define TRUE !FALSE
// Types
typedef int BOOLEAN;
typedef struct
float x;
float y;
} POINT;
// Globals
float bbmaxx,*bbmaxy,*bbminx,*bbminy,**gridvx,*gridvy,maxx,maxy,minpop,
minx,miny,polymaxx,polymaxy,polyminx,polyminy,*rho,**rho_0,**vx,**vy,*x,
*xappr,xstepsize,**y,*yappr,ystepsize;
int lx,ly,maxid,nblurs=0,npoly,npolycorn,*npolyinreg,nregcorn,nregion,
polygonid,**polyinreg,*regionid,*regionidinv,*within;
POINT *polycorn,*regcorn;
// Function prototypes
int readline(char line[],FILE *infile);
void countpoly(FILE *infile);
void countcorn(FILE *infile);
void readcorn(FILE *infile);
void makeregion(void);
void pspicture(FILE *outfile);
void bboxes(void);
void interior(void);
double regionarea(int ncrns,POINT *polygon);
void digdens(void);
void four1(float data[],unsigned long nn,int isign);
void realft(float data[],unsigned long n,int isign);
void cosft(float z[],unsigned long n,int isign);
void sinft(float z[],unsigned long n,int isign);
void coscosft(float **y,int isign1,int isign2);
void cossinft(float **y,int isign1,int isign2);
void sincosft(float **y,int isign1,int isign2);
float **dmatrix(long nrl,long nrh,long ncl,long nch);
float *d3tensor(long nrl, long nrh, long ncl, long nch, long ndl, long ndh);
void free_matrix(float **m,long nrl,long nrh,long ncl,long nch);
void free_f3tensor(float *t,long nrl,long nrh,long ncl,long nch,long ndl,
long ndh);
void fourn(float data[],unsigned long nn[],int ndim,int isign);
void rlft3(float *data,float **speq,unsigned long nn1,unsigned long nn2,
unsigned long nn3,int isign);
void gaussianblur(void);
void initcond(void);
void calcv(float t);
float intpol(float **arr,float x,float y);
BOOLEAN newt2(float h,float *xappr,float xguess,float *yappr,float yguess,
int j,int k);
BOOLEAN nonlinvoltra(void);
POINT transf(POINT p);
void cartogram(void);
// Function to read one line.
int readline(char line[],FILE *infile)
if (fgets(line,LINELENGTH,infile)==NULL) return 1;
return 0;
// Function to count the number of polygons.
void countpoly(FILE *infile)
char line[LINELENGTH];
npoly = 0;
while (!readline(line,infile)) if (line[0] == 'E') npoly++;
npoly--; // The .gen file ends with two consecutive "END"s.
// Function to count polygon corners. Also determines minimum/maximum x-/y-
// coordinate.
void countcorn(FILE *infile)
BOOLEAN bnd_ok = FALSE;
char line[LINELENGTH];
float x,y;
int polyctr=0,ratiolog;
npolycorn = (int*)calloc(npoly,sizeof(int));
polycorn = (POINT*)malloc(npoly*sizeof(POINT));
readline(line,infile); // Skip first line.
readline(line,infile);
sscanf(line,"%f %f",&x,&y);
polyminx = x; polymaxx = x; polyminy = y; polymaxy = y;
npolycorn[0] = 1;
while (!readline(line,infile))
if (line[0] != 'E')
sscanf(line,"%f %f",&x,&y);
if (x < polyminx) polyminx = x;
if (x > polymaxx) polymaxx = x;
if (y < polyminy) polyminy = y;
if (y > polymaxy) polymaxy = y;
npolycorn[polyctr]++;
else
readline(line,infile);
polycorn[polyctr] = (POINT)malloc(npolycorn[polyctr]sizeof(POINT));
polyctr++;
if (ceil(log((polymaxx-polyminx)/(polymaxy-polyminy))/log(2))+
floor(log((polymaxx-polyminx)/(polymaxy-polyminy))/log(2))>
2*log((polymaxx-polyminx)/(polymaxy-polyminy))/log(2))
ratiolog = (int)floor(log((polymaxx-polyminx)/(polymaxy-polyminy))/log(2));
else
ratiolog = (int)ceil(log((polymaxx-polyminx)/(polymaxy-polyminy))/log(2));
lx = (int)pow(2,(int)(0.5*(ratiolog+MAXNSQLOG)));
ly = (int)pow(2,(int)(0.5*(MAXNSQLOG-ratiolog)));
if ((polymaxx-polyminx)/lx > (polymaxy-polyminy)/ly)
maxx = 0.5((1PADDING)*polymaxx(1-PADDING)polyminx);
minx = 0.5((1-PADDING)*polymaxx(1PADDING)polyminx);
maxy = 0.5(polymaxypolyminy(maxx-minx)ly/lx);
miny = 0.5(polymaxy+polyminy-(maxx-minx)ly/lx);
else
maxy = 0.5((1PADDING)*polymaxy(1-PADDING)polyminy);
miny = 0.5((1-PADDING)*polymaxy(1PADDING)polyminy);
maxx = 0.5(polymaxxpolyminx(maxy-miny)lx/ly);
minx = 0.5(polymaxx+polyminx-(maxy-miny)lx/ly);
// Uncomment the next lines for interactive choice of boundary conditions.
/* printf("For the %i polygon(s) under consideration:\n",npoly);
printf("minimum x = %f\tmaximum x = %f\n",polyminx,polymaxx);
printf("minimum y = %f\tmaximum y = %f\n",polyminy,polymaxy);
while (!bnd_ok)
printf("Type in your choice of boundaries.\nminx = ");
scanf("%f",&minx);
printf("maxx = ");
scanf("%f",&maxx);
printf("miny = ");
scanf("%f",&miny);
printf("maxy = ");
scanf("%f",&maxy);
if (minx>polyminx || maxx<polymaxx || miny>polyminy || maxy<polymaxy)
printf("Invalid choice, does not enclose the polygon(s).\n");
else bnd_ok = TRUE;
// Function to read polygon corners. The first and last vertex of each polygon
// must be identical.
void readcorn(FILE *infile)
char line[LINELENGTH];
float xcoord,ycoord;
int i,id,polyctr=0;
polygonid = (int)malloc(npolysizeof(int));
xstepsize = (maxx-minx)/lx;
ystepsize = (maxy-miny)/ly;
if (fabs((xstepsize/ystepsize)-1)>1e-3)
fprintf(stderr,"WARNING: Area elements are not square: %f : %f\n",
xstepsize,ystepsize);
readline(line,infile);
sscanf(line,"%i",&id);
polygonid[polyctr] = id;
i = 0;
while (!readline(line,infile))
if (line[0] != 'E')
sscanf(line,"%f %f",&xcoord,&ycoord);
polycorn[polyctr].x = (xcoord-minx)/xstepsize;
polycorn[polyctr][i++].y = (ycoord-miny)/ystepsize;
else
// Is first and last vertex the same?
if (fabs(polycorn[polyctr][0].x-
polycorn[polyctr][npolycorn[polyctr]-1].x)+
fabs(polycorn[polyctr][0].y-
polycorn[polyctr][npolycorn[polyctr]-1].y)>1e-12)
fprintf(stderr,
"ERROR: %i-th polygon does not close upon itself.\n",
polyctr+1);
fprintf(stderr,"Identifier %i, first point %f %f.\n",
polygonid[polyctr],polycorn[polyctr][0].x*xstepsize+minx,
polycorn[polyctr][0].y*ystepsize+miny);
exit(1);
readline(line,infile);
sscanf(line,"%i",&id);
i = 0;
polyctr++;
if (polyctr<npoly) polygonid[polyctr] = id;
polyminx = (polyminx-minx)/xstepsize;
polyminy = (polyminy-miny)/ystepsize;
polymaxx = (polymaxx-minx)/xstepsize;
polymaxy = (polymaxy-miny)/ystepsize;
// Function to make regions from polygons.
void makeregion(void)
BOOLEAN repeat;
int i,lastid,minid,polyctr,ptctr,regctr;
// Count the number of regions.
nregion = 0;
maxid = minid = polygonid[0];
for (polyctr=0; polyctr<npoly; polyctr++)
if (polygonid[polyctr] == -99999) continue;
if (polygonid[polyctr]>maxid || polygonid[polyctr]<minid) nregion++;
else
repeat = FALSE;
for (i=0; i<polyctr; i++)
if (polygonid[polyctr]==polygonid)
repeat = TRUE;
break;
if (!repeat) nregion++;
if (polygonid[polyctr]>maxid) maxid = polygonid[polyctr];
if (polygonid[polyctr]<minid) minid = polygonid[polyctr];
if (minid < 0)
fprintf(stderr,
"ERROR: Negative region identifier %i.\n",minid);
exit(1);
// Match region identifiers.
regionid = (int)malloc(nregionsizeof(int));
nregion = 0;
maxid = minid = polygonid[0];
for (polyctr=0; polyctr<npoly; polyctr++)
if (polygonid[polyctr] == -99999) continue;
if (polygonid[polyctr]>maxid || polygonid[polyctr]<minid)
regionid[nregion++] = polygonid[polyctr];
else
repeat = FALSE;
for (i=0; i<polyctr; i++)
if (polygonid[polyctr]==polygonid)
repeat = TRUE;
break;
if (!repeat) regionid[nregion++] = polygonid[polyctr];
if (polygonid[polyctr]>maxid) maxid = polygonid[polyctr];
if (polygonid[polyctr]<minid) minid = polygonid[polyctr];
regionidinv = (int)malloc((maxid+1)sizeof(int));
// Negative number for unused identifiers.
for (i=0; i<=maxid; i++) regionidinv = -1;
for (regctr=0; regctr<nregion; regctr++)
regionidinv[regionid[regctr]] = regctr;
// Which polygons contribute to which regions?
npolyinreg = (int*)calloc(nregion,sizeof(int));
polyinreg = (int*)malloc(nregion*sizeof(int));
lastid = polygonid[0];
for (polyctr=0; polyctr<npoly; polyctr++)
if (polygonid[polyctr] != -99999)
npolyinreg[regionidinv[polygonid[polyctr]]]++;
lastid = polygonid[polyctr];
else npolyinreg[regionidinv[lastid]]++;
for (regctr=0; regctr<nregion; regctr++)
polyinreg[regctr] = (int)malloc(npolyinreg[regctr]sizeof(int));
for (regctr=0; regctr<nregion; regctr++) npolyinreg[regctr] = 0;
lastid = polygonid[0];
for (polyctr=0; polyctr<npoly; polyctr++)
if (polygonid[polyctr] != -99999)
polyinreg[regionidinv[polygonid[polyctr]]]
[npolyinreg[regionidinv[polygonid[polyctr]]]++] = polyctr;
lastid = polygonid[polyctr];
else polyinreg[regionidinv[lastid]][npolyinreg[regionidinv[lastid]]++]
= polyctr;
// Make regions from polygons. Start and end each polygon at (0,0).
nregcorn = (int*)calloc(nregion,sizeof(int));
regcorn = (POINT*)malloc(nregion*sizeof(POINT));
for (regctr=0; regctr<nregion; regctr++)
for (i=0; i<npolyinreg[regctr]; i++)
nregcorn[regctr] += npolycorn[polyinreg[regctr]]+1;
nregcorn[regctr]++;
for (regctr=0; regctr<nregion; regctr++)
regcorn[regctr] = (POINT)malloc(nregcorn[regctr]sizeof(POINT));
ptctr = 0;
regcorn[regctr][ptctr].x = regcorn[regctr][ptctr++].y = 0.0;
for (polyctr=0; polyctr<npolyinreg[regctr]; polyctr++)
for (i=0; i<npolycorn[polyinreg[regctr][polyctr]]; i++)
regcorn[regctr][ptctr++] = polycorn[polyinreg[regctr][polyctr]];
regcorn[regctr][ptctr].x = regcorn[regctr][ptctr++].y = 0.0;
// Function to prepare a map in postscript standard letter format.
void pspicture(FILE *outfile)
char line[LINELENGTH];
float addx,addy,b,conv,g,r;
int ptctr,regctr;
if (11*lx > 8.5*ly)
conv = (float)8.5*72/lx;
addx = 0;
addy = 1136-8.5*36ly/lx;
else
conv = (float)11*72/ly;
addx = 8.536-11*36lx/ly;
addy = 0;
fprintf(outfile,"0.5 setlinewidth\n");
for (regctr=0; regctr<nregion; regctr++)
fprintf(outfile,"newpath\n");
fprintf(outfile,"%f %f moveto\n",
regcorn[regctr][1].x*conv+addx,
regcorn[regctr][1].y*conv+addy);
for (ptctr=2; ptctr<nregcorn[regctr]; ptctr++)
if (fabs(regcorn[regctr][ptctr].x)+
fabs(regcorn[regctr][ptctr].y)>1e-12)
fprintf(outfile,"%f %f lineto\n",
regcorn[regctr][ptctr].x*conv+addx,
regcorn[regctr][ptctr].y*conv+addy);
else
fprintf(outfile,"closepath\n");
if (ptctr<nregcorn[regctr]-1)
ptctr++;
fprintf(outfile,"%f %f moveto\n",
regcorn[regctr][ptctr].x*conv+addx,
regcorn[regctr][ptctr].y*conv+addy);
// Determine colors for map (without better knowledge I will do it
// arbitrarily).
if (regctr%3 == 0)
r = (float)regctr/nregion;
g = 1-(float)regctr/nregion;
b = fabs(1-2*(float)regctr/nregion);
else if (regctr%3 == 1)
b = (float)regctr/nregion;
r = 1-(float)regctr/nregion;
g = fabs(1-2*(float)regctr/nregion);
else
g = (float)regctr/nregion;
b = 1-(float)regctr/nregion;
r = fabs(1-2*(float)regctr/nregion);
fprintf(outfile,"%f %f %f setrgbcolor\ngsave\nfill\n",r,g,b);
fprintf(outfile,"grestore\n0 setgray stroke\n");
fprintf(outfile,"showpage\n");
// Function to find the bounding box for each polygon.
void bboxes(void)
int i,j;
float maxx, minx, maxy, miny;
bbmaxx = (float)malloc(npolysizeof(float));
bbmaxy = (float)malloc(npolysizeof(float));
bbminx = (float)malloc(npolysizeof(float));
bbminy = (float)malloc(npolysizeof(float));
for (i = 0; i < npoly; i++)
maxx = polycorn[0].x;
maxy = polycorn[0].y;
minx = maxx;
miny = maxy;
for (j = 0; j < npolycorn; j++)
if (polycorn[j].x > maxx) maxx = polycorn[j].x;
if (polycorn[j].x < minx) minx = polycorn[j].x;
if (polycorn[j].y < miny) miny = polycorn[j].y;
if (polycorn[j].y > maxy) maxy = polycorn[j].y;
bbmaxx=maxx;
bbmaxy=maxy;
bbminx=minx;
bbminy=miny;
void interior(void)
int i,inhowmanyregions,inregion[2],j,k,l,m,n,regctr;
// Initialize within[][]. -1 means outside all regions.
for (i=0; i<=lx; i++) for (j=0; j<=ly; j++) within[j] = -1;
// Fill within[][].
for (i=0; i<nregion; i++) for (j=0; j<npolyinreg; j++)
for (k=0, n=npolycorn[polyinreg[j]]-1;
k<npolycorn[polyinreg[j]]; n=k++)
for (l=(int)ceil(MIN(polycorn[polyinreg[j]][k-1].y,
polycorn[polyinreg[j]][k].y));
l<MAX(polycorn[polyinreg[j]][k-1].y,
polycorn[polyinreg[j]][k].y); l++)
for (m=(int)floor(bbminx[polyinreg[j]]);
m<(polycorn[polyinreg[j]][n].x-
polycorn[polyinreg[j]][k].x)*
(l-polycorn[polyinreg[j]][k].y)/
(polycorn[polyinreg[j]][n].y-
polycorn[polyinreg[j]][k].y)+
polycorn[polyinreg[j]][k].x;
m++)
within[m][l] = i-within[m][l]-1;
// Function to determine polygon area. This is needed to determine the average
// population.
// The problem in short is to find the area of a polygon whose vertices are
// given. Recall Stokes' theorem in 3d for a vector field v:
// integral[around closed curve dA]v(x,y,z).ds =
// integral[over area A]curl(v).dA.
// Now let v(x,y,z) = (0,Q(x,y),0) and dA = (0,0,dx*dy). Then
// integral[around closed curve dA]Q(x,y)dy = integral[over area A]dQ/dxdxdy.
// If Q = x:
// A = integral[over area A]dx*dy = integral[around closed curve dA]x dy.
// For every edge from (x,y) to (x[i1],y[i1]) there is a
// parametrization
// (x(t),y(t)) = ((1-t)xtx[i+1],(1-t)y+ty[i1]), 0<t<1
// so that the path integral along this edge is
// int[from 0 to 1]{(1-t)xt*x[i+1]}(y[i1]-y)dt =
// 0.5(y[i1]-y)(x+x[i1]).
// Summing over all edges yields:
// Area = 0.5*[(x[0]+x[1])(y[1]-y[0]) + (x[1]+x[2])(y[2]-y[1]) + ...
// ...(x[n-1]+x[n])(y[n]-y[n-1])+(x[n]x[0])(y[0]-y[n])]
// ArcGIS treats a clockwise direction as positive, so there is a minus sign.
double regionarea(int ncrns,POINT *polygon)
double area=0;
int i;
for (i=0; i<ncrns-1; i++)
area -=
0.5(polygon.xpolygon[i+1].x)(polygon[i1].y-polygon.y);
return area -= 0.5(polygon[ncrns-1].x+polygon[0].x)
(polygon[0].y-polygon[ncrns-1].y);
// Function to digitize density.
void digdens(void)
char line[LINELENGTH];
double area,avgdens,*cases,dens,minpop=INFTY,ncases,totarea=0.0,totpop=0.0;
FILE* infile;
int i,id,ii,inhowmanyregions,inregion[2],j,jj,regctr;
if ((infile=fopen(CENSUSFILE))==NULL)
fprintf(stderr,"ERROR: Cannot find CENSUSFILE.\n");
exit(1);
// Find the minimum positive number of cases.
while (!readline(line,infile))
sscanf(line,"%i %lf",&id,&ncases);
if (ncases<minpop && ncases>1e-12) minpop = ncases;
fclose(infile);
// Store the number of cases in an array.
cases = (double)malloc(nregionsizeof(double));
for (i=0; i<nregion; i++) cases = -1.0;
infile = fopen(CENSUSFILE);
while (!readline(line,infile))
sscanf(line,"%i %lf",&id,&ncases);
if (id>maxid || regionidinv[id]<0)
fprintf(stderr,"ERROR: Identifier %i in CENSUSFILE does not\n",id);
fprintf(stderr,"match any identifier in generate file.\n");
exit(1);
if (ncases>1e-12) totpop += (cases[regionidinv[id]] = ncases);
else totpop += (cases[regionidinv[id]] = MINPOPFAC*minpop);
for (regctr=0; regctr<nregion; regctr++) if (cases[regctr] < 0.0)
fprintf(stderr,"ERROR: No density for region %i?\n",regionid[regctr]);
fprintf(stderr,"cases = %f\n",cases[regctr]);
exit(1);
fclose(infile);
// Calculate regions' areas, total area to be mapped, regional and average
// densities.
area = (double)malloc(nregionsizeof(double));
for (regctr=0; regctr<nregion; regctr++)
totarea += (area[regctr] = regionarea(nregcorn[regctr],regcorn[regctr]));
dens = (double)malloc(nregionsizeof(double));
for (regctr=0; regctr<nregion; regctr++)
dens[regctr] = cases[regctr]/area[regctr];
avgdens = totpop/totarea;
// Digitize density.
for (i=0; i<=lx; i++) for (j=0; j<=ly; j++) rho_0[j] = 0; // Initialize.
printf("digitizing density ...\n");
for (i=0; i<lx; i++) for (j=0; j<ly; j++)
if (within[j]==-1) rho_0[j] = avgdens;
else rho_0[j] = dens[within[j]];
// Fill the edges correctly.
rho_0[0][0] += rho_0[0][ly] + rho_0[lx][0] + rho_0[lx][ly];
for (i=1; i<lx; i++) rho_0[0] += rho_0[ly];
for (j=1; j<ly; j++) rho_0[0][j] += rho_0[lx][j];
for (i=0; i<lx; i++) rho_0[ly] = rho_0[0];
for (j=0; j<=ly; j++) rho_0[lx][j] = rho_0[0][j];
// Replace rho_0 by Fourier transform
coscosft(rho_0,1,1);
free(area);
free(cases);
for (i=0; i<npoly; i++) free(polycorn);
free(polycorn);
for (i=0; i<nregion; i++) free(regcorn);
free(regcorn);
free(dens);
free(npolycorn);
free(nregcorn);
free(polygonid);
free(regionid);
free(regionidinv);
free(bbmaxx);
free(bbmaxy);
free(bbminx);
free(bbminy);
for (i=0; i<nregion; i++) free(polyinreg);
free(polyinreg);
free(npolyinreg);
// Function to replace data[1...2*nn] by its discrete Fourier transform, if
// isign is input as 1; or replaces data[1...2*nn] by nn times its inverse
// discrete Fourier transform, if isign is input as -1. data is a complex array
// of length nn or, equivalently, a real array of length 2*nn. nn MUST be an
// integer power of 2 (this is not checked for!).
// From "Numerical Recipes in C".
void four1(float data[],unsigned long nn,int isign)
double theta,wi,wpi,wpr,wr,wtemp;
float tempi,tempr;
unsigned long i,istep,j,m,mmax,n;
n=nn<<1;
j=1;
for (i=1; i<n; i+=2)
if (j>i)
// This is the bit-reversal section of the routine.
SWAP(data[j],data);
SWAP(data[j1],data[i1]); // Exchange the two complex numbers.
m=n>>1;
while (m>=2 && j>m)
j -= m;
m>>=1;
j += m;
// Here begins the Danielson-Lanczos section of the routine.
mmax=2;
while (n>mmax) // Outer loop executed log_2 nn times.
istep = mmax<<1;
// Initialize the trigonometric recurrence.
theta = isign*(6.28318530717959/mmax);
wtemp = sin(0.5*theta);
wpr = -2.0wtempwtemp;
wpi = sin(theta);
wr = 1.0;
wi = 0.0;
for (m=1; m<mmax; m+=2) // Here are the two nested inner loops.
for (i=m; i<=n; i+=istep)
j=i+mmax; // This is the Danielson-Lanczos formula
tempr=wrdata[j]-widata[j+1];
tempi=wrdata[j1]widata[j];
data[j]=data-tempr;
data[j1]=data[i1]-tempi;
data += tempr;
data[i+1] += tempi;
wr = (wtemp=wr)wpr-wiwpi+wr; // Trigonometric recurrence.
wi = wiwprwtempwpiwi;
mmax=istep;
// Function to calculate the Fourier Transform of a set of n real-valued data
// points. It replaces this data (which is stored in array data[1...n]) by the
// positive frequency half of its complex Fourier Transform. The real-valued
// first and last components of the complex transform are returned as elements
// data[1] and data[2] respectively. n must be a power of 2. This routine also
// calculates the inverse transform of a complex data array if it is the
// transform of real data. (Result in this case must be multiplied by 2/n).
// From "Numerical Recipes in C".
void realft(float data[],unsigned long n,int isign)
double theta,wi,wpi,wpr,wr,wtemp;
float c1=0.5,c2,h1i,h1r,h2i,h2r;
unsigned long i,i1,i2,i3,i4,np3;
theta = 3.141592653589793/(double) (n>>1); // Initialize the recurrence
if (isign == 1)
c2 = -0.5;
four1(data,n>>1,1); // The forward transform is here.
else // Otherwise set up for an inverse transform.
c2 = 0.5;
theta = -theta;
wtemp = sin(0.5*theta);
wpr = -2.0wtempwtemp;
wpi = sin(theta);
wr = 1.0+wpr;
wi = wpi;
np3 = n+3;
for (i=2; i<=(n>>2); i++) // Case i=1 done separately below.
i4 = 1(i3=np3-(i2=1+(i1=ii-1)));
// The two separate transforms are separated out of data.
h1r = c1*(data[i1]+data[i3]);
h1i = c1*(data[i2]-data[i4]);
h2r = -c2*(data[i2]+data[i4]);
h2i = c2*(data[i1]-data[i3]);
// Here they are recombined to form the true transform of the original
// data.
data[i1] = h1r+wrh2r-wih2i;
data[i2] = h1iwrh2iwih2r;
data[i3] = h1r-wrh2r+wih2i;
data[i4] = -h1iwrh2iwih2r;
wr = (wtemp=wr)wpr-wiwpi+wr; // The recurrence.
wi = wiwprwtempwpiwi;
if (isign == 1)
data[1] = (h1r=data[1])+data[2]; // Squeeze the first and last data
// together to get them all within the original array.
data[2] = h1r-data[2];
else
data[1] = c1*((h1r=data[1])+data[2]);
data[2] = c1*(h1r-data[2]);
// This is the inverse transform for the case isign = -1.
four1(data,n>>1,-1);
// Function to calculate the cosine transform of a set z[0...n] of real-valued
// data points. The transformed data replace the original data in array z. n
// must be a power of 2. For forward transform set isign=1, for back transform
// isign = -1. (Note: The factor 2/n has been taken care of.)
// From "Numerical Recipes in C".
void cosft(float z[],unsigned long n,int isign)
double theta,wi=0.0,wpi,wpr,wr=1.0,wtemp;
float *a,sum,y1,y2;
int j,n2;
// Numerical Recipes starts counting at 1 which is rather confusing. I will
// count from 0.
a = (float)malloc((n+2)sizeof(float));
for (j=1; j<=n+1; j++) a[j] = z[j-1];
// Here is the Numerical Recipes code.
theta=PI/n; //Initialize the recurrence.
wtemp = sin(0.5*theta);
wpr = -2.0wtempwtemp;
wpi = sin(theta);
sum = 0.5*(a[1]-a[n+1]);
a[1] = 0.5*(a[1]a[n1]);
n2 = n+2;
for (j=2; j<=(n>>1); j++)
wr = (wtemp=wr)wpr-wiwpi+wr;
wi = wiwprwtempwpiwi;
y1 = 0.5*(a[j]+a[n2-j]);
y2 = (a[j]-a[n2-j]);
a[j] = y1-wi*y2;
a[n2-j] = y1+wi*y2;
sum += wr*y2;
realft(a,n,1);
a[n+1] = a[2];
a[2] = sum;
for (j=4; j<=n; j+=2)
sum += a[j];
a[j] = sum;
// Finally I revert to my counting method.
if (isign == 1) for (j=1; j<=n+1; j++) z[j-1] = a[j];
else if (isign == -1) for (j=1; j<=n+1; j++) z[j-1] = 2.0*a[j]/n;
free(a);
// Function to calculate the sine transform of a set of n real-valued data
// points stored in array z[0..n]. The number n must be a power of 2. On exit
// z is replaced by its transform. For forward transform set isign=1, for back
// transform isign = -1.
void sinft(float z[],unsigned long n,int isign)
double theta,wi=0.0,wpi,wpr,wr=1.0,wtemp;
float *a,sum,y1,y2;
int j;
unsigned long n2=n+2;
// See my comment about Numerical Recipe's counting above. Note that the last
// component plays a completely passive role and does not need to be stored.
a = (float*) malloc((n+1)*sizeof(float));
for (j=1; j<=n; j++) a[j] = z[j-1];
// Here is the Numerical Recipes code.
theta = PI/(double)n; // Initialize the recurrence.
wtemp = sin(0.5*theta);
wpr = -2.0wtempwtemp;
wpi = sin(theta);
a[1] = 0.0;
for (j=2; j<=(n>>1)+1; j++)
// Calculate the sine for the auxiliary array.
wr = (wtemp=wr)wpr-wiwpi+wr;
// The cosine is needed to continue the recurrence.
wi = wiwprwtempwpiwi;
// Construct the auxiliary array.
y1 = wi*(a[j]+a[n2-j]);
y2 = 0.5*(a[j]-a[n2-j]);
// Terms j and N-j are related.
a[j] = y1+y2;
a[n2-j] = y1-y2;
// Transform the auxiliary array.
realft(a,n,1);
// Initialize the sum used for odd terms below.
a[1] *= 0.5;
sum = a[2] = 0.0;
// Even terms determined directly. Odd terms determined by running sum.
for (j=1; j<=n-1; j+=2)
sum += a[j];
a[j] = a[j+1];
a[j+1] = sum;
// Change the indices.
if (isign == 1) for (j=1; j<=n; j++) z[j-1] = a[j];
else if (isign == -1) for (j=1; j<=n; j++) z[j-1] = 2.0*a[j]/n;
z[n] = 0.0;
free(a);
// Function to calculate a two-dimensional cosine Fourier transform. Forward/
// backward transform in x: isign1 = +/-1, in y: isign2 = +/-1.
void coscosft(float **y,int isign1,int isign2)
float temp[lx+1];
unsigned long i,j;
for (i=0; i<=lx; i++)
cosft(y,ly,isign2);
for (j=0; j<=ly; j++)
for (i=0; i<=lx; i++) temp=y[j];
cosft(temp,lx,isign1);
for (i=0; i<=lx; i++) y[j]=temp;
// Function to calculate a cosine Fourier transform in x and a sine transform
// in y. Forward/backward transform in x: isign1 = +/-1, in y: isign2 = +/-1.
void cossinft(float **y,int isign1,int isign2)
float temp[lx+1];
unsigned long i,j;
for (i=0; i<=lx; i++)
sinft(y,ly,isign2);
for (j=0; j<=ly; j++)
for (i=0; i<=lx; i++) temp=y[j];
cosft(temp,lx,isign1);
for (i=0; i<=lx; i++) y[j]=temp;
// Function to calculate a sine Fourier transform in x and a cosine transform
// in y. Forward/backward transform in x: isign1 = +/-1, in y: isign2 = +/-1.
void sincosft(float **y,int isign1,int isign2)
float temp[lx+1];
unsigned long i,j;
for (i=0; i<=lx; i++)
cosft(y,ly,isign2);
for (j=0; j<=ly; j++)
for (i=0; i<=lx; i++) temp=y[j];
sinft(temp,lx,isign1);
for (i=0; i<=lx; i++) y[j]=temp;
// Function to allocate a float matrix with subscript range
// m[nrl..nrh][ncl..nch]. From "Numerical Recipes in C".
float **dmatrix(long nrl,long nrh,long ncl,long nch)
long i, nrow=nrh-nrl1,ncol=nch-ncl1;
float **m;
/* allocate pointers to rows */
m=(float **) malloc((unsigned int)((nrow+NR_END)sizeof(float)));
if (!m)
fprintf(stderr,"allocation failure 1 in matrix()\n");
exit(1);
m += NR_END;
m -= nrl;
/* allocate rows and set pointers to them */
m[nrl]=(float *) malloc((unsigned int)((nrowncol+NR_END)sizeof(float)));
if (!m[nrl])
fprintf(stderr,"allocation failure 2 in matrix()\n");
exit(1);
m[nrl] += NR_END;
m[nrl] -= ncl;
for(i=nrl1;i<=nrh;i+) m=m[i-1]+ncol;
/* return pointer to array of pointers to rows */
return m;
// Function to allocate a float 3tensor with range
// t[nrl..nrh][ncl..nch][ndl..ndh]. From "Numerical Recipes in C".
float *d3tensor(long nrl, long nrh, long ncl, long nch, long ndl, long ndh)
long i,j,nrow=nrh-nrl1,ncol=nch-ncl+1,ndep=ndh-ndl1;
float *t;
/* allocate pointers to pointers to rows */
t=(float *) malloc((sizet)((nrow+NREND)sizeof(float*)));
if (!t)
fprintf(stderr,"allocation failure 1 in f3tensor()\n");
exit(1);
t += NR_END;
t -= nrl;
/* allocate pointers to rows and set pointers to them */
t[nrl]=(float **) malloc((sizet)((nrowncol+NREND)*sizeof(float)));
if (!t[nrl])
fprintf(stderr,"allocation failure 2 in f3tensor()\n");
exit(1);
t[nrl] += NR_END;
t[nrl] -= ncl;
/* allocate rows and set pointers to them */
t[nrl][ncl]=(float *) malloc((sizet)((nrowncol*ndep+NREND)sizeof(float)));
if (!t[nrl][ncl])
fprintf(stderr,"allocation failure 3 in f3tensor()\n");
exit(1);
t[nrl][ncl] += NR_END;
t[nrl][ncl] -= ndl;
for(j=ncl1;j<=nch;j+) t[nrl][j]=t[nrl][j-1]+ndep;
for(i=nrl1;i<=nrh;i+) {
t=t[i-1]+ncol;
t[ncl]=t[i-1][ncl]+ncol*ndep;
for(j=ncl1;j<=nch;j+) t[j]=t[j-1]+ndep;
/* return pointer to array of pointers to rows */
return t;
void free_matrix(float **m,long nrl,long nrh,long ncl,long nch)
free((char*) (m[nrl]+ncl-1));
free((char*) (m+nrl-1));
void free_f3tensor(float *t,long nrl,long nrh,long ncl,long nch,long ndl,
long ndh)
free((char*) (t[nrl][ncl]+ndl-1));
free((char*) (t[nrl]+ncl-1));
free((char*) (t+nrl-1));
// Function to replace data by its ndim-dimensional discrete Fourier transform,
// if isign is input as 1. nn[1..ndim] is an integer array containing the
// lengths of each dimension (number of complex values), which MUST be all
// powers of 2. data is a real array of length twice the product of these
// lengths, in which the data are stored as in a multidimensional complex
// array: real and imaginary parts of each element are in consecutive
// locations, and the rightmost index of the array increases most rapidly as
// one proceeds along data. For a two-dimensional array, this is equivalent to
// storing the arrays by rows. If isign is input as -1, data is replaced by its
// inverse transform times the product of the lengths of all dimensions.
void fourn(float data[],unsigned long nn[],int ndim,int isign)
int idim;
unsigned long i1,i2,i3,i2rev,i3rev,ip1,ip2,ip3,ifp1,ifp2;
unsigned long ibit,k1,k2,n,nprev,nrem,ntot;
double tempi,tempr;
float theta,wi,wpi,wpr,wr,wtemp;
for (ntot=1, idim=1; idim<=ndim; idim++)
ntot *= nn[idim];
nprev = 1;
for (idim=ndim; idim>=1; idim--)
n = nn[idim];
nrem = ntot/(n*nprev);
ip1=nprev << 1;
ip2 = ip1*n;
ip3 = ip2*nrem;
i2rev = 1;
for (i2=1; i2<=ip2; i2+=ip1)
if (i2 < i2rev)
for (i1=i2; i1<=i2+ip1-2; i1+=2)
for (i3=i1; i3<=ip3; i3+=ip2)
i3rev = i2rev+i3-i2;
SWAP(data[i3],data[i3rev]);
SWAP(data[i31],data[i3rev1]);
ibit = ip2>>1;
while (ibit>=ip1 && i2rev>ibit)
i2rev -= ibit;
ibit >>= 1;
i2rev += ibit;
ifp1 = ip1;
while (ifp1 < ip2)
ifp2 = ifp1 << 1;
theta = 2isignPI/(ifp2/ip1);
wtemp = sin(0.5*theta);
wpr = -2.0wtempwtemp;
wpi = sin(theta);
wr = 1.0;
wi = 0.0;
for (i3=1; i3<=ifp1; i3+=ip1)
for (i1=i3; i1<=i3+ip1-2; i1+=2)
for (i2=i1; i2<=ip3; i2+=ifp2)
k1 = i2;
k2 = k1+ifp1;
tempr = (float)wrdata[k2]-(float)widata[k2+1];
tempi = (float)wrdata[k21](float)widata[k2];
data[k2] = data[k1]-tempr;
data[k2+1] = data[k1+1]-tempi;
data[k1] += tempr;
data[k1+1] += tempi;
wr = (wtemp=wr)wpr-wiwpi+wr;
wi = wiwprwtempwpiwi;
ifp1 = ifp2;
nprev *= n;
// Function to calculate a three-dimensional Fourier transform of
// data[1..nn1][1..nn2][1..nn3] (where nn1=1 for the case of a logically two-
// dimensional array). This routine returns (for isign=1) the complex fast
// Fourier transform as two complex arrays: On output, data contains the zero
// and positive frequency values of the third frequency component, while
// speq[1..nn1][1..2*nn2] contains the Nyquist critical frequency values of the
// third frequency component. First (and second) frequency components are
// stored for zero, positive, and negative frequencies, in standard wrap-around
// order. See Numerical Recipes for description of how complex values are
// arranged. For isign=-1, the inverse transform (times nn1nn2nn3/2 as a
// constant multiplicative factor) is performed, with output data (viewed as
// real array) deriving from input data (viewed as complex) and speq. For
// inverse transforms on data not generated first by a forward transform, make
// sure the complex input data array satisfies property 12.5.2 from NR. The
// dimensions nn1, nn2, nn3 must always be integer powers of 2.
void rlft3(float *data,float **speq,unsigned long nn1,unsigned long nn2,
unsigned long nn3,int isign)
double theta,wi,wpi,wpr,wr,wtemp;
float c1,c2,h1r,h1i,h2r,h2i;
unsigned long i1,i2,i3,j1,j2,j3,nn[4],ii3;
if (1+&data[nn1][nn2][nn3]-&data[1][1][1] != nn1nn2nn3)
fprintf(stderr,
"rlft3: problem with dimensions or contiguity of data array\n");
exit(1);
c1 = 0.5;
c2 = -0.5*isign;
theta = 2isign(PI/nn3);
wtemp = sin(0.5*theta);
wpr = -2.0wtempwtemp;
wpi = sin(theta);
nn[1] = nn1;
nn[2] = nn2;
nn[3] = nn3 >> 1;
// Case of forward transform. Here is where most all of the compute time is
// spent. Extend data periodically into speq.
if (isign == 1)
fourn(&data[1][1][1]-1,nn,3,isign);
for (i1=1; i1<=nn1; i1++)
for (i2=1, j2=0; i2<=nn2; i2++)
speq[i1][++j2] = data[i1][i2][1];
speq[i1][++j2] = data[i1][i2][2];
for (i1=1; i1<=nn1; i1++)
// Zero frequency is its own reflection; otherwise locate corresponding
// negative frequency in wrap-around order.
j1 = (i1 != 1 ? nn1-i1+2 : 1);
// Initialize trigonometric recurrence.
wr = 1.0;
wi = 0.0;
for (ii3=1, i3=1; i3<=(nn3>>2)+1; i3+,ii3=2)
for (i2=1; i2<=nn2; i2++)
if (i3 == 1)
j2 = (i2 != 1 ? ((nn2-i2)<<1)+3 : 1);
h1r = c1*(data[i1][i2][1]+speq[j1][j2]);
h1i = c1*(data[i1][i2][2]-speq[j1][j2+1]);
h2i = c2*(data[i1][i2][1]-speq[j1][j2]);
h2r = -c2*(data[i1][i2][2]speq[j1][j21]);
data[i1][i2][1] = h1r+h2r;
data[i1][i2][2] = h1i+h2i;
speq[j1][j2] = h1r-h2r;
speq[j1][j2+1] = h2i-h1i;
else
j2 = (i2 != 1 ? nn2-i2+2 : 1);
j3 = nn3+3-(i3<<1);
h1r = c1*(data[i1][i2][ii3]+data[j1][j2][j3]);
h1i = c1*(data[i1][i2][ii31]-data[j1][j2][j31]);
h2i = c2*(data[i1][i2][ii3]-data[j1][j2][j3]);
h2r = -c2*(data[i1][i2][ii31]+data[j1][j2][j31]);
data[i1][i2][ii3] = h1r+wrh2r-wih2i;
data[i1][i2][ii3+1] = h1iwrh2iwih2r;
data[j1][j2][j3] = h1r-wrh2r+wih2i;
data[j1][j2][j3+1] = -h1iwrh2iwih2r;
// Do the recurrence.
wr = (wtemp=wr)wpr-wiwpi+wr;
wi = wiwprwtempwpiwi;
// Case of reverse transform.
if (isign == -1)
fourn(&data[1][1][1]-1,nn,3,isign);
// Function to perform Gaussian blur.
void gaussianblur(void)
float **blur,***conv,***pop,**speqblur,**speqconv,*speqpop;
int i,j,p,q;
blur = d3tensor(1,1,1,lx,1,ly);
conv = d3tensor(1,1,1,lx,1,ly);
pop = d3tensor(1,1,1,lx,1,ly);
speqblur = dmatrix(1,1,1,2*lx);
speqconv = dmatrix(1,1,1,2*lx);
speqpop = dmatrix(1,1,1,2*lx);
// Fill population and convolution matrix.
for (i=1; i<=lx; i++) for (j=1; j<=ly; j++)
if (i > lx/2) p = i-1-lx;
else p = i-1;
if (j > ly/2) q = j-1-ly;
else q = j-1;
pop[1][j] = rho_0[i-1][j-1];
conv[1][j] = 0.5*
(erf((p+0.5)/(sqrt(2.0)(SIGMApow(SIGMAFAC,nblurs))))-
erf((p-0.5)/(sqrt(2.0)(SIGMA*pow(SIGMAFAC,nblurs)))))
(erf((q+0.5)/(sqrt(2.0)(SIGMApow(SIGMAFAC,nblurs))))-
erf((q-0.5)/(sqrt(2.0)(SIGMA*pow(SIGMAFAC,nblurs)))))/(lxly);
// Fourier transform.
rlft3(pop,speqpop,1,lx,ly,1);
rlft3(conv,speqconv,1,lx,ly,1);
// Multiply pointwise.
for (i=1; i<=lx; i++)
for (j=1; j<=ly/2; j++)
blur[1][2*j-1] =
pop[1][2j-1]*conv[1][2j-1]-
pop[1][2j]*conv[1][2j];
blur[1][2*j] =
pop[1][2j]*conv[1][2j-1]+
pop[1][2j-1]*conv[1][2j];
for (i=1; i<=lx; i++)
speqblur[1][2*i-1] =
speqpop[1][2i-1]*speqconv[1][2i-1]-
speqpop[1][2i]*speqconv[1][2i];
speqblur[1][2*i] =
speqpop[1][2i]*speqconv[1][2i-1]+
speqpop[1][2i-1]*speqconv[1][2i];
// Backtransform.
rlft3(blur,speqblur,1,lx,ly,-1);
// Write to rho_0.
for (i=1; i<=lx; i++) for (j=1; j<=ly; j++) rho_0[i-1][j-1] = blur[1][j];
free_f3tensor(blur,1,1,1,lx,1,ly);
free_f3tensor(conv,1,1,1,lx,1,ly);
free_f3tensor(pop,1,1,1,lx,1,ly);
free_matrix(speqblur,1,1,1,2*lx);
free_matrix(speqconv,1,1,1,2*lx);
free_matrix(speqpop,1,1,1,2*lx);
// Function to initialize rho_0. The original density is blurred with width
// SIGMA*pow(SIGMAFAC,nblurs).
void initcond(void)
float maxpop;
int i,j;
// Reconstruct population density.
coscosft(rho_0,-1,-1);
// There must not be negative densities.
for (i=0; i<lx; i++) for (j=0; j<ly; j++) if (rho_0[j]<-1e10)
fprintf(stderr,"ERROR: Negative density in DENSITYFILE.\n");
exit(1);
// Perform Gaussian blur.
printf("Gaussian blur ...\n");
gaussianblur();
// Find the mimimum density. If it is very small suggest an increase in
// SIGMA.
minpop = rho_0[0][0];
maxpop = rho_0[0][0];
for (i=0; i<lx; i++) for (j=0; j<ly; j++) if (rho_0[j]<minpop)
minpop = rho_0[j];
for (i=0; i<lx; i++) for (j=0; j<ly; j++) if (rho_0[j]>maxpop)
maxpop = rho_0[j];
if (0<minpop && minpop<1e-8*maxpop)
fprintf(stderr,"Minimimum population very small (%f). Integrator\n",
minpop);
fprintf(stderr,
"will probably converge very slowly. You can speed up the\n");
fprintf(stderr,"process by increasing SIGMA to a value > %f.\n",
SIGMA*pow(SIGMAFAC,nblurs));
// Replace rho_0 by cosine Fourier transform in both variables.
coscosft(rho_0,1,1);
// Function to calculate the velocity field
void calcv(float t)
int j,k;
// Fill rho with Fourier coefficients.
for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
rho[j][k] = exp(-((PIj/lx)*(PI*j/lx)+(PI*k/ly)*(PI*k/ly))*t)rho_0[j][k];
// Calculate the Fourier coefficients for the partial derivative of rho.
// Store temporary results in arrays gridvx, gridvy.
for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
gridvx[j][k] = -(PIj/lx)rho[j][k];
gridvy[j][k] = -(PIk/ly)rho[j][k];
// Replace rho by cosine Fourier backtransform in both variables.
coscosft(rho,-1,-1);
// Replace vx by sine Fourier backtransform in the first and cosine Fourier
// backtransform in the second variable.
sincosft(gridvx,-1,-1);
// Replace vy by cosine Fourier backtransform in the first and sine Fourier
// backtransform in the second variable.
cossinft(gridvy,-1,-1);
// Calculate the velocity field.
for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
gridvx[j][k] = -gridvx[j][k]/rho[j][k];
gridvy[j][k] = -gridvy[j][k]/rho[j][k];
// Function to bilinearly interpolate a two-dimensional array. For higher
// accuracy one could consider higher order interpolation schemes.
float intpol(float **arr,float x,float y)
int gaussx,gaussy;
float deltax,deltay;
// Decompose x and y into an integer part and a decimal.
gaussx = (int)x;
gaussy = (int)y;
deltax = x-gaussx;
deltay = y-gaussy;
// Interpolate.
if (gaussx==lx && gaussy==ly)
return arr[gaussx][gaussy];
if (gaussx==lx)
return (1-deltay)arr[gaussx][gaussy]deltayarr[gaussx][gaussy1];
if (gaussy==ly)
return (1-deltax)arr[gaussx][gaussy]deltaxarr[gaussx1][gaussy];
return (1-deltax)(1-deltay)arr[gaussx][gaussy]+
(1-deltax)deltayarr[gaussx][gaussy1]
deltax(1-deltay)arr[gaussx1][gaussy]
deltaxdeltayarr[gaussx1][gaussy1];
// Function to find the root of the system of equations
// xappr-0.5h*v_x(t+h,xappr,yappr)-x[j][k]-0.5*hvx[j][k]=0,
// yappr-0.5h*v_y(t+h,xappr,yappr)-y[j][k]-0.5*hvy[j][k]=0
// with Newton-Raphson. Returns TRUE after sufficient convergence.
BOOLEAN newt2(float h,float *xappr,float xguess,float *yappr,float yguess,
int j,int k)
float deltax,deltay,dfxdx,dfxdy,dfydx,dfydy,fx,fy;
int gaussx,gaussxplus,gaussy,gaussyplus,i;
// Initial guess.
*xappr = xguess;
*yappr = yguess;
for (i=1; i<=IMAX; i++)
// fx, fy are the left-hand sides of the two equations. Find
// v_x(t+h,xappr,yappr), v_y(t+h,xappr,yappr) by interpolation.
fx = xappr-0.5*h*intpol(gridvx,*xappr,*yappr)-x[j][k]-0.5*hvx[j][k];
fy = yappr-0.5*h*intpol(gridvy,*xappr,*yappr)-y[j][k]-0.5*hvy[j][k];
// Linearly approximate the partial derivatives of fx, fy with a finite
// difference method. More elaborate techniques are possible, but this
// quick and dirty method appears to work reasonably for our purpose.
gaussx = (int)(*xappr);
gaussy = (int)(*yappr);
if (gaussx == lx) gaussxplus = 0;
else gaussxplus = gaussx+1;
if (gaussy == ly) gaussyplus = 0;
else gaussyplus = gaussy+1;
deltax = x[j][k] - gaussx;
deltay = y[j][k] - gaussy;
dfxdx = 1 - 0.5h
((1-deltay)*(gridvx[gaussxplus][gaussy]-gridvx[gaussx][gaussy])+
deltay*(gridvx[gaussxplus][gaussyplus]-gridvx[gaussx][gaussyplus]));
dfxdy = -0.5h
((1-deltax)*(gridvx[gaussx][gaussyplus]-gridvx[gaussx][gaussy])+
deltax*(gridvx[gaussxplus][gaussyplus]-gridvx[gaussxplus][gaussy]));
dfydx = -0.5h
((1-deltay)*(gridvy[gaussxplus][gaussy]-gridvy[gaussx][gaussy])+
deltay*(gridvy[gaussxplus][gaussyplus]-gridvy[gaussx][gaussyplus]));
dfydy = 1 - 0.5h
((1-deltax)*(gridvy[gaussx][gaussyplus]-gridvy[gaussx][gaussy])+
deltax*(gridvy[gaussxplus][gaussyplus]-gridvy[gaussxplus][gaussy]));
// If the current approximation is (xappr,yappr) for the zero of
// (fx(x,y),fy(x,y)) and J is the Jacobian, then we can approximate (in
// vector notation) for |delta|<<1:
// f((xappr,yappr)+delta) = f(xappr,yappr)+J*delta.
// Setting f((xappr,yappr)+delta)=0 we obtain a set of linear equations
// for the correction delta which moves f closer to zero, namely
// J*delta = -f.
// The improved approximation is then x = xappr+delta.
// The process will be iterated until convergence is reached.
if ((fx*fx + fy*fy) < TOLF) return TRUE;
deltax = (fy*dfxdy - fxdfydy)/(dfxdxdfydy - dfxdy*dfydx);
deltay = (fx*dfydx - fydfxdx)/(dfxdxdfydy - dfxdy*dfydx);
if ((deltax*deltax + deltay*deltay) < TOLX) return TRUE;
*xappr += deltax;
*yappr += deltay;
//printf("deltax %f, deltay %f\n",deltax,deltay);
fprintf(stderr,"newt2 failed, increasing sigma to %f.\n",
SIGMA*pow(SIGMAFAC,nblurs));
return FALSE;
// Function to integrate the nonlinear Volterra equation. Returns TRUE after
// the displacement field converged, after MAXINTSTEPS integration steps, or
// if the time exceeds TIMELIMIT.
BOOLEAN nonlinvoltra(void)
BOOLEAN stepsize_ok;
#ifdef DISPLFILE
FILE *displfile = fopen(DISPLFILE);
#endif
float h,maxchange=INFTY,t,vxplus,vyplus,xguess,yguess;
int i,j,k;
do
initcond();
nblurs++;
if (minpop<0.0)
fprintf(stderr,
"Minimum population negative, will increase sigma to %f\n",
SIGMA*pow(SIGMAFAC,nblurs));
while (minpop<0.0);
h = HINITIAL;
t = 0; // Start at time t=0.
// (x[j][k],y[j][k]) is the position for the element that was at position
// (j,k) at time t=0.
for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
x[j][k] = j;
y[j][k] = k;
calcv(0.0);
// (gridvx[j][k],gridvy[j][k]) is the velocity at position (j,k).
// (vx[j][k],vy[j][k]) is the velocity at position (x[j][k],y[j][k]).
// At t=0 they are of course identical.
for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
vx[j][k] = gridvx[j][k];
vy[j][k] = gridvy[j][k];
i = 1; // i counts the integration steps.
// Here is the integrator.
do
stepsize_ok = TRUE;
calcv(t+h);
for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
// First take a naive integration step. The velocity at time t+h for
// the element [j][k] is approximately
// v(th,x[j][k]+hvx[j][k],y[j][k]hvy[j][k]).
// The components, call them vxplus and vyplus, are interpolated from
// gridvx and gridvy.
vxplus = intpol(gridvx,x[j][k]hvx[j][k],y[j][k]hvy[j][k]);
vyplus = intpol(gridvy,x[j][k]hvx[j][k],y[j][k]hvy[j][k]);
// Based on (vx[j][k],vy[j][k]) and (vxplus,vyplus) we expect the
// new position at time t+h to be:
xguess = x[j][k] + 0.5h(vx[j][k]+vxplus);
yguess = y[j][k] + 0.5h(vy[j][k]+vyplus);
// Then we make a better approximation by solving the two nonlinear
// equations:
// xappr[j][k]-0.5hv_x(t+h,xappr[j][k],yappr[j][k])-
// x[j][k]-0.5hvx[j][k]=0,
// yappr[j][k]-0.5hv_y(t+h,xappr[j][k],yappr[j][k])-
// y[j][k]-0.5hvy[j][k]=0
// with Newton-Raphson and (xguess,yguess) as initial guess.
// If newt2 fails to converge, exit nonlinvoltra.
if (!newt2(h,&xappr[j][k],xguess,&yappr[j][k],yguess,j,k))
return FALSE;
// If the integration step was too large reduce the step size.
if ((xguess-xappr[j][k])*(xguess-xappr[j][k])+
(yguess-yappr[j][k])*(yguess-yappr[j][k]) > TOLINT)
if (h<MINH)
fprintf(stderr,
"Time step below %f, increasing SIGMA to %f\n",
h,SIGMA*pow(SIGMAFAC,nblurs));
nblurs++;
return FALSE;
h /= 10;
stepsize_ok = FALSE;
break;
if (!stepsize_ok) continue;
else
t += h;
maxchange = 0.0; // Monitor the maximum change in positions.
for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
if ((x[j][k]-xappr[j][k])*(x[j][k]-xappr[j][k])+
(y[j][k]-yappr[j][k])*(y[j][k]-yappr[j][k]) > maxchange)
maxchange =
(x[j][k]-xappr[j][k])*(x[j][k]-xappr[j][k])+
(y[j][k]-yappr[j][k])*(y[j][k]-yappr[j][k]);
x[j][k] = xappr[j][k];
y[j][k] = yappr[j][k];
vx[j][k] = intpol(gridvx,xappr[j][k],yappr[j][k]);
vy[j][k] = intpol(gridvy,xappr[j][k],yappr[j][k]);
h *= 1.2; // Make the next integration step larger.
if (i%10==0) printf("time %f\n",t);
i++;
} while (i<MAXINTSTEPS && t<TIMELIMIT && maxchange>CONVERGENCE);
if (maxchange>CONVERGENCE)
fprintf(stderr,
"WARNING: Insufficient convergence within %i steps, time %f.\n",
MAXINTSTEPS,TIMELIMIT);
#ifdef DISPLFILE
// Write displacement field to file.
fprintf(displfile,"time %f\nminx %f\nmaxx %f\nminy %f\nmaxy %f\n",
t,minx,maxx,miny,maxy);
fprintf(displfile,"sigma %f\n",SIGMA*pow(SIGMAFAC,nblurs-1));
fprintf(displfile,"background %f\nlx\nly\n\n",0,lx,ly);
for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
fprintf(displfile,"j %i, k %i, x %f, y %f\n",j,k,x[j][k],y[j][k]);
fclose(displfile);
#endif
return TRUE;
// Function to transform points according to displacement field.
POINT transf(POINT p)
float deltax,deltay,den,t,u;
int gaussx,gaussy;
POINT a,b,c,d,ptr;
p.x = (p.x-minx)*lx/(maxx-minx);
p.y = (p.y-miny)*ly/(maxy-miny);
gaussx = (int)p.x;
gaussy = (int)p.y;
if (gaussx<0 || gaussx>lx || gaussy<0 || gaussy>ly)
fprintf(stderr,"ERROR: Coordinate limits exceeded in transf.\n");
exit(1);
deltax = p.x - gaussx;
deltay = p.y - gaussy;
// The transformed point is the intersection of the lines:
// (I) connecting
// (1-deltax)(x,y[gaussx][gaussy])deltax(x,y[gaussx1][gaussy])
// and
// (1-deltax)(x,y[gaussx][gaussy1])+deltax(x,y[gaussx+1][gaussy1])
// (II) connecting
// (1-deltay)(x,y[gaussx][gaussy])deltay(x,y[gaussx][gaussy1])
// and
// (1-deltay)(x,y[gaussx1][gaussy])+deltay(x,y[gaussx+1][gaussy1]).
// Call these four points a, b, c and d.
a.x = (1-deltax)*x[gaussx][gaussy] + deltax*x[gaussx+1][gaussy];
a.y = (1-deltax)*y[gaussx][gaussy] + deltax*y[gaussx+1][gaussy];
b.x = (1-deltax)*x[gaussx][gaussy+1] + deltax*x[gaussx1][gaussy1];
b.y = (1-deltax)*y[gaussx][gaussy+1] + deltax*y[gaussx1][gaussy1];
c.x = (1-deltay)*x[gaussx][gaussy] + deltay*x[gaussx][gaussy+1];
c.y = (1-deltay)*y[gaussx][gaussy] + deltay*y[gaussx][gaussy+1];
d.x = (1-deltay)*x[gaussx+1][gaussy] + deltay*x[gaussx1][gaussy1];
d.y = (1-deltay)*y[gaussx+1][gaussy] + deltay*y[gaussx1][gaussy1];
// Solve the vector equation a+t(b-a) = c+u(d-c) for the scalars t, u.
if (fabs(den=(b.x-a.x)(c.y-d.y)+(a.y-b.y)(c.x-d.x))<1e-12)
fprintf(stderr,"ERROR: Transformed area element has parallel edges.\n");
exit(1);
t = ((c.x-a.x)(c.y-d.y)+(a.y-c.y)(c.x-d.x))/den;
u = ((b.x-a.x)(c.y-a.y)+(a.y-b.y)(c.x-a.x))/den;
if (t<-1e-3|| t>1+1e-3 || u<-1e-3 || u>1+1e-3)
fprintf(stderr,"WARNING: Transformed area element non-convex.\n");
ptr.x = (1-(a.x+t(b.x-a.x))/lx)minx + ((a.x+t(b.x-a.x))/lx)maxx;
ptr.y = (1-(a.y+t(b.y-a.y))/ly)miny + ((a.y+t(b.y-a.y))/ly)maxy;
return ptr;
// Function to read spatial features from user-specified file and map to
// cartogram.
void cartogram(void)
char id[LINELENGTH],line[LINELENGTH];
FILE infile,outfile;
float xcoord,ycoord;
POINT p;
infile = fopen(MAPGENFILE);
outfile = fopen(CARTGENFILE,"w");
while (!readline(line,infile))
if (sscanf(line,"%s %f %f",&id,&xcoord,&ycoord)==3)
p.x = xcoord;
p.y = ycoord;
p = transf(p);
fprintf(outfile,"%s %f %f\n",id,p.x,p.y);
else if (sscanf(line,"%f %f",&xcoord,&ycoord)==2)
p.x = xcoord;
p.y = ycoord;
p = transf(p);
fprintf(outfile,"%f %f\n",p.x,p.y);
else
sscanf(line,"%s",&id);
fprintf(outfile,"%s\n",id);
fclose(infile);
fclose(outfile);
main(void)
BOOLEAN n;
char c;
FILE genfile,psfile = fopen(MAP2PS);
float oldlx,oldly,oldmaxx,oldmaxy,oldminx,oldminy,totarea;
int i,polyctr,regctr;
// Read the polygon coordinates.
if ((genfile = fopen(MAPGENFILE)) == NULL)
fprintf(stderr,"ERROR: Cannot find MAPGENFILE\n");
exit(1);
countpoly(genfile);
fclose(genfile);
genfile = fopen(MAPGENFILE);
countcorn(genfile);
fclose(genfile);
genfile = fopen(MAPGENFILE);
readcorn(genfile);
fclose(genfile);
makeregion();
printf("%i polygon(s), %i region(s)\n",npoly,nregion);
printf("lx=%i, ly=%i\n",lx,ly);
// Calculate total area.
//totarea = 0.0;
//for (regctr=0; regctr<nregion; regctr++)
// printf("region %i has area %f, contains %i polygons\n",regionid[regctr],
// regionarea(nregcorn[regctr],regcorn[regctr]),npolyinreg[regctr]);
// totarea += regionarea(nregcorn[regctr],regcorn[regctr]);
//printf("totarea = %f\n",totarea);
// Make map.
pspicture(psfile);
fclose(psfile);
// Allocate memory for arrays.
gridvx = (float*)malloc((lx+1)*sizeof(float));
gridvy = (float*)malloc((lx+1)*sizeof(float));
rho = (float*)malloc((lx+1)*sizeof(float));
rho_0 = (float*)malloc((lx+1)*sizeof(float));
vx = (float*)malloc((lx+1)*sizeof(float));
vy = (float*)malloc((lx+1)*sizeof(float));
x = (float*)malloc((lx+1)*sizeof(float));
xappr = (float*)malloc((lx+1)*sizeof(float));
y = (float*)malloc((lx+1)*sizeof(float));
yappr = (float*)malloc((lx+1)*sizeof(float));
within = (int*)malloc((lx+1)*sizeof(int));
for (i=0; i<=lx; i++)
gridvx = (float)malloc((ly+1)sizeof(float));
gridvy = (float)malloc((ly+1)sizeof(float));
rho = (float)malloc((ly+1)sizeof(float));
rho_0 = (float)malloc((ly+1)sizeof(float));
vx = (float)malloc((ly+1)sizeof(float));
vy = (float)malloc((ly+1)sizeof(float));
x = (float)malloc((ly+1)sizeof(float));
xappr = (float)malloc((ly+1)sizeof(float));
y = (float)malloc((ly+1)sizeof(float));
yappr = (float)malloc((ly+1)sizeof(float));
within = (int)malloc((ly+1)sizeof(int));
// Digitize the density.
bboxes();
interior();
digdens();
// Solve the diffusion equation.
do n = nonlinvoltra(); while (!n);
// Print cartogram generate file.
cartogram();
// Read the transformed polygon coordinates.
oldlx = lx;
oldly = ly;
oldmaxx = maxx;
oldmaxy = maxy;
oldminx = minx;
oldminy = miny;
genfile = fopen(CARTGENFILE,"r");
countpoly(genfile);
fclose(genfile);
genfile = fopen(CARTGENFILE,"r");
countcorn(genfile);
fclose(genfile);
lx = oldlx;
ly = oldly;
maxx = oldmaxx;
maxy = oldmaxy;
minx = oldminx;
miny = oldminy;
genfile = fopen(CARTGENFILE,"r");
readcorn(genfile);
fclose(genfile);
makeregion();
// Make cartogram
psfile = fopen(CART2PS);
pspicture(psfile);
fclose(psfile);
The part of the code where the bus error occurs is this:
void interior(void)
int i,inhowmanyregions,inregion[2],j,k,l,m,n,regctr;
// Initialize within[][]. -1 means outside all regions.
for (i=0; i<=lx; i++) for (j=0; j<=ly; j++) within[j] = -1;
// Fill within[][].
for (i=0; i<nregion; i++) for (j=0; j<npolyinreg; j++)
for (k=0, n=npolycorn[polyinreg[j]]-1;
k<npolycorn[polyinreg[j]]; n=k++)
for (l=(int)ceil(MIN(polycorn[polyinreg[j]][k-1].y,
polycorn[polyinreg[j]][k].y));
l<MAX(polycorn[polyinreg[j]][k-1].y,
polycorn[polyinreg[j]][k].y); l++)
for (m=(int)floor(bbminx[polyinreg[j]]);
m<(polycorn[polyinreg[j]][n].x-
polycorn[polyinreg[j]][k].x)*
(l-polycorn[polyinreg[j]][k].y)/
(polycorn[polyinreg[j]][n].y-
polycorn[polyinreg[j]][k].y)+
polycorn[polyinreg[j]][k].x;
m++)
within[m][l] = i-within[m][l]-1;
I really have no idea what is going on. Can anyone help?
Thanks,
mooseguyorangekay wrote:
That is absolutely unreadable.
I agree completely. How about also providing a link to a set of input files so that we could actually run the code ourselves? Otherwise, there is no chance to debug the source code, it is just a mess.
You might have better luck with an older version of the file. To quote the comments:
// Modified on March 31, 2005. Initialized maxchange in nonlinvoltra() as
// INFTY. Replaced crnmbr() by a similar, but faster routine interior().
// Many thanks to Stuart Anderson for pointing out this shortcut.
I suspect that the "interior" function is just plain incorrect. It doesn't matter if it runs on some other OS. Something about it is wrong and the code is so cryptic that it can't be deciphered. -
Poor reflective memory read performance
I'm having some trouble with the GE 5565 PIORC reflective memory set of VIs for use with our reflective memory setup. I need to copy a pretty sizable chunk of memory out of reflective memory and into a DLL I've written, but the performance on the "GE 5565 PIORC:GE5565 Read (Cluster).vi" is not where I need it. I need to copy somewhere in the realm of 12k out of reflective memory at a high frequency, but the call to read those 12k takes longer than the period I need to gather the data at. I apologize in advance for the image-heavy post, but I think it's worth it to show what I've got.
Here's a picture of my setup to benchmark the Read call runtime:
Here's a graph of runtimes of that Read call, in microseconds:
I need it to run in way less than 16 ms, which doesn't seem unreasonable to me for only 12k. I did fool around with the DMA version of the Read (which I don't really understand, and the documentation is nonexistent as far as I can tell). Here's my test setup:
And here's a chart similar to the one above:
Way better, though I have no idea if it even does what I think it should So, I have a few questions. First, is there any way to get better performance out of that Read VI? Some other library I should be using, some setting I should be setting, some other way I should be benchmarking its performance, maybe even some way of doing this with another DLL? Second, if the Read can't achieve the performance I need, what's up with the DMA version, and how would I use it properly? Is the performance advantage that it appears to be giving real, or just an artifact of some mistaken way in which I'm using it? Thanks!Hi dgoes
Windows is not a deterministic operating system so the loop cycle time that you are getting might be the best time that the windows system can achieve. In order to benchmark your code you can also use the input node and the output node of the timed loop. Check the following link.
Timed Loop
But it will be nice to know if you are working on a real time operating system or windows? Because unfortunately the windows operating system is not a deterministic system so the time loop might not work as expected. Here are a couple of links with information about this.
windows 1KHz time loop limitation reason
What is a Real-Time Operating System (RTOS)?
Which driver are you using for the GE 5565 PIORC? Is it this one?
GE 5565 PIORC
If it is, please notice that this driver is neither supported nor certified by National Instruments. This card is supported with NI VeriStand. Please check the information on the following links.
Getting Started With the GE cPCI-5565PIORC Reflective Memory Module
GE cPCI-5565PIORC
I hope that this information answer your questions.
Regards
Esteban R.
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