How can I calculate area under a curve?

I would like to use an integral equation to obtain positive and negative areas from graphed data. For example, I have a graph representing power for a 24 hour period and want to integrate the curve to obtain daily energy.

One common way to approximate the area under a curve is to divide it into a series of trapezoids, with the area of each calculated as avg height x width. Then sum the areas.
So with this table:
x
y
trapezoid
1
0
3
2
6
11
3
16
23
4
30
39
5
48
59
6
70
83
7
96
218
You could use this formula in C2, filled down through the rest of the body cells in that column:
=IFERROR((B3+B2)÷2×(A3−A2),"")
This calculates the area of each trapezoid.
The first row is defined as a Header Row, the last row as a Footer Row. It's important not to have blank row(s) before the Footer Row. The sum formula in the Footer Row in C9 is:
=SUM(C)
Of course, the greater the number of x-y data points the better the estimate of the area under the curve.
SG

Similar Messages

How do I calculate areas under the curves above and below the x axis at 0?

The xy graph generated is similar to a sinusoidal representing the magnetic intensity of the poles of a motor. For each of the four areas above and below the x axis at 0 I would like to calculate the area then do a variance analysis on the 8 areas. Can anyone suggest a method to calculate each of the 8 areas. See the attached vi to understand better what I'm trying to do.
Thank you.
Attachments:
MIN MAX A.vi ‏16 KB

Hi all,
If you are simply looking to do numeric integration, there is built in functionality to do that. The help file is here:
http://zone.ni.com/reference/en-XX/help/371361H-01/gmath/numeric_integration/
You will may have to do some edge checking if you want to break this down into individual components.
Let us know if you need any more assistance
Applications Engineer
National Instruments

How can i find area under a closed curve

I am having set of Y-values w.r.t X-values.When i am using numerical integration.vi to measure area, it is showing wrong answer.Is there any other vi to find the area under a closed curve.

Is the dt constant between your values? The numerical integration.vi needs them to be...
What's the correct answer depends on how you are to interpolate between the points. The numerical integration.vi allows you to select between a number of approaches (Simpson's rule, trapezoidal etc..). It does not allow integrating the values as if it were a histogram...If that is what you want to do then all you need to do is to add the values and then multiply the result by dt...
When you say that the answer is incorrect, could you give an example array, dt and correct result?
If the curve is supposed to be a special function you could use regression analysis to find the formula of the curve and then integrate that...
MTO

How to calculate area under the waveform

I need to calculate absolute energy of the waveform. Do you have a math function to do this? I used Integrate funtion but the return value is 0.

You didn't say much about what you are doing. The CNiMath::Integrate function should be able to do this for you. Maybe you don't understand the function. You would input your waveform as a vector (say 1000 elements), then the delta time between each element (1/sampling rate), then the first and last value of the discrete integral (waveform[-1] and waveform[n]). Then, on output, the vector would contain the integrated data. You could get the sum of the elements to get the total area under the curve.
Best Regards,
Chris Matthews
National Instruments

Is how can I calculate how many transitions are inside an array?

Let’s assume that we have an array of 582 elements. Some of them are above 4 and some of them are below 1,let’s also say that values who are above 4 are equal to True (1) and the values below 1 are equal to False (0). The question is how can I calculate how many transitions are inside the array from 1 to 0?How many peaks I have? Can please someone suggest a code solution for that?
Solved!
Go to Solution.

If you only care about actual transitions and not the type of them, I'm a fan of the simple XOR.
There are only two ways to tell somebody thanks: Kudos and Marked Solutions
Unofficial Forum Rules and Guidelines
Attachments:
Count Transitions.png ‏19 KB

How can I calculate the waveform integral in a defined time interval?

Hi:
I need your help. How can I calculate the waveform integral in a defined time interval? For example: from "0" to "2pi"?!
Thanks.

Hello Clecio,
You might want to try the Integral x(t) VI. The documentation for this VI notes:
Performs the discrete integration of the sampled signal X. Integral x(t) calculates a definite integral. The value of the output array at any value x is the area under the curve of the input array between 0 and x.
You would pass the samples of the waveform that fall between your particular window, then pass 1/number of samples for the d(t) parameter.
Hope that helps.
Wendy L
LabWindows/CVI Developer Newsletter - ni.com/cvinews

Regression area under the curve

hello
i was trying to get the area under the curve. mathematically the
integration can b done directly from 'numeric integration' vi. but what
my problem is i cant define the time t1 to t3( as i need to set the
threshold level to eliminate noise). what i previously did was defining
the threshold level, find the 2 point of t1 and t2. but i left out the
coloured portion. using regression will it help to get t3?if yes. how
this will b done?
thanks
regards
Attachments:
graph(dt)1.PNG ‏8 KB

This has been going on for a while:
http://forums.ni.com/ni/board/message?board.id=170&message.id=226483#M226483
http://forums.ni.com/ni/board/message?board.id=MathScript&message.id=145#M145
http://forums.ni.com/ni/board/message?board.id=170&message.id=227008#M227008
If I understand this correctly, you use a threshold to find the peak, but then you want the entire area, including the "wings".
As I said before, if you pick the baseline right, your integration boundary does not need to be exact and can be significantly outside because the areas outside the peak will average to zero.
If you have a mathematical model for the peak (e.g. gaussian), you can fit it and calculate the area from the fit.
LabVIEW Champion . Do more with less code and in less time .

Calculating area under a curve - trapezium rule

Hi,
I'm trying to calculate the 'area under the curve' using the trapezium rule for a set of data points. i.e. I have a set of values, sampled at irregular intervals.
create table measurements (
measurement_value integer,
measurement_time timestamp
insert into measurements (measurement_value,measurement_time) values (50,TIMESTAMP'2011-01-01 00:00:00');
insert into measurements (measurement_value,measurement_time) values (40,TIMESTAMP'2011-01-01 01:00:00');
insert into measurements (measurement_value,measurement_time) values (40,TIMESTAMP'2011-01-01 03:00:00');
insert into measurements (measurement_value,measurement_time) values (50,TIMESTAMP'2011-01-01 03:30:00');
insert into measurements (measurement_value,measurement_time) values (40,TIMESTAMP'2011-01-01 05:00:00');
insert into measurements (measurement_value,measurement_time) values (40,TIMESTAMP'2011-01-01 06:00:00');
insert into measurements (measurement_value,measurement_time) values (60,TIMESTAMP'2011-01-01 07:00:00');I'd like to calculate the area of the 'curve' where the value was below a threshold of, e.g. 45.
I can use the trapezium rule and assume a straight line between subsequent measurement, i.e. for the first 2 data points, the value drops from 50 to 40 linearly over the hour, and so the area for those measurements is (30min * 5)/2. For the 2nd and 3rd data points, the area is (120min * 5), for the 3rd and 4th, the area is (15min * 5)/2. And so on. The values are not necessarily round numbers, almost any value is possible.
I've started by using 'lead' to obtain the subsequent measurement value and time, but I'm getting stuck dealing with the end points and non-trivial interpolation. Does anyone have any pointers to get me going?
Thanks,
Dan Scott

Maybe this will do it:
SELECT SUM(CASE
            WHEN curr_value > :threshold AND next_value < :threshold
            THEN -- Area of rectangle specified by threshold
                 (new_measurement_time_sec-curr_measurement_time_sec)*:threshold
               + -- Area of remaining trapezoid
                 ABS((next_measurement_time_sec - new_measurement_time_sec)*((next_value - :threshold)/2))
            WHEN next_value > :threshold AND curr_value < :threshold
            THEN -- Area of rectangle specified by threshold
                 (next_measurement_time_sec-new_measurement_time_sec)*:threshold
               + -- Area of remaining trapezoid
                 (new_measurement_time_sec - curr_measurement_time_sec)*((:threshold - curr_value)/2)
            WHEN (:threshold < curr_value AND :threshold < next_value)
              OR (:threshold > curr_value AND :threshold > next_value)
            THEN (next_measurement_time_sec-curr_measurement_time_sec)*:threshold
            ELSE -- Area of trapezoid
                 ABS((next_measurement_time_sec - curr_measurement_time_sec)*((next_value - curr_value)/2))
       END) AS area
FROM   (
         SELECT measurement_time
              , curr_measurement_time_sec
              , next_measurement_time_sec
              , curr_value
              , next_value
              , (:threshold - LEAD(intercept) OVER (ORDER BY measurement_time))/LEAD(slope) OVER (ORDER BY measurement_time) AS new_measurement_time_sec
         FROM   ( SELECT measurement_time
                       , TO_CHAR(measurement_time,'J')*24*60*60 + TO_CHAR(measurement_time,'SSSSS') AS curr_measurement_time_sec
                       , TO_CHAR(LEAD(measurement_time) OVER (ORDER BY measurement_time),'J')*24*60*60 + TO_CHAR(LEAD(measurement_time) OVER (ORDER BY measurement_time),'SSSSS') AS next_measurement_time_sec
                       , measurement_value                                        AS curr_value
                       , LEAD(measurement_value) OVER (ORDER BY measurement_time) AS next_value
                       , REGR_SLOPE(measurement_value, TO_CHAR(measurement_time,'J')*24*60*60 + TO_CHAR(measurement_time,'SSSSS')) OVER (ORDER BY measurement_time) AS slope
                       , REGR_INTERCEPT(measurement_value, TO_CHAR(measurement_time,'J')*24*60*60 + TO_CHAR(measurement_time,'SSSSS')) OVER (ORDER BY measurement_time) AS intercept
                  FROM   measurements
       )Results:
SQL> var threshold NUMBER;
SQL> exec :threshold := 45;
SQL> /
      AREA
1191437.2The units are the time values were converted to seconds since January 1, 4712 BC (roughly).
Edited by: Centinul on Jul 7, 2011 10:39 AM

How can i calculate tempsize and logdir size ?

Hello:
I have one database on a primary server and its replica on a replica server.
Since one week to now, Mexican Exchange have had a considerable growth on transactions.
My database works in line, every night all data is cleaned waiting for new data on next day.
From last Thursday (29 april 2010) my replicas have had problems on drop all data using delete from.
I use delete from because those tables are Oracle cache groups defined.
Looking for error on tterrors logs (yesterday I got this error) I could see that replica was ran out of temporal memory.
On line database and replica database I have defined same temporal memory size, on this case 512Mb. But primary database did not send any error about this parameter, so if I checked “monitor” columns on database, my temp_in_use size is too less than temp_allocate_size.
My problem is, how can I calculate temp_allocate_size ?
So I have had close to 3,000,000 record on a simple table, I mean, I could have 2 or 3 tables with same number of rows.
If I have this parameter (may be 9,000,000) rows to be deleted, is there any way to calculate temp_allocate_size ?
But now, I suppose that I need enogh space on “LogDir”, my high_water_mark for permanent memory is 10GB, I have defined 16 gb for LogDir, but if I stopped replication since the operation starts, I had 100% space used at middle of my operation, so 5Gb on real database used, it is using close to 16 gb on LogDir.
My second doubt … is there any way to calculate LogDir size having the maximum database size ??
Thanks a lot for your help.
Regards.

I think that approaching this from the perspective of increasing temporary space and log space is not the best way.
Firstly, there are better ways to delete all rows from a table instead of using delete...
1. For regular tables (ones that are not part of a cache group) you can use TRUNCATE TABLE ... This operation is replicated but the voilume of replicated data is vastly smaller than if you delete all rows individually. Also, it should take a lot less Temp space on both the source and target system.
2. For cache tables, you could use UNLOAD CACHE GROUP ... This is similar to TRUNCATE but for cache tables. Again, this operation is replicated. Note that if you are using AWT or SWT cache groups and you DELETE in TimesTen then the data is also deleted from Oracle... is that wjhat is desired?
If you have to use DELETE then it is very important that you delete the rows in small batches rather than as one huge transaction. Trying to replicate a delete of 3M rows will cause huge problems for replication. A much better solution is to delete in smaller batches using some application logic as follows:
loop:
commit;
DELETE FIRST 1000 FROM sometable;
If rowcount > 0 then goto loop;
commit;
This approach has 5 benefits:
1. Much less Temp space will be needed.
2. Replication will be able to process the delets as they occur rather than waiting until all 3M rows have been deleted and then trying to tepliate a single transaction of 3M deletes. This will greatly improve replication performance and also prevent excessive log file buildup.
3. Checkpointing will be able to purge log files as the delete progresses rather than having to wait until all rowsw have been deleted. This will prevent excessive log file buildup.
4. The overall time required will be much reduced compared to deleting all rows in a single delete.
You should not stop replication while the delete s are being done as this just causes log file accumulation.
To answer your original question. it is not possible ot 'calculate' the required temp space pof log space; rather one must use observed data from when the system is running to determine the necessary size. For Temp size, you can look at the Temp high water mark to see the maximum space used and then set TempSize to somewhat more than that value. For log space, you need enough to sustain the maximum amount of log data generated with some contingency. Running our of log space is a very bad idea...
If you adopt my suggestions above then you can avoid these issues and also complete the cleanup of data in a shorter time.
Chris

How can I calculate which is the index (x-value) correspondant to a certain value of a signal?

I just want to calculate the quality of the peak in a FFT, defined as you can see in the attached file.
For that, I would need to know how can I calculate in Labview the index or indices (x-value) correspondant to a certain amplitude value of the function.
Kind regards, and thank you for reading,
Jose
Solved!
Go to Solution.
Attachments:
quality.jpg ‏6 KB

If you know the lineshape (e.g. Lorentzian), you can use nonlinear fit. This will give you the most accurate value.
In the most simple case (insignificant offset and noise, no other peaks) you can apply the following code (if there are other peaks, then take a apropriate array subset before applying the code). To get correct units, just scale with df.
LabVIEW Champion . Do more with less code and in less time .
Attachments:
WidthAtHalfHeight.png ‏52 KB

How can I calculate the request time ?

Hello,
How can I calculate the total consume time in each request ?
For example, I want to start calculating the time when I click on a Link or a button and the end time when it completed load the page !
Eric

You could use a filter like this one:
import java.io.*;
import java.net.*;
import java.util.*;
import java.text.*;
import javax.servlet.*;
import javax.servlet.http.*;
import javax.servlet.Filter;
import javax.servlet.FilterChain;
import javax.servlet.FilterConfig;
import javax.servlet.ServletContext;
import javax.servlet.ServletException;
import javax.servlet.ServletRequest;
import javax.servlet.ServletResponse;
public class TimeFilter implements Filter {
    // The filter configuration object we are associated with. If
    // this value is null, this filter instance is not currently
    // configured.
    private FilterConfig filterConfig = null;
    private static final boolean debug = false;
    private long start = 0;
    private long end = 0;
    public TimeFilter() {
    private void doBeforeProcessing(ServletRequest request, ServletResponse response)
    throws IOException, ServletException {
        if (debug) log("CalendarFilter:DoBeforeProcessing");
        System.out.print("In Filter ");
        this.start = System.currentTimeMillis();
        System.out.println((new java.util.Date()).toString() +
                           " start request ");
    private void doAfterProcessing(ServletRequest request, ServletResponse response)
    throws IOException, ServletException {
        if (debug) log("TimeFilter:DoAfterProcessing");
        System.out.println("Completion Time = " + (System.currentTimeMillis() - start));
     * @param request The servlet request we are processing
     * @param result The servlet response we are creating
     * @param chain The filter chain we are processing
     * @exception IOException if an input/output error occurs
     * @exception ServletException if a servlet error occurs
    public void doFilter(ServletRequest request, ServletResponse response,
    FilterChain chain)
    throws IOException, ServletException {
        if (debug) log("TimeFilter:doFilter()");
        doBeforeProcessing(request, response);
        Throwable problem = null;
        try {
            chain.doFilter(request, response);
        catch(Throwable t) {
            problem = t;
            t.printStackTrace();
        doAfterProcessing(request, response);
        // If there was a problem, we want to rethrow it if it is
        // a known type, otherwise log it.
        if (problem != null) {
            if (problem instanceof ServletException) throw (ServletException)problem;
            if (problem instanceof IOException) throw (IOException)problem;
            sendProcessingError(problem, response);
     * Return the filter configuration object for this filter.
    public FilterConfig getFilterConfig() {
        return (this.filterConfig);
     * Set the filter configuration object for this filter.
     * @param filterConfig The filter configuration object
    public void setFilterConfig(FilterConfig filterConfig) {
        this.filterConfig = filterConfig;
     * Destroy method for this filter
    public void destroy() {
     * Init method for this filter
    public void init(FilterConfig filterConfig) {
        this.filterConfig = filterConfig;
        if (filterConfig != null) {
            if (debug) {
                log("TimeFilter:Initializing filter");
     * Return a String representation of this object.
    public String toString() {
        if (filterConfig == null) return ("TimeFilter()");
        StringBuffer sb = new StringBuffer("TimeFilter(");
        sb.append(filterConfig);
        sb.append(")");
        return (sb.toString());
    private void sendProcessingError(Throwable t, ServletResponse response) {
        String stackTrace = getStackTrace(t);
        if(stackTrace != null && !stackTrace.equals("")) {
            try {
                response.setContentType("text/html");
                PrintStream ps = new PrintStream(response.getOutputStream());
                PrintWriter pw = new PrintWriter(ps);
                pw.print("<html>\n<head>\n</head>\n<body>\n"); //NOI18N
                // PENDING! Localize this for next official release
                pw.print("<h1>The resource did not process correctly</h1>\n<pre>\n");
                pw.print(stackTrace);
                pw.print("</pre></body>\n</html>"); //NOI18N
                pw.close();
                ps.close();
                response.getOutputStream().close();;
            catch(Exception ex){ }
        else {
            try {
                PrintStream ps = new PrintStream(response.getOutputStream());
                t.printStackTrace(ps);
                ps.close();
                response.getOutputStream().close();;
            catch(Exception ex){ }
    public static String getStackTrace(Throwable t) {
        String stackTrace = null;
        try {
            StringWriter sw = new StringWriter();
            PrintWriter pw = new PrintWriter(sw);
            t.printStackTrace(pw);
            pw.close();
            sw.close();
            stackTrace = sw.getBuffer().toString();
        catch(Exception ex) {}
        return stackTrace;
    public void log(String msg) {
        filterConfig.getServletContext().log(msg);
}and in the web.xml :
   <filter>
        <filter-name>TimeFilter</filter-name>
        <filter-class>
            com.filter.TimeFilter
        </filter>
    <filter-mapping>
        <filter-name>TimeFilter</filter-name>
        <url-pattern>/services/*</url-pattern>
    </filter-mapping >

How can i calculate ACCRUAL_RATE

Dear friends,
How can i calculate the ACCRUAL_RATE ,
I am using the PTO_SIMPLE_BALANCE_MULTIPLIER .
Yearly Leave Entitlement for varioius Grades are Grade A = 20 ,
Grade B=25 and Grade C=30.
Frequincy = M
Multiplier =1
i am using the monthly accrual
Can i make ACCRUAL_RATE like this YEARLY_ENTITLEMENT/12
thanks
zamora

Dear friends,
How can i calculate the ACCRUAL_RATE ,
I am using the PTO_SIMPLE_BALANCE_MULTIPLIER .
Yearly Leave Entitlement for varioius Grades are Grade A = 20 ,
Grade B=25 and Grade C=30.
Frequincy = M
Multiplier =1
i am using the monthly accrual
Can i make ACCRUAL_RATE like this YEARLY_ENTITLEMENT/12
thanks
zamora

How can I calculate disk space/DB space and storage spaces.

Hi all,
How can I calculate space clauses and memory related parameters for tables and table spaces? Updation is not allowed in these tables.
I have to create a database also.
I expect a reply with examples.
[email protected]
[email protected]
Thanks for all replies .

Boby,
The formula to estimate the storage parameters for tables and indexes are the following:
Table size = db block size * (# of Estimated rows in 12 months * average row length)/(db block size-90) *(1-PCTFREE/100)
Let assume that you want to create a table called Jose_tab,
db block size = 4092
Estimated row length in 12 months = 1000
Average row len = 100
PCTFREE(Updation is not allowed) = 0
Then, your INITIAL storage parameter will be estimated as follows:
4092*1000*100
(4092-90)*(1-0/100)
= About 10M
Your create table command will look like this,
CREATE TABLE jose_tab
(col1 VARCHAR2(10), col2 NUMBER(2),
....coln VARCHAR2(100))
STORAGE(INITIAL 10M NEXT 10M
PCTINCREASE 0)
PCTFREE 0 PCTUSED 80
TABLESPACE tablespace_name;
Storage parameters for tablespace depends on the amount of disk space available. You can ignore tablespace storage parameters since the size of the tablespace is determined by the size(s) of the data files. Refer to the DBA manual for details.
John

Calculate area under XY graph

Hello to all, I am plotting the data acquired from the system as amplitude v/s time on XY graph. My task is to calculate are under the graph and am using integrator tool to achieve this. However, feel that am not using correctly as answer is not matching with expected value. For example, I have plotted y=x function and as per the definition area is equal to 0.5*height*base for area under the graph. It is not matching, kindly help as I want to find out area under the curve for any two points of X-axis.
Attachments:
xy-graph.vi ‏22 KB

The integration gets accurate in your case if you change the integration method to 'trapezoidal' instead of the default 'Simpson's Rule'.
Simpson's Rule probably doesnt work because you don't provide suitable Initial and Final conditions. This method needs an assumption about the borders of the integration interval.
Cheers
Edgar

Text on path: How can I calculate the text length?

Hi
I have a text on path (spline item). Now I need the length of this text and the length of the spline item.
I try to calculate the text length using IWaxLine::GetWidth(), but this is always 0.
- How can I calculate the length of this text?
- How can I calculate the length of the spline item?
Thanks
Hans

It would be interesting if you could describe the purpose of your "length", but I don't have an answer anyway. Would the bounding box be sufficient?
Considering that TOP may be combined with arbitrary spline paths, this could become an exercise in higher math. I haven't yet encountered a function that returns the mathematical length of such a spline.
Otherwise it could be solved if you iterate and sum up the relevant points of the bounding box (ascender, descender, baseline?) of individual glyphs.
Be warned that the whole TOP looks alien, as if it were a transplant from a different program. Experience also shows that documented and actually used interfaces / commands are completely different animals ...
Dirk

How can I calculate area under a curve?

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