#==================
# AUTO Demo of trc
#==================

# this is a demo for the transcritical bifurcation
# using the normal form: x'=x*(x-mu); 

# Load the files trc.f90 and c.trc into the AUTO
trc = load('trc')

# Run and store the result in the Python variable 'res0'
res0 = run(trc)

# the results are:
# BR =1 (branch), single branch for now.
# PT =1..19 (points) of type EP (end points) 
# and the values of mu, x and the L2-NORM of x.

#################
# Run backwards in terms of the parameter 'mu', 
# and append to results to 'res1'
res0 = res0 + run(trc,DS='-')

# now we can see that we have a branch point - BP
# at mu~=0

# Relabel solutions
res0 = relabel(res0)

# Save to b.res0, s.res0, and d.res0
save(res0,'res0')

# Plot bifurcation diagram (partial - only on the origin)
p = plot(res0)
# change the y coordinate:
p.config(bifurcation_y=['x'])
p.config(stability=1)


# Set the new start label to the first BP label 
# in b.res1 and s.res1
# the point but different load for each branch
# ISW=1 defualt branch
bp0 = load(res0('BP1'), ISW=1)

#ISW=-1 switch branch
bp1 = load(res0('BP1'), ISW=-1)


# recomput (i.e., delete the previous as we are not appending) the zero branch from the bifurcation point
# both forward and backward, save in the variable res1 
res1 = run(bp0)
res1 = res1 + run(bp0,DS='-')

# Continue from this label in the other branch, 
# save in the variable res1
res2 = run(bp1)
res2 = res2 + run(bp1,DS='-')

# create variable res, so in the plot, 
# both branches will appear.
res = res1 +res2

res = relabel(res)

# save to b.trc, s.trc, and d.trc
save(res,'trc')

# Plot the bifurcation diagram (both branches)
p = plot(res)
p.config(bifurcation_y=['x'])
p.config(stability=1)

#clean the directory
clean()
wait()