# Demonstration of PyCUTEr use - constrained problem (HS71) from pyopus.problems import cutermgr from numpy import array if __name__ == '__main__': # Clear cache - this is not neccessary because the cache entry is removed # by prepareProblem() before the problem interface is built. cutermgr.clearCache('HS71') # Prepare two problems cutermgr.prepareProblem('HS71') # Import HS71 (unconstrained problem) # prepareProblem() returns a reference to the imported module. # Use this only if the problem interface is already available in the cache. cproblem=cutermgr.importProblem('HS71') # HS71 # # f = x1 x4 (x1 + x2 + x3) + x3 # subject to # (C1) x1 x2 x3 x4 - 25 >= 0 # (C2) x1^2 + x2^2 + x3^2 + x4^2 - 40 = 0 # (bounds) 1 <= x1, x2, x3, x4 <= 5 # # g = [ x4 (x1 + x2 + x3) + x1 x4 x1 x4 x1 x4 + 1 x1 (x1 + x2 + x3) ] # # [ 2 x4 x4 x4 2 x1 + x2 + x3 ] # [ ] # [ x4 0 0 x1 ] # H = [ ] # [ x4 0 0 x1 ] # [ ] # [ 2 x1 + x2 + x3 x1 x1 0 ] # # [ x2 x3 x4 x1 x3 x4 x1 x2 x4 x1 x2 x3 ] # J = [ ] # [ 2*x1 2 x2 2 x3 2 x4 ] # # [ 0 x3 x4 x2 x4 x2 x3 ] # [ ] # [ x3 x4 0 x1 x4 x1 x3 ] # HC1 = [ ] # [ x2 x4 x1 x4 0 x1 x2 ] # [ ] # [ x2 x3 x1 x3 x1 x2 0 ] # # [ 2 0 0 0 ] # [ ] # [ 0 2 0 0 ] # HC2 = [ ] # [ 0 0 2 0 ] # [ ] # [ 0 0 0 2 ] # # at x0 = [ 1.0 5.0 5.0 1.0 ] # # f = 16.0 # c1 = 0.0 # c2 = 12.0 # # g = [ 12.0 1.0 2.0 11.0 ] # # [ 2.0 1.0 1.0 12.0 ] # [ ] # [ 1.0 0.0 0.0 1.0 ] # H = [ ] # [ 1.0 0.0 0.0 1.0 ] # [ ] # [ 12.0 1.0 1.0 0.0 ] # # [ 25.0 5.0 5.0 25.0 ] # J = [ ] # [ 2.0 10.0 10.0 2.0 ] # # [ 0.0 5.0 5.0 25.0 ] # [ ] # [ 5.0 0.0 1.0 5.0 ] # HC1 = [ ] # [ 5.0 1.0 0.0 5.0 ] # [ ] # [ 25.0 5.0 5.0 0.0 ] print("Constrained problem demo") info=cproblem.getinfo() print("Problem name : ", info['name']) print("Problem size : ", info['n']) print("Constraint count : ", info['m']) print("NNZ in UT Hessian : ", info['nnzh']) print("Lower bounds : ", info['bl']) print("Upper bounds : ", info['bu']) print("Initial point : ", info['x']) print("Variable type : ", info['vartype']) print("Variable names : ", cproblem.varnames()) print("Sifdecode params : ", info['sifparams']) print("Sifdecode options : ", info['sifoptions']) print("Constraint names : ", cproblem.connames()) print("Eq. constr. first : ", info['efirst']) print("Lin. constr. first : ", info['lfirst']) print("NNZ in Jacobian : ", info['nnzj']) print("Equality constr. : ", info['equatn']) print("Linear constr. : ", info['linear']) print("Lower constraint : ", info['cl']) print("Upper constraint : ", info['cu']) print("Init. Lagr. mult. : ", info['v']) x0=info['x'] print("\nEvaluating objective at x0") f=cproblem.obj(x0) print("f(x0)=", f) print("\nEvaluating function and gradient") (f, g)=cproblem.obj(x0, True) print("f(x0)=", f) print("g(x0)=", g) print("\nEvaluating function and constraints") (f, c)=cproblem.objcons(x0) print("f(x0)=", f) print("c(x0)=", c) print("\nEvaluating constraints") c=cproblem.cons(x0) print("c(x0)=", c) print("\nEvaluating single constraint (0)") c0=cproblem.cons(x0, False, 0) print("c0(x0) : ", c0) print("\nEvaluating constraints and Jacobian") (c, J)=cproblem.cons(x0, True) print("c(x0)=", c) print("J(x0)=", J) print("\nEvaluating single constraint (0) and its gradient") (c0, gc0)=cproblem.cons(x0, True, 0) print("c0(x0)=", c0) print("gc0(x0)=", gc0) print("\nEvaluating function gradient and constraints Jacobian") (g, J)=cproblem.lagjac(x0) print("g(x0)=", g) print("J(x0)=", J) print("\nEvaluating gradient of Lagrangian at v=[1, 1] and constraints Jacobian") (g, J)=cproblem.lagjac(x0, array([1.0, 1.0])) print("gl(x0,[1.0, 1.0])=", g) print("J(x0)=", J) print("\nEvaluating product of previous J and [1, 1, 1, 1]") r=cproblem.jprod(False, array([1.0, 1.0, 1.0, 1.0])) print("J*[1.0, 1.0, 1.0, 1.0]=", r) print("\nEvaluating product of J at x0 and [1, 1, 1, 1]") r=cproblem.jprod(False, array([1.0, 1.0, 1.0, 1.0]), x0) print("J(x0)*[1.0, 1.0, 1.0, 1.0]=", r) print("\nEvaluating product of previous transposed J and [1, 1]") r=cproblem.jprod(True, array([1.0, 1.0])) print("JT*[1.0, 1.0]=", r) print("\nEvaluating product of transposed J at x0 and [1, 1]") r=cproblem.jprod(True, array([1.0, 1.0]), x0) print("JT(x0)*[1.0, 1.0]=", r) print("\nEvaluating Hessian of Lagrangian at [1, 1] for constrained problem") Hl=cproblem.hess(x0, array([1.0, 1.0])) print("Hl(x0, [1.0, 1.0])-", Hl) print("\nEvaluating Hessian of objective") H=cproblem.ihess(x0) print("H(x0)=", H) print("\nEvaluating Hessian of constraint (0)") H0=cproblem.ihess(x0, 0) print("H0(x0)=", H0) print("\nEvaluating Hessian of constraint (1)") H1=cproblem.ihess(x0, 1) print("H1(x0)=", H1) print("\nEvaluating Hessian of the Lagrangian at (x0, [1.0, 1.0]) times [2.0, 2.0, 2.0, 2.0]") r=cproblem.hprod(array([2.0, 2.0, 2.0, 2.0]), x0, array([1.0, 1.0])) print("Hl(x0, [1.0, 1.0])*[2.0, 2.0, 2.0, 2.0]=", r) print("\nEvaluating previous Hess. of the Lagr. times [2.0, 2.0, 2.0, 2.0]") r=cproblem.hprod(array([2.0, 2.0, 2.0, 2.0])) print("Hl*[2.0, 2.0, 2.0, 2.0]=", r) print("\nEvaluating gradient of Lagrangian at (x0, [1.0, 1.0]), Jacobian, and Hessian of Lagrangian") (gl, J, Hl)=cproblem.gradhess(x0, array([1.0, 1.0]), True) print("gl(x0, [1.0, 1.0])=", gl) print("J(x0)=", J) print("Hl(x0, [1.0, 1.0])=", Hl) print("\nEvaluating grad. of obj. at x0, Jacobian, and Hessian of Lagrangian") (g, J, Hl)=cproblem.gradhess(x0, array([1.0, 1.0]), False) print("g(x0)=", g) print("J(x0)=", J) print("Hl(x0)=", Hl) print("\nEvaluating constraints and sparse Jacobian") (c, J)=cproblem.scons(x0) print("c(x0)=", c) print("J(x0)=", J.todense()) print("\nEvaluating constraint (0) and its sparse gradient") (c0, gc0)=cproblem.scons(x0, 0) print("c0(x0)=", c0) print("gc0(x0)=", gc0.todense()) print("\nEvaluating sparse objective gradient and sparse Jacobian") (g, J)=cproblem.slagjac(x0) print("g(x0)=", g.todense()) print("J(x0)=", J.todense()) print("\nEvaluating sparse Lagrangian gradient and sparse Jacobian at (x0, [1.0, 1.0])") (gl, J)=cproblem.slagjac(x0, array([1.0, 01.0])) print("gl(x0)=", gl.todense()) print("J(x0)=", J.todense()) print("\nEvaluating sparse Hessian of Lagrangian at (x0, [1, 1]) for constrained problem") Hl=cproblem.sphess(x0, array([1.0, 1.0])) print("Hl(x0, [1.0, 1.0])=", Hl.todense()) print("\nEvaluating sparse Hessian of objective") H=cproblem.isphess(x0) print("H(x0)=", H.todense()) print("\nEvaluating sparse Hessian of single constraint (0)") H0=cproblem.isphess(x0, 0) print("H0(x0)=", H0.todense()) print("\nEvaluating sparse Hessian of single constraint (1)") H1=cproblem.isphess(x0, 1) print("H0(x0)=", H1.todense()) print("\nEvaluating grad. of obj., constr. Jac., and Hess. of Lagr. at (x0, [0.0, 0.0])") (g, J, Hl)=cproblem.gradsphess(x0, array([1.0, 1.0])) print("g(x0)=", g.todense()) print("J(x0)=", J.todense()) print("Hl(x0, [1.0, 1.0])=", Hl.todense()) print("\nEvaluating grad. of Lagr., constr. Jac., and Hess. of Lagr. at (x0, [0.0, 0.0])") (gl, J, Hl)=cproblem.gradsphess(x0, array([1.0, 1.0]), True) print("gl(x0)=", gl.todense()) print("J(x0)=", J.todense()) print("Hl(x0, [1.0, 1.0])=", Hl.todense()) print("\nCollecting report") rep=cproblem.report() print("Setup time : ", rep['tsetup']) print("Run time : ", rep['trun']) print("Num. of f eval : ", rep['f']) print("Num. of g eval : ", rep['g']) print("Num. of H eval : ", rep['H']) print("Num. of H prod : ", rep['Hprod']) print("Num. of c eval : ", rep['c']) print("Num. of cg eval : ", rep['cg']) print("Num. of cH eval : ", rep['cH'])