Graphing in Fortran, Algorithm Assistance Needed - algorithm

I am trying to create a fortran program that will plot X,Y coordinates to the screen. I have the program receive plots from an input file. in the input file the first entry is the amount of points. every line after that has an x value then a space then the corresponding y values. I then have the program bubble sort the x values from smallest to greatest. next i want to graph these values. i want to graph them so that the scale of the x axis is xmax-xmin/#of points and the y axis is the same. how would i go about printing a '*' for points as a dirty graph??? im not looking for the entire answer just some direction of how to form the algorithm for the write. Listed below is the code that i have so far and a sample input file
Input File
10
-4 16
-3 9
-2 4
-1 1
0 0
1 1
2 4
3 9
4 16
5 25
Code
*START OF CODE
PROGRAM MAIN
*DECLARATIONS
INTEGER EXISTS, DONE, POINTS, USED, I, E
REAL XSTEP, YSTEP, XMIN, XMAX, YMIN, YMAX
REAL X(100), Y(100), A, B
CHARACTER INNAME*30, OUTNAME*30
LOGICAL MORE
CHARACTER (70) LINE
*INITIALIZATIONS
INNAME='NULL.DOC'
EXISTS=0
DONE=0
POINTS=0
USED=0
I=0
E=0
MORE = .TRUE.
A=0
B=0
XSTEP = 0
YSTEP = 0
XMIN=0
XMAX=0
YMIN=0
YMAX=0
*CLEAR THE ARRAYS
DO I=1,100
X(I)=0
Y(I)=0
END DO
I=0
*FORMATS
5 FORMAT(' ','POINT #', I3, ' X=', F5.2,' Y=', F5.2)
10 FORMAT(' ','XMIN=',F5.2, ' XMAX=', F5.2)
15 FORMAT(' ','YMIN=',F5.2, ' YMAX=', F5.2)
20 FORMAT(' ','X STEP=',F5.2, ' Y STEP=', F5.2)
*MAIN CODE
****************************************************************
*PROMPT FOR NAME OF FILE AND INPUT
PRINT *,'PLEASE INPUT A FILE NAME INCLUDING AN EXTENSION'
PRINT *,'ENTER QUIT OR Q TO EXIT'
READ (*,*) INNAME
*OPEN IF(0)
IF(INNAME.EQ.'Q'.OR.INNAME.EQ.'QUIT')THEN
PRINT *,'GOODBYE'
ELSE
*TEST FOR FILE
INQUIRE(FILE=INNAME, EXIST=EXISTS)
*IF EXIST=FALSE, DISPLAY MESSAGE
IF(.NOT.EXISTS) THEN
PRINT *,'FILE DOES NOT EXIST, PLEASE TRY AGAIN'
*ELSE EXIST=TRUE, OPEN (UNIT=1)
ELSE
OPEN(UNIT=1, FILE=INNAME, STATUS='OLD')
END IF
*************************************************************
*ASK CHOICES FOR OUTPUT
PRINT *,'PLEASE ENTER A NAME FOR AN OUTPUT FILE W/ EXTENSION'
PRINT *,'ENTER QUIT OR Q TO EXIT'
READ(*,*)OUTNAME
IF(OUTNAME.EQ.'Q'.OR.OUTNAME.EQ.'QUIT')THEN
PRINT *,'GOODBYE'
ELSE
*************************************************************
*CHECK IF DONE (IF 1)
IF(DONE.EQ.0)THEN
*OPEN THE OUTPUT FILE DO(2)
DO WHILE(USED.EQ.0)
INQUIRE(FILE=OUTNAME,EXIST=EXISTS)
*OPEN IF(2) FOR IF FILE ALREADY EXISTS
IF(EXISTS.EQ.1)THEN
OPEN(UNIT=2,FILE=OUTNAME,STATUS='OLD')
*END IF FOR IF FILE ALREADY EXISTS AMD OPEN IF DID NOT EXIST,
ELSE
OPEN(UNIT=2,FILE=OUTNAME,STATUS='NEW')
*END IF (2)
END IF
*READ IN 1 INTEGER (MAXIMUM VALUE OF 100) FOR # OF POINTS IN FILE
READ(1,*, END=111),POINTS
*READ IN X AND Y VALUES WITH MAX OF 100
DO I=1, POINTS
READ(1,*,END=111) X(I),Y(I)
END DO
*SORT POINTS
E = POINTS - 1
MORE = .TRUE.
DO WHILE (MORE .EQ. .TRUE.)
MORE = .FALSE.
DO I=1, E
IF(X(I).GT.X(I+1)) THEN
MORE = .TRUE.
A=X(I)
B=y(I)
X(I)=X(I+1)
Y(I)=Y(I+1)
X(I+1)=A
Y(I+1)=B
END IF
END DO
E=E-1
END DO
*FIND MIN AND MAX OF X AND Y
I=1
XMIN = X(I)
XMAX = X(POINTS)
YMIN = Y(I)
YMAX = Y(I)
DO I=1, POINTS
IF(Y(I) .LT. YMIN) THEN
YMIN = Y(I)
END IF
IF(Y(I) .GT. YMAX) THEN
YMAX = Y(I)
END IF
END DO
*fIND X AND Y STEPS
XSTEP = (XMAX-XMIN)/POINTS
YSTEP = (YMAX-YMIN)/POINTS
*PRINT TO THE OUTPUT FILE
DO I=1, POINTS
WRITE(2,5)I,X(I),Y(I)
END DO
WRITE(2,10)XMIN,XMAX
WRITE(2,15)YMIN,YMAX
WRITE(2,20)XSTEP,YSTEP
*PRINT GRAPH
*END DO (2)
END DO
*END IF (1)
END IF
*END IF QUIT(S)
END IF
END IF
*CLOSE THE FILES
CLOSE(UNIT=1)
CLOSE(UNIT=2)
111 PRINT * , 'The Program Has Now Ended'
*STOP
STOP
*END
END

if you want something quick and dirty, the easiest approach by far is to plot the graph sideways (not as bad as it sounds if you are going to print to paper). then you can just print each line with a length proportional to the y (now x) value (with a * at the end, or all *s for a histogram):
+-------------------------------------> y
| *
| *
| *
. etc
otherwise, if you don't want to use a library, things get complicated quite quickly. the next simplest approach is to make a 2d array of characters (the size of your screen), initially filled with spaces, and then "plot" to that; once done you can print it by reading the characters row by row and printing them. the advantage there is that it separates the axes from the data - if you try to do everything as you print a line, the different tasks become mixed up.
but plotting soon becomes more complex than you expected. for example, choosing tick marks and printing labels is itself a major task to do well. you're really better using a library (which is why i suggested the sideways approach first - if this is so quick + dirty than you don't want to use a library, then that is often good enough).
(this is the kind if thing you can do very quickly - i threw that together in a few minutes)
update: for tickmarks (it's getting too complicated!) you want the graphics gem algorithm - it's pretty much the standard, and the paper is easy to understand. that gives you your total range (as well as the tick spacing), and then scaling is easy (a character is "worth" (xmax-xmin)/nchars, as you say - not sure what more to explain?).

Related

Parallel loops and image processing in matlab

I am going to implement a salient object detection method based on a simple linear feedback control system (LFCS). The control system model is represented as in the following equation:
I've come up with the following program codes but the result would not be what should be. Specifically, the output should be something like the following image:
But the code produces this output:
The codes are as follows.
%Calculation of euclidian distance between adjacent superpixels stores in variable of Euc
A = imread('aa.jpg');
[rows, columns, cnumberOfColorChannels] = size(A);
[L,N] = superpixels(A,400);
%% Determination of adjacent superpixels
glcms = graycomatrix(L,'NumLevels',N,'GrayLimits',[1,N],'Offset',[0,1;1,0]); %Create gray-level co-occurrence matrix from image
glcms = sum(glcms,3); % add together the two matrices
glcms = glcms + glcms.'; % add upper and lower triangles together, make it symmetric
glcms(1:N+1:end) = 0; % set the diagonal to zero, we don't want to see "1 is neighbor of 1"
idx = label2idx(L); % Convert label matrix to cell array of linear indices
numRows = size(A,1);
numCols = size(A,2);
%%Mean color in Lab color space for each channel
data = zeros(N,3);
for labelVal = 1:N
redIdx = idx{labelVal};
greenIdx = idx{labelVal}+numRows*numCols;
blueIdx = idx{labelVal}+2*numRows*numCols;
data(labelVal,1) = mean(A(redIdx));
data(labelVal,2) = mean(A(greenIdx));
data(labelVal,3) = mean(A(blueIdx));
end
Euc=zeros(N);
%%Calculation of euclidian distance between adjacent superpixels stores in Euc
for a=1:N
for b=1:N
if glcms(a,b)~=0
Euc(a,b)=sqrt(((data(a,1)-data(b,1))^2)+((data(a,2)-data(b,2))^2)+((data(a,3)-data(b,3))^2));
end
end
end
%%Creation of Connectivity matrix "W" between adjacent superpixels
W=zeros(N);
W_num=zeros(N);
W_den=zeros(N);
OMG1=0.1;
for c=1:N
for d=1:N
if(Euc(c,d)~=0)
W_num(c,d)=exp(-OMG1*(Euc(c,d)));
W_den(c,c)=W_num(c,d)+W_den(c,c); %
end
end
end
%Connectivity matrix W between adjacent superpixels
for e=1:N
for f=1:N
if(Euc(e,f)~=0)
W(e,f)=(W_num(e,f))/(W_den(e,e));
end
end
end
%%calculation of geodesic distance between nonadjacent superpixels stores in variable "s_star_temp"
s_star_temp=zeros(N); %temporary variable for geodesic distance measurement
W_sparse=zeros(N);
W_sparse=sparse(W);
for g=1:N
for h=1:N
if W(g,h)==0 & g~=h;
s_star_temp(g,h)=graphshortestpath(W_sparse,g,h,'directed',false);
end
end
end
%%Calculation of connectivity matrix for nonadjacent superpixels stores in "S_star" variable"
S_star=zeros(N);
OMG2=8;
for i=1:N
for j=1:N
if s_star_temp(i,j)~=0
S_star(i,j)=exp(-OMG2*s_star_temp(i,j));
end
end
end
%%Calculation of connectivity matrix "S" for measuring connectivity between all superpixels
S=zeros(N);
S=S_star+W;
%% Defining non-isolation level for connectivity matrix "W"
g_star=zeros(N);
for k=1:N
g_star(k,k)=max(W(k,:));
end
%%Limiting the range of g_star and calculation of isolation cue matrix "G"
alpha1=0.15;
alpha2=0.85;
G=zeros(N);
for l=1:N
G(l,l)=alpha1*(g_star(l,l)- min(g_star(:)))/(max(g_star(:))- min(g_star(:)))+(alpha2 - alpha1);
end
%%Determining the supperpixels that surrounding the image boundary
lr = L([1,end],:);
tb = L(:,[1,end]);
labels = unique([lr(:);tb(:)]);
%% Calculation of background likelihood for each superpixels stores in"BgLike"
sum_temp=0;
temp=zeros(1,N);
BgLike=zeros(N,1);
BgLike_num=zeros(N);
BgLike_den=zeros(N);
for m=1:N
for n=1:N
if ismember(n,labels)==1
BgLike_num(m,m)=S(m,n)+ BgLike_num(m,m);
end
end
end
for o=1:N
for p=1:N
for q=1:N
if W(p,q)~=0
temp(q)=S(o,p)-S(o,q);
end
end
sum_temp=max(temp)+sum_temp;
temp=0;
end
BgLike_den(o,o)=sum_temp;
sum_temp=0;
end
for r=1:N
BgLike(r,1)= BgLike_num(r,r)/BgLike_den(r,r);
end
%%%%Calculation of Foreground likelihood for each superpixels stores in "FgLike"
FgLike=zeros(N,1);
for s=1:N
for t=1:N
FgLike(s,1)=(exp(-BgLike(t,1))) * Euc(s,t)+ FgLike(s,1);
end
end
The above codes are prerequisite for the following sections (in fact, they produce necessary data and matrices for the next section. The aforementioned codes provided to make the whole process reproducible).
Specifically, I think that this section did not give the desired results. I'm afraid I did not properly simulate the parallelism using for loops. Moreover, the terminating conditions (employed with for and if statements to simulate do-while loop) are never satisfied and the loops continue until the last iteration (instead terminating when a specified condition occurs). A major concern here is that if the terminating conditions are properly implemented.
The pseudo algorithm for the following code is as the image below:
%%parallel operations for background and foreground implemented here
T0 = 0 ;
Tf = 20 ;
Ts = 0.1 ;
Ti = T0:Ts:Tf ;
Nt=numel(Ti);
Y_Bg=zeros(N,Nt);
Y_Fg=zeros(N,Nt);
P_Back_Bg=zeros(N,N);
P_Back_Fg=zeros(N,N);
u_Bg=zeros(N,Nt);
u_Fg=zeros(N,Nt);
u_Bg_Star=zeros(N,Nt);
u_Fg_Star=zeros(N,Nt);
u_Bg_Normalized=zeros(N,Nt);
u_Fg_Normalized=zeros(N,Nt);
tau=0.1;
sigma_Bg=zeros(Nt,N);
Temp_Bg=0;
Temp_Fg=0;
C_Bg=zeros(Nt,N);
C_Fg=zeros(Nt,N);
%%System Initialization
for u=1:N
u_Bg(u,1)=(BgLike(u,1)- min(BgLike(:)))/(max(BgLike(:))- min(BgLike(:)));
u_Fg(u,1)=(FgLike(u,1)- min(FgLike(:)))/(max(FgLike(:))- min(FgLike(:)));
end
%% P_state and P_input
P_state=G*W;
P_input=eye(N)-G;
% State Initialization
X_Bg=zeros(N,Nt);
X_Fg=zeros(N,Nt);
for v=1:20 % v starts from 1 because we have no matrices with 0th column number
%The first column of X_Bg and X_Fg is 0 for system initialization
X_Bg(:,v+1)=P_state*X_Bg(:,v) + P_input*u_Bg(:,v);
X_Fg(:,v+1)=P_state*X_Fg(:,v) + P_input*u_Fg(:,v);
v=v+1;
if v==2
C_Bg(1,:)=1;
C_Fg(1,:)=1;
else
for w=1:N
for x=1:N
Temp_Fg=S(w,x)*X_Fg(x,v-1)+Temp_Fg;
Temp_Bg=S(w,x)*X_Bg(x,v-1)+Temp_Bg;
end
C_Fg(v-1,w)=inv(X_Fg(w,v-1)+((Temp_Bg)/(Temp_Fg)*(1-X_Fg(w,v-1))));
C_Bg(v-1,w)=inv(X_Bg(w,v-1)+((Temp_Fg)/(Temp_Bg))*(1-X_Bg(w,v-1)));
Temp_Bg=0;
Temp_Fg=0;
end
end
P_Bg=diag(C_Bg(v-1,:));
P_Fg=diag(C_Fg(v-1,:));
Y_Bg(:,v)= P_Bg*X_Bg(:,v);
Y_Fg(:,v)= P_Fg*X_Fg(:,v);
for y=1:N
Temp_sig_Bg=0;
Temp_sig_Fg=0;
for z=1:N
Temp_sig_Bg = Temp_sig_Bg +S(y,z)*abs(Y_Bg(y,v)- Y_Bg(z,v));
Temp_sig_Fg = Temp_sig_Fg +S(y,z)*abs(Y_Fg(y,v)- Y_Fg(z,v));
end
if Y_Bg(y,v)>= Y_Bg(y,v-1)
sign_Bg=1;
else
sign_Bg=-1;
end
if Y_Fg(y,v)>= Y_Fg(y,v-1)
sign_Fg=1;
else
sign_Fg=-1;
end
sigma_Bg(v-1,y)=sign_Bg*Temp_sig_Bg;
sigma_Fg(v-1,y)=sign_Fg*Temp_sig_Fg;
end
%Calculation of P_Back for background and foreground
P_Back_Bg=tau*diag(sigma_Bg(v-1,:));
P_Back_Fg=tau*diag(sigma_Fg(v-1,:));
u_Bg_Star(:,v)=u_Bg(:,v-1)+P_Back_Bg*Y_Bg(:,v);
u_Fg_Star(:,v)=u_Fg(:,v-1)+P_Back_Fg*Y_Fg(:,v);
for aa=1:N %Normalization of u_Bg and u_Fg
u_Bg(aa,v)=(u_Bg_Star(aa,v)- min(u_Bg_Star(:,v)))/(max(u_Bg_Star(:,v))-min(u_Bg_Star(:,v)));
u_Fg(aa,v)=(u_Fg_Star(aa,v)- min(u_Fg_Star(:,v)))/(max(u_Fg_Star(:,v))-min(u_Fg_Star(:,v)));
end
if (max(abs(Y_Fg(:,v)-Y_Fg(:,v-1)))<=0.0118) &&(max(abs(Y_Bg(:,v)-Y_Bg(:,v-1)))<=0.0118) %% epsilon= 0.0118
break;
end
end
Finally, the saliency map will be generated by using the following codes.
K=4;
T=0.4;
phi_1=(2-(1-T)^(K-1))/((1-T)^(K-2));
phi_2=(1-T)^(K-1);
phi_3=1-phi_1;
for bb=1:N
Y_Output_Preliminary(bb,1)=Y_Fg(bb,v)/((Y_Fg(bb,v)+Y_Bg(bb,v)));
end
for hh=1:N
Y_Output(hh,1)=(phi_1*(T^K))/(phi_2*(1-Y_Output_Preliminary(hh,1))^K+(T^K))+phi_3;
end
V_rs=zeros(N);
V_Final=zeros(rows,columns);
for cc=1:rows
for dd=1:columns
V_rs(cc,dd)=Y_Output(L(cc,dd),1);
end
end
maxDist = 10; % Maximum chessboard distance from image
wSF=zeros(rows,columns);
wSB=zeros(rows,columns);
% Get the range of x and y indices who's chessboard distance from pixel (0,0) are less than 'maxDist'
xRange = (-(maxDist-1)):(maxDist-1);
yRange = (-(maxDist-1)):(maxDist-1);
% Create a mesgrid to get the pairs of (x,y) of the pixels
[pointsX, pointsY] = meshgrid(xRange, yRange);
pointsX = pointsX(:);
pointsY = pointsY(:);
% Remove pixel (0,0)
pixIndToRemove = (pointsX == 0 & pointsY == 0);
pointsX(pixIndToRemove) = [];
pointsY(pixIndToRemove) = [];
for ee=1:rows
for ff=1:columns
% Get a shifted copy of 'pointsX' and 'pointsY' that is centered
% around (x, y)
pointsX1 = pointsX + ee;
pointsY1 = pointsY + ff;
% Remove the the pixels that are out of the image bounds
inBounds =...
pointsX1 >= 1 & pointsX1 <= rows &...
pointsY1 >= 1 & pointsY1 <= columns;
pointsX1 = pointsX1(inBounds);
pointsY1 = pointsY1(inBounds);
% Do stuff with 'pointsX1' and 'pointsY1'
wSF_temp=0;
wSB_temp=0;
for gg=1:size(pointsX1)
Temp=exp(-OMG1*(sqrt(double(A(pointsX1(gg),pointsY1(gg),1))-double(A(ee,ff,1)))^2+(double(A(pointsX1(gg),pointsY1(gg),2))-double(A(ee,ff,2)))^2 + (double(A(pointsX1(gg),pointsY1(gg),3))-double(A(ee,ff,3)))^2));
wSF_temp=wSF_temp+(Temp*V_rs(pointsX1(gg),pointsY1(gg)));
wSB_temp=wSB_temp+(Temp*(1-V_rs(pointsX1(gg),pointsY1(gg))));
end
wSF(ee,ff)= wSF_temp;
wSB(ee,ff)= wSB_temp;
V_Final(ee,ff)=V_rs(ee,ff)/(V_rs(ee,ff)+(wSB(ee,ff)/wSF(ee,ff))*(1-V_rs(ee,ff)));
end
end
imshow(V_Final,[]); %%Saliency map of the image
Part of your terminating criterion is this:
max(abs(Y_a(:,t)-Y_a(:,t-1)))<=eps
Say Y_a tends to 2. You are really close... In fact, the closest you can get without subsequent values being identical is Y_a(t)-Y_a(t-1) == 4.4409e-16. If the two values were any closer, their difference would be 0, because this is the precision with which floating-point values can be represented. So you have reached this fantastic level of closeness to your goal. Subsequent iterations are changing the target value by the smallest possible amount, 4.4409e-16. But your test is returning false! Why? Because eps == 2.2204e-16!
eps is short-hand for eps(1), the difference between 1 and the next representable larger value. Because how floating-point values are represented, this difference is half the difference between 2 and the next representable larger value (which is given by eps(2).
However, if Y_a tends to 1e-16, subsequent iterations could double or halve the value of Y_a and you'd still meet the stopping criterion!
Thus, what you need is to come up with a reasonable stopping criterion that is a fraction of the target value, something like this:
max(abs(Y_a(:,t)-Y_a(:,t-1))) <= 1e6 * eps(max(abs(Y_a(:,t))))
Unsolicited advice
You should really look into vectorized operations in MATLAB. For example,
for y=1:N
Temp_sig_a=0;
for z=1:N
Temp_sig_a = Temp_sig_a + abs(Y_a(y,t)- Y_a(z,t));
end
sigma_a(t-1,y)= Temp_sig_a;
end
can be written as
for y=1:N
sigma_a(t-1,y) = sum(abs(Y_a(y,t) - Y_a(:,t)));
end
which in turn can be written as
sigma_a(t-1,:) = sum(abs(Y_a(:,t).' - Y_a(:,t)));
Avoiding loops is not only usually more efficient, but it also leads to shorter code that is easier to read.
Also, this:
P_FB_a = diag(sigma_a(t-1,:));
u_a(:,t) = u_a(:,t-1) + P_FB_a * Y_a(:,t);
is the same as
u_a(:,t) = u_a(:,t-1) + sigma_a(t-1,:).' .* Y_a(:,t);
but of course creating a diagonal matrix and doing a matrix multiplication with so many zeros is much more expensive than directly computing an element-wise multiplication.

Grouping data using loops (signal processing in MATLAB)

I am working in MATLAB with a signal data that consist of consecutive dips as shown below. I am trying to write a code which sorts the contents of each dip into a separate group. How should the general structure of such a code look like?
The following is my data. I am only interested in the portion of the signal that lies below a certain threshold d (the red line):
And here is the desired grouping:
Here is an unsuccessful attempt:
k=0; % Group number
for i = 1 : length(signal)
if signal(i) < d
k=k+1;
while signal(i) < d
NewSignal(i, k) = signal(i);
i = i + 1;
end
end
end
The code above generated 310 groups instead of the desired 12 groups.
Any explanation would be greatly appreciated.
Taking Benl generated data you can do the following:
%generate data
x=1:1000;
y=sin(x/20);
for ii=1:9
y=y+-10*exp(-(x-ii*100).^2./10);
end
y=awgn(y,4);
%set threshold
t=-4;
%threshold data
Y = char(double(y<t) + '0'); %// convert to string of zeros and ones
%search for start and ends
This idea is taken from here
[s, e] = regexp(Y, '1+', 'start', 'end');
%and now plot and see that each pair of starts and end
% represents a group
plot(x,y)
hold on
for k=1:numel(s)
line(s(k)*ones(2,1),ylim,'Color','k','LineStyle','--')
line(e(k)*ones(2,1),ylim,'Color','k','LineStyle','-')
end
hold off
legend('Data','Starts','Ends')
Comments: First of all I choose an arbitrary threshold, it is up to you to find the "best" one in your data. Additionally I didn't group the data explicitly but rather this approach gives you the start and end of each epoch with a dip (you might call it group). So you could say that each index is the grouping index. Finally I did not debug this approach for corner cases, when dips fall on starts and ends...
In MATLAB you cannot change the loop index of a for loop. A for loop:
for i = array
loops over each column of array in turn. In your code, 1 : length(signal) is an array, each of its elements is visited in turn. Inside this loop there is a while loop that increments i. However, when this while loop ends and the next iteration of the for loop runs, i is reset to the next item in the array.
This code therefore needs two while loops:
i = 1; % Index
k = 0; % Group number
while i <= numel(signal)
if signal(i) < d
k = k + 1;
while signal(i) < d
NewSignal(i,k) = signal(i);
i = i + 1;
end
end
i = i + 1;
end
Easy, the function you're looking for is bwlabel, which when combined with logical indexing makes this simple.
To start I made some fake data which resembled your data
x=1:1000;
y=sin(x/20);
for ii=1:9
y=y+-10*exp(-(x-ii*100).^2./10);
end
y=awgn(y,4);
plot(x,y)
Then set your threshold and use 'bwlabel'
d=-4;% set the threshold
groupid=bwlabel(y<d);
bwlabel labels connected groups in a black and white image, what we've effectively done here is make a black and white (logical 0 & 1) 1D image in the logical vector y<d. bwlabel returns the number of the region at the index of the region. We're not interested in the 0 region, so to get the x values or y values of the nth region, simply use x(groupid==n), for example with my test data
x_4=x(groupid==4)
y_4=y(groupid==4)
x_4 = 398 399 400 401 402
y_4 = -5.5601 -7.8280 -9.1965 -7.9083 -5.8751

Generate uniform pseudo-random numbers in a closed interval

What's the best way to generate pseudo-random numbers in the closed interval [0,1] instead of the usual [0,1)? One idea I've came up with is to reject values in (1/2,1), then double the number. I wonder if there is a better method.
real x
do
call random_number(x)
if (x <= 0.5) exit
end do
x = 2*x
print *, x
end
The most important requirement is that the algorithm should not make a worse distribution (in terms of uniformity and correlation) than that generated by random_number(). Also I'd favour simplicity. A wrapper around random_number() would be perfectly good, I'm not looking to implement a whole new generator.
As #francescalus points out in the comments, with the algorithm above lots of numbers in [0,1] will have zero probability of appearing. The following code implements a slightly different approach: the interval is enlarged a bit, then values in excess of 1 are cut out. It should behave better in that aspect.
real x
do
call random_number(x)
x = x*(1 + 1e-6)
if (x <= 1.) exit
end do
print *, x
end
What about swapping x and 1-x? Sorry, my Fortran is rusty
real function RNG()
real :: x
logical, save :: swap = .TRUE.
call random_number(x)
if (swap .EQV. .TRUE.)
RNG = x
swap = .FALSE.
else
RNG = 1.0 - x
swap = .TRUE.
end if
end
And if you want to use Box-Muller, use 1-U everywhere and it should work
z0 = sqrt(-2.0*log(1.0-U1))*sin(TWOPI*U2)
z1 = sqrt(-2.0*log(1.0-U1))*cos(TWOPI*U2)
same for rejection version of Box-Muller

How to round float number with while loop in MATLAB?

I have a rather unorthodox homework assignment where I am to write a simple function where a double value is rounded to an integer with using only a while loop.
The main goal is to write something similar to the round function.
I made some progress where I should add or subtract a very small double value and I would eventually hit a number that will become an integer:
while(~isinteger(inumberup))
inumberup=inumberup+realmin('double');
end
However, this results in a never-ending loop. Is there a way to accomplish this task?
I'm not allowed to use round, ceil, floor, for, rem or mod for this question.
Assumption: if statements and the abs function are allowed as the list of forbidden functions does not include this.
Here's one solution. What you can do is keep subtracting the input value by 1 until you get to a point where it becomes less than 1. The number produced after this point is the fractional component of the number (i.e. if our number was 3.4, the fractional component is 0.4). You would then check to see if the fractional component, which we will call f, is less than 0.5. If it is, that means you need to round down and so you would subtract the input number with f. If the number is larger than 0.5 or equal to 0.5, you would add the input number by (1 - f) in order to go up to the next highest number. However, this only handles the case for positive values. For negative values, round in MATLAB rounds towards negative infinity, so what we ought to do is take the absolute value of the input number and do this subtraction to find the fractional part.
Once we do this, we then check to see what the fractional part is equal to, and then depending on the sign of the number, we either add or subtract accordingly. If the fractional part is less than 0.5 and if the number is positive, we need to subtract by f else we need to add by f. If the fractional part is greater than or equal to 0.5, if the number is positive we need to add by (1 - f), else we subtract by (1 - f)
Therefore, assuming that num is the input number of interest, you would do:
function out = round_hack(num)
%// Repeatedly subtract until we get a value that less than 1
%// i.e. the fractional part
%// Also make sure to take the absolute value
f = abs(num);
while f > 1
f = f - 1;
end
%// Case where we need to round down
if f < 0.5
if num > 0
out = num - f;
else
out = num + f;
end
%// Case where we need to round up
else
if num > 0
out = num + (1 - f);
else
out = num - (1 - f);
end
end
Be advised that this will be slow for larger values of num. I've also wrapped this into a function for ease of debugging. Here are a few example runs:
>> round_hack(29.1)
ans =
29
>> round_hack(29.6)
ans =
30
>> round_hack(3.4)
ans =
3
>> round_hack(3.5)
ans =
4
>> round_hack(-0.4)
ans =
0
>> round_hack(-0.6)
ans =
-1
>> round_hack(-29.7)
ans =
-30
You can check that this agrees with MATLAB's round function for the above test cases.
You can do it without loop: you can use num2str to convert the number into a string, then find the position of the . in the string and extract the string fron its beginning up to the position of the .; then you convert it back to a numebr with str2num
To round it you have to check the value of the first char (converted into a number) after the ..
r=rand*100
s=num2str(r)
idx=strfind(num2str(r),'.')
v=str2num(s(idx+1))
if(v <= 5)
rounded_val=str2num(s(1:idx-1))
else
rounded_val=str2num(s(1:idx-1))+1
end
Hope this helps.
Qapla'

Sage immutable vector error

I'm trying to implement something in sage and I keep getting the following error:
*Error in lines 38-53
Traceback (most recent call last):
File "/projects/42e45a19-7a43-4495-8dcd-353625dfce66/.sagemathcloud/sage_server.py", line 879, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "", line 13, in <module>
File "sage/modules/vector_integer_dense.pyx", line 185, in sage.modules.vector_integer_dense.Vector_integer_dense.__setitem__ (build/cythonized/sage/modules/vector_integer_dense.c:3700)
raise ValueError("vector is immutable; please change a copy instead (use copy())")
ValueError: vector is immutable; please change a copy instead (use copy())*
I have pinpointed the exact location (the line between "print 'marker 1'" and "print 'marker 2'" in the while-loop at the end, see code below) and it seems that I'm not allowed to change the entries of the matrix "weights" (which I defined before the loop) from inside the loop. The error message says to use the copy() function, but I don't see how that would solve my problem since I would only be making a local copy and the next iteration of the loop wouldn't get these changed values, right? So does anyone know how to define this matrix so that I can change it from inside the loop? If it's not possible, can someone explain why?
Thanks for your help.
Code:
m = 3 # Dimension of inputs to nodes
n = 1 # Dimension of output
v = 4 # Number of training vectors
r = 0.1 # Learning Rate
T = 10 # Number of iterations
# Input static Biases, i.e. sum must be smaller than this vector. For dynamic biases, set this vector to 0, increase m by one and set xi[0]=-1 for all inputs i (and start the acual input at xi[1])
bias = list(var('s_%d' % i) for i in range(n))
bias[0] = 0.5
# Input the training vectors and targets
x0 = list(var('s_%d' % i) for i in range(m))
x0[0]=1
x0[1]=0
x0[2]=0
target00=1
x1 = list(var('s_%d' % i) for i in range(m))
x1[0]=1
x1[1]=0
x1[2]=1
target10=1
x2 = list(var('s_%d' % i) for i in range(m))
x2[0]=1
x2[1]=1
x2[2]=0
target20=1
x3 = list(var('s_%d' % i) for i in range(m))
x3[0]=1
x3[1]=1
x3[2]=1
target30=0
targets = matrix(v,n,[[target00],[target10],[target20],[target30]])
g=matrix([x0,x1,x2,x3])
inputs=copy(g)
# Initialize weights, or leave at 0 (i.e.,change nothing)
weights=matrix(m,n)
print weights.transpose()
z = 0
a = list(var('s_%d' % j) for j in range(n))
while(z<T):
Q = inputs*weights
S = copy(Q)
for i in range(v):
y = copy(a)
for j in range(n):
if S[i][j] > bias[j]:
y[j] = 1
else:
y[j] = 0
for k in range(m):
print 'marker 1'
weights[k][j] = weights[k][j] + r*(targets[i][j]-y[j])*inputs[i][k]
print 'marker 2'
print weights.transpose
z +=1
This is a basic property of Sage vectors - they are immutable Python objects by default.
sage: M = matrix([[2,3],[3,2]])
sage: M[0][1] = 5
---------------------------------------------------------------------------
<snip>
ValueError: vector is immutable; please change a copy instead (use copy())
Notice that the error is that the vector is immutable. That is because you have taken the 0 row, which is a vector (immutable, hashable I guess, etc.).
But if you use the following syntax, you should be golden.
sage: M[0,1] = 5
sage: M
[2 5]
[3 2]
Here you are modifying the element directly. Hope this helps, enjoy Sage!

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