Consider multiplying Y by the following matrix

i.e.

The covariance matrix has now been diagonalized. This is useful because zero covariance implies independence for normally distributed random variables and so it follows that

Conditiong on Y2 it follows that the conditional distribution is

Notice how the variance of the conditional normal distribution is the marginal variance of Y1 minus something. That is to say the variance of Y1 is reduced given the knowledge of Y2. The variance can be recognized as the Schur complement of the covariance matrix with respect to V22. A similar treatment yields

The post Multivariate Normal Conditional Distribution appeared first on Lindons Log.

Hence the inverse of a block matrix can be written neatly in one of two ways:

The post Block Matrix Inverse appeared first on Lindons Log.

Now consider taking the inverse of the matrices above, yielding

Multiplying the matrices on the RHS yields

These two results can be used to form neat expressions for the inverse of a partitioned block matrix. It follows that

The equality holds for each block or element, so two expressions can be found for the Woodbury matrix inverse formula, namely:

and

where the dot notation corresponds to the Schur complement i.e.

The post Invert a Matrix using the Woodbury Matrix Inverse Formula Identity appeared first on Lindons Log.

So finally


Notice how this is a UDL factorization. It is entirely possible to do things a little differently and result with the LDU decomposition
Consider right and left multiplying this matrix by

where

i.e. the Schur complement of matrix V with respect to block 11. So finally

The post Diagonalize a Positive-Definite Symmetric Matrix using the Schur Complement and LDU Decomposition appeared first on Lindons Log.


mkdir news
for file in *;
do awk '{if (NR!=1 && NR!=2) {print}}' "$file" > new_"$file";
mv new_"$file" news/"$file";
done

cd news;
rm script;
rm news;


This uses awk to remove lines 1 and 2 from all of the files in the current directory and store the reduced files in the newly created directory “news”. Just run the shell script in the directory containing all the files.

The post AWK Remove Lines of Multiple Files appeared first on Lindons Log.

You can use the stat() function to populate a structure containing information about a file, including its size, which you can then use to dynamically allocate memory. Here’s some example code:

#include 
#include 
#include 
#include 


int main(void){
    FILE *fp;
    char *buffer;
    struct stat statistics;
    fp = fopen("test.txt", "rb");
    stat("test.txt", &statistics);
    buffer = (char *) malloc(statistics.st_size);
    fread(buffer, 1, statistics.st_size, fp);
    fclose(fp);  
}

First, you want to include the last two header files. Next you declare the struct stat structure where you want to store all the data. The stat() function takes two arguements. Number 1 being the file in question, number 2 the memory address of the structure where you want to store the information. So stat() will populate your structure. You can then call one of the members of this strucutre, statistics.st_size (which is of type off_t) to see how big in bytes the file is. Now a char is ALWAYS 1 byte, the standard says so, so you then allocate this number of bytes(==characters) for your array. fread() reads statistics.st_size objects, each of size 1, from fp and stores them in buffer. It advances the file position indicator by the number of bytes read.

The post Struct stat and stat() appeared first on Lindons Log.

#include 
#include 
#include 


int main(void){
int i;
int x;
x=44;
#pragma omp parallel for private(x) 
for(i=0;i<=10;i++){
x=i;
printf("Thread number: %d     x: %d\n",omp_get_thread_num(),x);
}
printf("x is %d\n", x);


}

Yields...

Thread number: 0     x: 0
Thread number: 0     x: 1
Thread number: 0     x: 2
Thread number: 3     x: 9
Thread number: 3     x: 10
Thread number: 2     x: 6
Thread number: 2     x: 7
Thread number: 2     x: 8
Thread number: 1     x: 3
Thread number: 1     x: 4
Thread number: 1     x: 5
x is 44

You'll notice that x is exactly the value it was before the parallel region.

Suppose we wanted to keep the last value of x after the parallel region. This can be achieved with lastprivate. Replace private(x) with lastprivate(x) and this is the result:

Thread number: 3     x: 9
Thread number: 3     x: 10
Thread number: 1     x: 3
Thread number: 1     x: 4
Thread number: 1     x: 5
Thread number: 0     x: 0
Thread number: 0     x: 1
Thread number: 0     x: 2
Thread number: 2     x: 6
Thread number: 2     x: 7
Thread number: 2     x: 8
x is 10

Notice that it is 10 and not 8. That is to say, it is the last iteration which is kept, not the last operation. Now what if we replace lastprivate(x) with firstprivate(x). What do you think it will do? This:

Thread number: 3     x: 9
Thread number: 3     x: 10
Thread number: 1     x: 3
Thread number: 1     x: 4
Thread number: 1     x: 5
Thread number: 0     x: 0
Thread number: 0     x: 1
Thread number: 0     x: 2
Thread number: 2     x: 6
Thread number: 2     x: 7
Thread number: 2     x: 8
x is 44

If you were like me, you were expecting to get the value 0 i.e. the value of x on the first iteration. NO

firstprivate Specifies that each thread should have its own instance of a variable, and that the variable should be initialized with the value of the variable, because it exists before the parallel construct.

That is, every thread gets its own instance of x and that instance equals 44.

The post OpenMP Tutorial – firstprivate and lastprivate appeared first on Lindons Log.

Home$ rsync -avzu office:.matlab/myfunctions/figs/ .
receiving incremental file list
./
1_a_0_neg.eps
1_a_0_pos.eps
1_a_10_neg.eps
1_a_10_pos.eps

sent 90 bytes  received 12464 bytes  2789.78 bytes/sec
total size is 36238  speedup is 2.89

-a –archive
Stands for archive mode. Basically this means that the structure from the office machine is kept on the local machine (i.e. same symbolic links etc.)

-v, –verbose
Increases verbosity

-z, –compress
Compresses the files for transfer purposes and then uncompresses them on the local machine. Really great if transferring massive data.

-u, –update
This means that if the destination folder has files with a timestamp which is newer than the files in the source folder, then the files in the destination folder will not be overwritten with the older source ones.

These are just a few most common arguments. Lastly, a good argument to remember

-n, –dry-run
This won’t actually do any transfer of data, it merely shows you what rsync WOULD do if you removed this argument. A good choice if you want to be careful.

The post rsync Tutorial and Help with Examples appeared first on Lindons Log.

lindon$ ps2pdf -dPDFSETTINGS=/prepress -dEPSCrop test.eps

and now the pdf doesn’t included the unnecessary white space border.

The post How to crop a pdf when using the ps2pdf converter via -dEPSCrop appeared first on Lindons Log.

wget -r -l5 -np -k -nH --cut-dirs=5 --load-cookies cookies.txt http://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/px421/

-r
Means wget acts recursively i.e. it follows links found on the current page (much like a search engine spider.

-l
Specifies the depth, which means how many of these links it can follow. If you imagine all the links on the current page forming branches away from it, then the links on those pages forming branches away from those, then -l5 sets the maximum branch distance away from the current page.

-np
No Parent, means wget will only progress down the directory tree i.e. it will not work its way back into http://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/

-k
Convert Hyperlinks. When wget downloads a page, say index.html, there will be links on that page just like viewed in your browser but -k will convert them to local links, so that you can navigate your way through the pages on your local machine.

-nH
No host directories. Basically wget would otherwise create a folder named “http://www2.warwick.ac.uk/” and all the downloaded stuff would get stored in there, which is normally undesirable.

–cut-dirs=5
Otherwise wget would create 5 directories

sci/
physics/
current/
teach/
module_home/

in a directory tree which you don’t want to have to click through…

–load-cookies
Normally content is restricted and you need to login, so you need to supply wget with some cookies. If you are a firefox user then there is an extension called ‘cookie exporter’, which you can use to output your cookies to a file called cookies.txt.

That’s it!

The post GNU Wget Tutorial appeared first on Lindons Log.