import cvxpy as cvx
import numpy

n = 6;  # number of variables (chosen because it can print on one line in my moniter)
m = 10; # number of constraints. These are included so that the problem is not unbounded

# generate some constraints
numpy.random.seed(0) # for repeatibility
A = numpy.random.randn(m,n)
b = 10 * numpy.random.random([m,1])

# and the parameter
p = cvx.Parameter(1,n)
p.value = numpy.random.random([1,n]) # returnes values in the interval [0.0, 1.0)

x = cvx.Variable(n,1) # (n,1) will give a colum vector

objective = cvx.Maximize(p * cvx.sqrt(x))
constraint = [A*x <= b]
problem = cvx.Problem(objective, constraint)

# Try solving the problem. Print error if any.
try:
    problem.solve()
except Exception as e:
    print e

print "objective.is_dcp(): ", objective.is_dcp()
print "p * cvx.sqrt(x) curvature: ", (p * cvx.sqrt(x)).curvature

print "\np value: ", p.value
print "p >= 0: ", p.value >= 0
print "sqrt(x) curvature: ", cvx.sqrt(x).curvature

print "p:"
print "sign property: ", p.sign
print "value property >= 0: ", p.value >= 0


q = cvx.Parameter(1,n,nonneg=True)
print "q:"
print "sign property: ", q.sign
try:
    print q.value
except Exception as e:
    print e

negative_values = numpy.array([range(n)]) - n
print "Values to assign to q: ", negative_values

try:
    q.value = numpy.array([range(n)]) - n
except Exception as e:
    print e

print "\nSetting the sign of p for cvx:"
try: 
    p.sign = 'positive'
except Exception as e:
    print e

temp_p_value = p.value
p = cvx.Parameter(1,n,nonneg=True)
p.value = temp_p_value

print p.value
print p.sign

objective = cvx.Maximize(p * cvx.sqrt(x))
problem = cvx.Problem(objective, constraint)

print "DCP rules test: ", problem.is_dcp()
try: 
    print "solving... "
    problem.solve()
except Exception as e:
    print(e)

# print some stuff
print problem.status
print "Optimal value: ", problem.value
print "\nx:\n", x.value
print "\nResidual of constraints:\n", A.dot(x.value) - b