classify_linear.m

function ret = classify_linear(e,v)
 %
 %   Takes vector expression e, and symbolic primitives v
 %   Returns classification vector
 %   For each element in e, determines if:
 %     - element is nonlinear in v               (2)
 %     - element is    linear in v               (1)
 %     - element does not depend on v at all     (0)
 %     
 %   This method can be sped up a lot with JacSparsityTraits::sp
 %
 %  Example:
 % x =SX.sym('x');
 % y =SX.sym('y');
 % p =SX.sym('p');
 % e = [0 x y p x*y x*p sin(x) cos(y) sqrt(x+y) p*p*x x*y*p]'; 
 % classify_linear(e,[x;y])
 % 
 % > 0     1     1     0     2     1     2     2     2     1     2
  import casadi.*
  f = Function('f',{v},{jacobian(e,v)});

  ret = ((sum2(IM(f.sparsity_out(0),1))==0)==0);
  ret = ret.nonzeros();
  pattern = IM(f.sparsity_jac(0,0),1).reshape(size(e,1),-1);
  pattern_sum = sum2(pattern);
  for k=pattern_sum.row()
    ret(k+1)=2;
  end
end

classify_linear.py

from casadi import *

def classify_linear(e,v):
  """
    Takes vector expression e, and symbolic primitives v
    Returns classification vector
    For each element in e, determines if:
      - element is nonlinear in v               (2)
      - element is    linear in v               (1)
      - element does not depend on v at all     (0)
      
    This method can be sped up a lot with JacSparsityTraits::sp
  """
  
  f = Function("f",[v],[jacobian(e,v)])
  ret = ((sum2(IM(f.sparsity_out(0),1))==0)==0).nonzeros()
  pattern = IM(f.sparsity_jac(0,0),1).reshape((e.shape[0],-1))
  for k in sum2(pattern).row():
    ret[k]=2
  return ret
    
  
x =SX.sym("x")
y =SX.sym("y")

p =SX.sym("p")


e = vertcat(0,x,y,p,x*y,x*p,sin(x),cos(y),sqrt(x+y),p*p*x,x*y*p)
  
print classify_linear(e,vertcat(x,y))

classify_linear_casadi2.4.py

def classify_linear(e,v):
  """
    Takes vector expression e, and symbolic primitives v
    Returns classification vector
    For each element in e, determines if:
      - element is nonlinear in v               (2)
      - element is    linear in v               (1)
      - element does not depend on v at all     (0)
      
    This method can be sped up a lot with JacSparsityTraits::sp
  """
  
  try:
    f = SXFunction("f",[v],[jacobian(e,v)])
  except:
    f = MXFunction("f",[v],[jacobian(e,v)])
  ret = ((sumCols(IMatrix(f.outputSparsity(0),1))==0)==0).nonzeros()
  pattern = DMatrix(f.jacSparsity(0,0),1).reshape((e.shape[0],-1))
  s2 = sumCols(pattern)
  if pattern.isscalar() and pattern.size()==0:
    s2 = pattern
  for k in s2.row():
    ret[k]=2
  return ret
    
  
x =SX.sym("x")
y =SX.sym("y")

p =SX.sym("p")


e = vertcat([0,x,y,p,x*y,x*p,sin(x),cos(y),sqrt(x+y),p*p*x,x*y*p])
  
print classify_linear(e,vertcat([x,y]))

x =MX.sym("x")
y =MX.sym("y")

p =MX.sym("p")


e = vertcat([0,x,y,p,x*y,x*p,sin(x),cos(y),sqrt(x+y),p*p*x,x*y*p])
  
print classify_linear(e,vertcat([x,y]))

print classify_linear(x,x)
print classify_linear(y,x)
print classify_linear(x**2,x)