diff --git a/crocoddyl/__init__.py b/crocoddyl/__init__.py
index 068c48fb9b1ba2cef5abe456412e9fd75f453f2c..5661caec976610a3c604af69081cc44639e7111f 100644
--- a/crocoddyl/__init__.py
+++ b/crocoddyl/__init__.py
@@ -3,7 +3,8 @@ from .action import (ActionDataAbstract, ActionDataLQR, ActionDataNumDiff, Actio
 from .activation import (ActivationDataInequality, ActivationDataQuad, ActivationDataSmoothAbs,
                          ActivationDataWeightedQuad, ActivationModelInequality, ActivationModelQuad,
                          ActivationModelSmoothAbs, ActivationModelWeightedQuad)
-from .actuation import ActuationDataFreeFloating, ActuationDataFull, ActuationModelFreeFloating, ActuationModelFull, ActuationModelUAM
+from .actuation import (ActuationDataFreeFloating, ActuationDataFull, ActuationDataUAM, ActuationDataDoublePendulum,
+                        ActuationModelFreeFloating, ActuationModelFull, ActuationModelUAM, ActuationModelDoublePendulum)
 from .box_ddp import SolverBoxDDP
 from .box_kkt import SolverBoxKKT
 from .callbacks import CallbackDDPLogger, CallbackDDPVerbose, CallbackSolverDisplay, CallbackSolverTimer
@@ -14,7 +15,7 @@ from .cost import (CostDataCoM, CostDataControl, CostDataForce, CostDataFramePla
                    CostDataState, CostDataSum, CostModelCoM, CostModelControl, CostModelForce,
                    CostModelForceLinearCone, CostModelFramePlacement, CostModelFrameRotation,
                    CostModelFrameTranslation, CostModelFrameVelocity, CostModelFrameVelocityLinear, CostModelNumDiff,
-                   CostModelPinocchio, CostModelState, CostModelSum)
+                   CostModelPinocchio, CostModelState, CostModelSum, CostModelDoublePendulum, CostDataDoublePendulum)
 from .ddp import SolverDDP
 from .diagnostic import displayTrajectory, plotDDPConvergence, plotOCSolution
 from .differential_action import (DifferentialActionDataAbstract, DifferentialActionDataFullyActuated,
diff --git a/crocoddyl/actuation.py b/crocoddyl/actuation.py
index 4da7abda2299fa2aced15258d501787feae743d6..446ee7498e4830326db75f583b4b38c1f42f32ca 100644
--- a/crocoddyl/actuation.py
+++ b/crocoddyl/actuation.py
@@ -2,6 +2,41 @@ import warnings
 
 import numpy as np
 
+class ActuationModelDoublePendulum:
+    def __init__(self, pinocchioModel):
+        self.pinocchio = pinocchioModel
+        self.nq = pinocchioModel.nq
+        self.nv = pinocchioModel.nv
+        self.nx = self.nq + self.nv
+        self.ndx = self.nv * 2
+        self.nu = 1
+
+    def calc(self, data, x, u):
+        S = np.zeros([self.nv,self.nu])
+        #S[1] = 1
+        S[0] = 1
+        data.a = np.dot(S,u)
+        return data.a
+
+    def calcDiff(self, data, x, u, recalc=True):
+        if recalc:
+            self.calc(data, x, u)
+        return data.a
+
+    def createData(self, pinocchioData):
+        return ActuationDataDoublePendulum(self, pinocchioData)
+
+class ActuationDataDoublePendulum:
+    def __init__(self, model, pinocchioData):
+        self.pinocchio = pinocchioData
+        ndx, nv, nu = model.ndx, model.nv, model.nu
+        self.a = np.zeros(nv)  # result of calc
+        self.A = np.zeros([nv, ndx + nu])  # result of calcDiff
+        self.Ax = self.A[:, :ndx]
+        self.Au = self.A[:, ndx:]
+        # self.Au[1,0] = 1
+        self.Au[0,0] = 1
+
 class ActuationModelUAM:
     '''
     This model transforms an actuation u into a joint torque tau.
diff --git a/crocoddyl/cost.py b/crocoddyl/cost.py
index 223992044fd5a60ee2653d9aff722452058805e3..9a5b5bc7f3e638b5845bd6661e7b624d466d7f62 100644
--- a/crocoddyl/cost.py
+++ b/crocoddyl/cost.py
@@ -560,7 +560,11 @@ class CostModelControl(CostModelPinocchio):
         # data.Ru[:,:] = np.eye(nu)
         Ax, Axx = self.activation.calcDiff(data.activation, data.residuals, recalc=recalc)
         data.Lu[:] = Ax
-        data.Luu[:, :] = np.diag(m2a(Axx))
+        if type(Axx) is np.ndarray:
+            data.Luu[:, :] = np.diag(Axx)
+        else:
+            data.Luu[:, :] = np.diag(m2a(Axx))
+        #data.Luu[:, :] = np.diag(m2a(Axx))
 
 
 class CostDataControl(CostDataPinocchio):
@@ -676,3 +680,54 @@ class CostDataForceCone(CostDataPinocchio):
         CostDataPinocchio.__init__(self, model, pinocchioData)
         self.contact = contactData
         self.activation = model.activation.createData()
+
+class CostModelDoublePendulum(CostModelPinocchio):
+    def __init__(self, pinocchioModel, frame, ref, nu=None, activation=None):
+        self.CostDataType = CostDataDoublePendulum
+        CostModelPinocchio.__init__(self, pinocchioModel, ncost=6, nu=nu)
+        self.ref = ref
+        self.frame = frame
+        self.activation = activation if activation is not None else ActivationModelQuad()
+
+    def calc(self, data, x, u):
+        c1 = np.cos(x[0])
+        c2 = np.cos(x[1])
+        s1 = np.sin(x[0])
+        s2 = np.sin(x[1])
+        data.residuals = np.array([s1, s2, 1-c1, 1-c2, x[2], x[3]])
+        data.cost = sum(self.activation.calc(data.activation, data.residuals))
+        return data.cost
+
+    def calcDiff(self, data, x, u, recalc=True):
+        if recalc:
+            self.calc(data, x, u)
+        c1 = np.cos(x[0])
+        c2 = np.cos(x[1])
+        s1 = np.sin(x[0])
+        s2 = np.sin(x[1])
+        nq = self.nq
+        Ax, Axx = self.activation.calcDiff(data.activation, data.residuals, recalc=recalc)
+        J = np.zeros([6, 4])
+        J[:2,:2] = np.diag([c1, c2])
+        J[2:4,:2] = np.diag([s1, s2])
+        J[4:6,2:4] = np.diag([1,1])
+        data.Lx[:] = np.dot(np.transpose(J), Ax)
+        H = np.zeros([6, 4])
+        H[:2,:2] = np.diag([c1**2-s1**2, c2**2-s2**2])
+        H[2:4,:2] = np.diag([s1**2+(1-c1)*c1, s2**2+(1-c2)*c2])
+        J[4:6,2:4] = np.diag([1,1])
+        data.Lxx[:, :] = np.dot(np.transpose(H), Axx)
+        return data.cost
+
+
+class CostDataDoublePendulum(CostDataPinocchio):
+    def __init__(self, model, pinocchioData):
+        CostDataPinocchio.__init__(self, model, pinocchioData)
+        self.activation = model.activation.createData()
+        self.Lu = 0
+        self.Lv = 0
+        self.Lxu = 0
+        self.Luu = 0
+        self.Lvv = 0
+        self.Ru = 0
+        self.Rv = 0
diff --git a/crocoddyl/double_pendulum.py b/crocoddyl/double_pendulum.py
new file mode 100644
index 0000000000000000000000000000000000000000..cd1b73cfc79f515e59350e540012e06cee8a0cf3
--- /dev/null
+++ b/crocoddyl/double_pendulum.py
@@ -0,0 +1,73 @@
+import numpy as np
+import pinocchio
+
+from .differential_action import DifferentialActionDataAbstract, DifferentialActionModelAbstract
+from .state import StatePinocchio
+from .utils import a2m, m2a
+
+class DifferentialActionModelDoublePendulum(DifferentialActionModelAbstract):
+    def __init__(self, pinocchioModel, actuationModel, costModel):
+        DifferentialActionModelAbstract.__init__(self, pinocchioModel.nq, pinocchioModel.nv, actuationModel.nu)
+        self.DifferentialActionDataType = DifferentialActionDataDoublePendulum
+        self.pinocchio = pinocchioModel
+        self.State = StatePinocchio(self.pinocchio)
+        self.actuation = actuationModel
+        self.costs = costModel
+
+    @property
+    def ncost(self):
+        return self.costs.ncost
+
+    def calc(self, data, x, u=None):
+        if u is None:
+            u = self.unone
+        nq, nv = self.nq, self.nv
+        q = a2m(x[:nq])
+        v = a2m(x[-nv:])
+        tauq[:] = self.actuation.calc(data.actuation, x, u)
+
+        pinocchio.computeAllTerms(self.pinocchio, data.pinocchio, q, v)
+        data.M = data.pinocchio.M
+        data.Minv = np.linalg.inv(data.M)
+        data.r = data.tauq - m2a(data.pinocchio.nle)
+        data.xout[:] = np.dot(data.Minv, data.r)
+
+        # --- Cost
+        pinocchio.forwardKinematics(self.pinocchio, data.pinocchio, q, v)
+        pinocchio.updateFramePlacements(self.pinocchio, data.pinocchio)
+        data.cost = self.costs.calc(data.costs, x, u)
+        return data.xout, data.cost
+
+    def calcDiff(self, data, x, u=None, recalc=True):
+        if u is None:
+            u = self.unone
+        if recalc:
+            xout, cost = self.calc(data, x, u)
+        nq, nv = self.nq, self.nv
+        q = a2m(x[:nq])
+        v = a2m(x[-nv:])
+        tauq = a2m(u)
+        a = a2m(data.xout)
+        # --- Dynamics
+        if self.forceAba:
+            pinocchio.computeABADerivatives(self.pinocchio, data.pinocchio, q, v, tauq)
+            data.Fx[:, :nv] = data.pinocchio.ddq_dq
+            data.Fx[:, nv:] = data.pinocchio.ddq_dv
+            data.Fu[:, :] = data.pinocchio.Minv
+        else:
+            pinocchio.computeRNEADerivatives(self.pinocchio, data.pinocchio, q, v, a)
+            data.Fx[:, :nv] = -np.dot(data.Minv, data.pinocchio.dtau_dq)
+            data.Fx[:, nv:] = -np.dot(data.Minv, data.pinocchio.dtau_dv)
+            data.Fu[:, :] = data.Minv
+        # --- Cost
+        pinocchio.computeJointJacobians(self.pinocchio, data.pinocchio, q)
+        pinocchio.updateFramePlacements(self.pinocchio, data.pinocchio)
+        self.costs.calcDiff(data.costs, x, u, recalc=False)
+        return data.xout, data.cost
+
+
+class DifferentialActionDataDoublePendulum(DifferentialActionDataAbstract):
+    def __init__(self, model):
+        self.pinocchio = model.pinocchio.createData()
+        costData = model.costs.createData(self.pinocchio)
+        DifferentialActionDataAbstract.__init__(self, model, costData)
diff --git a/crocoddyl/flying.py b/crocoddyl/flying.py
index 3d12396adb14e0d0c66caab9bd11738f8a60bfb0..6d9d2400141d7144f771fb53045c06ec3adb125d 100644
--- a/crocoddyl/flying.py
+++ b/crocoddyl/flying.py
@@ -78,7 +78,6 @@ class DifferentialActionDataUAM(DifferentialActionDataAbstract):
         self.pinocchio = model.pinocchio.createData()
         self.actuation = model.actuation.createData(self.pinocchio)
         costData = model.costs.createData(self.pinocchio)
-        # print self.costs.Lu
         DifferentialActionDataAbstract.__init__(self, model, costData)
 
         nv = model.nv
diff --git a/crocoddyl/robots.py b/crocoddyl/robots.py
index 8008ad622f7a1d1dae2710494fffdc951e4ce1ce..6be2250e84b6f0255f6e3f869e6d227fb9f7388b 100644
--- a/crocoddyl/robots.py
+++ b/crocoddyl/robots.py
@@ -145,6 +145,6 @@ def loadKintonArm(modelPath='/opt/openrobots/share/example-robot-data'):
 def loadBorinotArm(modelPath='/opt/openrobots/share/example-robot-data'):
     URDF_FILENAME = "borinot_arm.urdf"
     URDF_SUBPATH = "/borinot_arm/urdf/" + URDF_FILENAME
-    robot = RobotWrapper.BuildFromURDF(modelPath + URDF_SUBPATH, [modelPath])
-    robot.q0.flat = [np.pi,0]
+    robot = RobotWrapper.BuildFromURDF(modelPath + URDF_SUBPATH, [modelPath], None)
+    robot.q0.flat = [np.pi]
     return robot
diff --git a/examples/notebooks/borinot_arm.ipynb b/examples/notebooks/borinot_arm.ipynb
index 492a1840bddaf2978f70214924c8eb9269e3d964..9f2584ccf315d147f988b8599fdf67c29e08f8d8 100644
--- a/examples/notebooks/borinot_arm.ipynb
+++ b/examples/notebooks/borinot_arm.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 98,
+   "execution_count": 76,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -13,7 +13,7 @@
     "robot = loadBorinotArm()\n",
     "robot.initViewer(loadModel=True)\n",
     "\n",
-    "q0 = [-3.14, 3.14]\n",
+    "q0 = [1, 0]\n",
     "robot.q0.flat = q0\n",
     "robot.framesForwardKinematics(robot.q0)\n",
     "robot.display(robot.q0)\n",
@@ -44,397 +44,4716 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 111,
+   "execution_count": 80,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 83.50136921]\n",
+      " [-85.98316903]]\n",
+      "[[ 84.70309115]\n",
+      " [-90.32383132]]\n",
+      "[[ 86.59918836]\n",
+      " [-96.95340459]]\n",
+      "[[  88.95862434]\n",
+      " [-104.52228931]]\n",
+      "[[  91.37907111]\n",
+      " [-110.6576778 ]]\n",
+      "[[  93.26402308]\n",
+      " [-111.80199792]]\n",
+      "[[  93.88473349]\n",
+      " [-103.51136159]]\n",
+      "[[ 92.5891125 ]\n",
+      " [-81.58454278]]\n",
+      "[[ 89.10194306]\n",
+      " [-43.82327148]]\n",
+      "[[83.65842531]\n",
+      " [ 8.80182813]]\n",
+      "[[76.71813123]\n",
+      " [72.86262902]]\n",
+      "[[ 68.38561553]\n",
+      " [144.58298192]]\n",
+      "[[ 57.97665644]\n",
+      " [221.42583416]]\n",
+      "[[ 44.0376546 ]\n",
+      " [302.03973374]]\n",
+      "[[ 24.92095193]\n",
+      " [384.74444739]]\n",
+      "[[1.95719954e-01]\n",
+      " [4.64134205e+02]]\n",
+      "[[-26.19296193]\n",
+      " [521.96147225]]\n",
+      "[[-39.55225879]\n",
+      " [503.6501806 ]]\n",
+      "[[ -9.96926312]\n",
+      " [296.59092812]]\n",
+      "[[  73.91310413]\n",
+      " [-136.22981776]]\n",
+      "[[ 148.97427591]\n",
+      " [-535.31189161]]\n",
+      "[[ 166.98309409]\n",
+      " [-719.42755562]]\n",
+      "[[ 146.51320183]\n",
+      " [-750.69994522]]\n",
+      "[[ 109.20935373]\n",
+      " [-674.28917521]]\n",
+      "[[  59.57975477]\n",
+      " [-475.74664519]]\n",
+      "[[  -4.1901011 ]\n",
+      " [-152.58091458]]\n",
+      "[[-68.72550257]\n",
+      " [190.22869197]]\n",
+      "[[-112.31675902]\n",
+      " [ 406.88071122]]\n",
+      "[[-132.65670823]\n",
+      " [ 473.9520921 ]]\n",
+      "[[-138.20051989]\n",
+      " [ 444.78248451]]\n",
+      "[[-133.65862871]\n",
+      " [ 362.44702047]]\n",
+      "[[-120.72450066]\n",
+      " [ 251.47298998]]\n",
+      "[[-102.40848719]\n",
+      " [ 133.23636595]]\n",
+      "[[-84.11812522]\n",
+      " [ 31.59577825]]\n",
+      "[[-70.83885461]\n",
+      " [-35.65977892]]\n",
+      "[[-64.27830644]\n",
+      " [-65.31802994]]\n",
+      "[[-63.18233419]\n",
+      " [-65.51744139]]\n",
+      "[[-65.32122936]\n",
+      " [-47.29375061]]\n",
+      "[[-68.80840565]\n",
+      " [-19.60167778]]\n",
+      "[[-72.40942032]\n",
+      " [ 11.5815572 ]]\n",
+      "[[-75.39354127]\n",
+      " [ 42.50429597]]\n",
+      "[[-77.32331316]\n",
+      " [ 70.75810643]]\n",
+      "[[-77.9196505 ]\n",
+      " [ 94.73858185]]\n",
+      "[[-77.01698334]\n",
+      " [113.47954328]]\n",
+      "[[-74.57622862]\n",
+      " [126.72699222]]\n",
+      "[[-70.70505115]\n",
+      " [135.04471066]]\n",
+      "[[-65.64180323]\n",
+      " [139.76835485]]\n",
+      "[[-59.6934461 ]\n",
+      " [142.76423238]]\n",
+      "[[-53.15808675]\n",
+      " [146.09876776]]\n",
+      "[[-46.28629094]\n",
+      " [151.74194256]]\n",
+      "[[-39.35649084]\n",
+      " [161.25993761]]\n",
+      "[[-33.02745554]\n",
+      " [175.06529172]]\n",
+      "[[-29.3916203 ]\n",
+      " [189.99582081]]\n",
+      "[[-34.37724601]\n",
+      " [193.25646162]]\n",
+      "[[-59.29030553]\n",
+      " [158.09427067]]\n",
+      "[[-107.08797816]\n",
+      " [  79.0040319 ]]\n",
+      "[[-148.33851072]\n",
+      " [  33.23996252]]\n",
+      "[[-159.59836753]\n",
+      " [  84.35558473]]\n",
+      "[[-158.1121612 ]\n",
+      " [ 204.82872277]]\n",
+      "[[-166.49609699]\n",
+      " [ 371.07636992]]\n",
+      "[[-199.30621075]\n",
+      " [ 608.69221474]]\n",
+      "[[-269.84773737]\n",
+      " [ 982.00990242]]\n",
+      "[[-330.4582086 ]\n",
+      " [1282.94944111]]\n",
+      "[[ 116.23592039]\n",
+      " [-816.8842808 ]]\n",
+      "[[  281.11251038]\n",
+      " [-1640.90958482]]\n",
+      "[[  124.78519414]\n",
+      " [-1067.92424959]]\n",
+      "[[  43.00371367]\n",
+      " [-820.61342287]]\n",
+      "[[   5.6041512 ]\n",
+      " [-739.20205904]]\n",
+      "[[  -1.54514748]\n",
+      " [-730.63366527]]\n",
+      "[[  19.02966305]\n",
+      " [-753.20338046]]\n",
+      "[[  67.14643624]\n",
+      " [-790.62855464]]\n",
+      "[[ 139.48676183]\n",
+      " [-846.67086153]]\n",
+      "[[ 226.43008473]\n",
+      " [-943.2491212 ]]\n",
+      "[[  306.12103578]\n",
+      " [-1086.05730091]]\n",
+      "[[ 284.59149339]\n",
+      " [-964.70215695]]\n",
+      "[[-76.74325139]\n",
+      " [445.34359995]]\n",
+      "[[-275.08855682]\n",
+      " [1137.42907253]]\n",
+      "[[-210.31203362]\n",
+      " [ 921.12652379]]\n",
+      "[[-131.01402138]\n",
+      " [ 730.62151147]]\n",
+      "[[-65.31104152]\n",
+      " [606.36844063]]\n",
+      "[[-13.91476792]\n",
+      " [512.26938765]]\n",
+      "[[ 23.68929673]\n",
+      " [428.20592428]]\n",
+      "[[ 48.91861012]\n",
+      " [347.48471097]]\n",
+      "[[ 64.34291271]\n",
+      " [270.15549592]]\n",
+      "[[ 73.07559504]\n",
+      " [198.18283392]]\n",
+      "[[ 77.99782555]\n",
+      " [132.93008617]]\n",
+      "[[81.28012072]\n",
+      " [74.62018697]]\n",
+      "[[84.24443647]\n",
+      " [22.92280275]]\n",
+      "[[ 87.43065295]\n",
+      " [-22.20342436]]\n",
+      "[[ 90.7709468 ]\n",
+      " [-60.05361653]]\n",
+      "[[ 93.85326609]\n",
+      " [-89.44726085]]\n",
+      "[[  96.23919343]\n",
+      " [-109.59265884]]\n",
+      "[[  97.71834995]\n",
+      " [-120.89257421]]\n",
+      "[[  98.37946681]\n",
+      " [-125.04245786]]\n",
+      "[[  98.50379508]\n",
+      " [-124.40396174]]\n",
+      "[[  98.39586512]\n",
+      " [-121.16638912]]\n",
+      "[[  98.25359974]\n",
+      " [-116.74418191]]\n",
+      "[[  98.10534433]\n",
+      " [-111.50996529]]\n",
+      "[[  97.79575173]\n",
+      " [-104.76236958]]\n",
+      "[[ 97.00189602]\n",
+      " [-94.84639814]]\n",
+      "[[ 95.27887513]\n",
+      " [-79.44890561]]\n",
+      "[[ 92.14414019]\n",
+      " [-56.15046655]]\n",
+      "[[ 87.1951339 ]\n",
+      " [-23.23533422]]\n",
+      "[[80.21832255]\n",
+      " [19.45794326]]\n",
+      "[[71.23151878]\n",
+      " [70.02079471]]\n",
+      "[[ 60.46310129]\n",
+      " [124.46294473]]\n",
+      "[[ 48.3933095 ]\n",
+      " [176.83820128]]\n",
+      "[[ 36.03964642]\n",
+      " [218.81180586]]\n",
+      "[[ 25.52579179]\n",
+      " [238.4071791 ]]\n",
+      "[[ 20.4994729 ]\n",
+      " [219.38149387]]\n",
+      "[[ 25.08312885]\n",
+      " [146.13738336]]\n",
+      "[[39.97206931]\n",
+      " [19.50745119]]\n",
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+      " [-156.5285996 ]]\n",
+      "[[  89.16895983]\n",
+      " [-200.35225742]]\n",
+      "[[ 100.9935178 ]\n",
+      " [-240.09878508]]\n",
+      "[[ 109.93069692]\n",
+      " [-261.01368954]]\n",
+      "[[ 111.74968242]\n",
+      " [-236.12864967]]\n",
+      "[[ 100.86088389]\n",
+      " [-132.98948742]]\n",
+      "[[76.06731095]\n",
+      " [52.38213081]]\n",
+      "[[ 45.10864037]\n",
+      " [267.69403295]]\n",
+      "[[ 16.0666715]\n",
+      " [448.7986496]]\n",
+      "[[ -9.72130562]\n",
+      " [565.74627916]]\n",
+      "[[-29.3249653 ]\n",
+      " [595.96783378]]\n",
+      "[[-28.17482113]\n",
+      " [486.1238522 ]]\n",
+      "[[ 12.25085347]\n",
+      " [182.58045938]]\n",
+      "[[  76.70269734]\n",
+      " [-224.58428582]]\n",
+      "[[ 114.875866  ]\n",
+      " [-513.40760587]]\n",
+      "[[ 106.74493552]\n",
+      " [-587.14771787]]\n",
+      "[[  65.02606846]\n",
+      " [-470.3777219 ]]\n",
+      "[[   5.62421503]\n",
+      " [-219.94501392]]\n",
+      "[[-54.32258939]\n",
+      " [ 60.85835574]]\n",
+      "[[-98.00469405]\n",
+      " [256.33446712]]\n",
+      "[[-119.46386141]\n",
+      " [ 323.28714248]]\n",
+      "[[-122.26644815]\n",
+      " [ 288.22779424]]\n",
+      "[[-112.49851022]\n",
+      " [ 196.91454578]]\n",
+      "[[-96.72366293]\n",
+      " [ 91.28427925]]\n",
+      "[[-81.04097278]\n",
+      " [  2.3073125 ]]\n",
+      "[[-69.16844967]\n",
+      " [-55.13390611]]\n",
+      "[[-61.76789962]\n",
+      " [-81.21252568]]\n",
+      "[[-57.61746019]\n",
+      " [-84.09513636]]\n",
+      "[[-55.08696815]\n",
+      " [-73.20745314]]\n",
+      "[[-52.91248672]\n",
+      " [-56.00135659]]\n",
+      "[[-50.34788212]\n",
+      " [-37.35459981]]\n",
+      "[[-47.05249239]\n",
+      " [-20.03853233]]\n",
+      "[[-42.9352718 ]\n",
+      " [ -5.38683461]]\n",
+      "[[-38.03150533]\n",
+      " [  6.13229813]]\n",
+      "[[-32.421879  ]\n",
+      " [ 14.49522356]]\n",
+      "[[-26.18481182]\n",
+      " [ 19.8359208 ]]\n",
+      "[[-19.37169266]\n",
+      " [ 22.26325479]]\n",
+      "[[-11.9976093 ]\n",
+      " [ 21.75597588]]\n",
+      "[[-4.04305347]\n",
+      " [18.11551066]]\n"
+     ]
+    }
+   ],
    "source": [
-    "state = StatePinocchio(robot.model)\n",
+    "import time \n",
+    "dt = 0.01\n",
+    "t = np.arange(0,20,dt)\n",
+    "q0 = np.array([[1, 0]]).T\n",
     "\n",
-    "goalOrientationCost1 = CostModelFrameRotation(robot.model, \n",
-    "                                             frame=robot.model.getFrameId('link1'), \n",
-    "                                             ref=Mref.rotation, \n",
-    "                                             nu=robot.model.nv)\n",
-    "goalOrientationCost2 = CostModelFrameRotation(robot.model, \n",
-    "                                             frame=robot.model.getFrameId('link2'), \n",
-    "                                             ref=Mref.rotation, \n",
-    "                                             nu=robot.model.nv)\n",
+    "q = q0\n",
+    "q_d = np.zeros([2,1])\n",
+    "q_dd = np.zeros([2,1])\n",
     "\n",
-    "xRegCost = CostModelState(robot.model, state, ref=state.zero(), nu=robot.model.nv)\n",
-    "uRegCost = CostModelControl(robot.model, nu=robot.model.nv)\n",
-    "uLimCost = CostModelControl(robot.model, \n",
-    "                            nu=robot.model.nv,\n",
-    "                            activation = ActivationModelInequality(np.array([-1e-3, -1e-3]), np.array([1e-3, 1e-3])))\n",
+    "for i in range(len(t)):\n",
+    "    pin.computeAllTerms(robot.model, robot.data, q, q_d)\n",
+    "    M = robot.data.M\n",
+    "    Minv = np.linalg.inv(M)\n",
+    "    nle = robot.data.nle\n",
+    "    q_dd = np.dot(Minv, m2a(-nle)).T\n",
+    "    q_d = q_d + q_dd*dt\n",
+    "    q = q + q_d*dt + 0.5*q_dd*dt**2\n",
+    "    print q_dd\n",
+    "    robot.framesForwardKinematics(q)\n",
+    "    robot.display(q)\n",
+    "    time.sleep(0.01)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 67,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "state = StatePinocchio(robot.model)\n",
     "\n",
+    "xRegCost = CostModelState(robot.model, state, ref=state.zero(), nu=1)\n",
+    "uRegCost = CostModelControl(robot.model, nu = 1)\n",
+    "xPendCost = CostModelDoublePendulum(robot.model, \n",
+    "                                    frame=state, \n",
+    "                                    ref=state.zero, \n",
+    "                                    nu=1,\n",
+    "                                    activation=ActivationModelWeightedQuad(np.np.array([1]*4+[0.001]*2))) \n",
     "\n",
+    "runningCostModel = CostModelSum(robot.model, nu=1)\n",
+    "terminalCostModel = CostModelSum(robot.model, nu=1)\n",
     "\n",
-    "runningCostModel = CostModelSum(robot.model)\n",
-    "terminalCostModel = CostModelSum(robot.model)\n",
+    "runningCostModel.addCost(name=\"regx\", weight=1e-6, cost=xRegCost)\n",
+    "runningCostModel.addCost(name=\"regu\", weight=1e-6, cost=uRegCost)\n",
+    "runningCostModel.addCost(name=\"pend\", weight=0.1, cost=xPendCost)\n",
+    "terminalCostModel.addCost(name=\"ori2\", weight=100, cost=xPendCost)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "actModel = ActuationModelDoublePendulum(robot.model)\n",
+    "runningModel = IntegratedActionModelEuler(DifferentialActionModelUAM(robot.model, actModel, runningCostModel))\n",
+    "terminalModel = IntegratedActionModelEuler(DifferentialActionModelUAM(robot.model, actModel, terminalCostModel))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Defining the time duration for running action models and the terminal one\n",
+    "dt = 5e-2\n",
+    "runningModel.timeStep = dt\n",
     "\n",
-    "runningCostModel.addCost(name=\"ori1\", weight=1e-2, cost=goalOrientationCost1)\n",
-    "runningCostModel.addCost(name=\"ori2\", weight=1e-2, cost=goalOrientationCost2)\n",
-    "runningCostModel.addCost(name=\"regx\", weight=1e-7, cost=xRegCost)\n",
-    "runningCostModel.addCost(name=\"regu\", weight=1e-1, cost=uRegCost)\n",
-    "runningCostModel.addCost(name=\"limu\", weight=10000, cost=uLimCost)\n",
-    "terminalCostModel.addCost(name=\"ori1\", weight=5, cost=goalOrientationCost1)\n",
-    "terminalCostModel.addCost(name=\"ori2\", weight=5, cost=goalOrientationCost2)"
+    "# For this optimal control problem, we define 250 knots (or running action\n",
+    "# models) plus a terminal knot\n",
+    "T = 100\n",
+    "x0 = np.np.array([3.14, 0, 0., 0. ])\n",
+    "problem = ShootingProblem(x0, [runningModel] * T, terminalModel)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 112,
+   "execution_count": 74,
    "metadata": {},
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'array' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-74-dbb70293a1df>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m xs = [np.array([3.14, 0.  , 0.  , 0.  ]),\n\u001b[0;32m----> 2\u001b[0;31m  \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m  \u001b[0;36m3.71059542\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0;34m-\u001b[0m\u001b[0;36m2.05541894\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0;36m11.41190835\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m41.10837881\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m  \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m  \u001b[0;36m3.76668242\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0;34m-\u001b[0m\u001b[0;36m2.83395101\u001b[0m\u001b[0;34m,\u001b[0m   \u001b[0;36m1.12174006\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m15.5706414\u001b[0m \u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m  \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m \u001b[0;36m3.89056434\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m2.99656298\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0;36m2.47763835\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m3.25223937\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m  \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m \u001b[0;36m3.71635446\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m3.12552479\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m3.48419748\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m2.57923624\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mNameError\u001b[0m: name 'array' is not defined"
+     ]
+    }
+   ],
+   "source": [
+    "xs = [np.np.array([3.14, 0.  , 0.  , 0.  ]),\n",
+    " np.array([  3.71059542,  -2.05541894,  11.41190835, -41.10837881]),\n",
+    " np.array([  3.76668242,  -2.83395101,   1.12174006, -15.5706414 ]),\n",
+    " np.array([ 3.89056434, -2.99656298,  2.47763835, -3.25223937]),\n",
+    " np.array([ 3.71635446, -3.12552479, -3.48419748, -2.57923624]),\n",
+    " np.array([ 3.5244489 , -2.92584309, -3.83811128,  3.99363411]),\n",
+    " np.array([  2.92679904,  -2.97209156, -11.95299728,  -0.92496958]),\n",
+    " np.array([  2.338523  ,  -2.87566759, -11.76552081,   1.92847956]),\n",
+    " np.array([ 1.95375756, -2.56138768, -7.69530875,  6.28559803]),\n",
+    " np.array([ 1.77584689, -2.1567364 , -3.55821333,  8.09302574]),\n",
+    " np.array([ 1.72344537, -1.86560016, -1.04803039,  5.82272469]),\n",
+    " np.array([ 1.367794  , -1.5842915 , -7.11302751,  5.62617331]),\n",
+    " np.array([ 1.34280047, -1.42985981, -0.49987048,  3.08863373]),\n",
+    " np.array([ 1.44705705, -1.50587472,  2.08513161, -1.52029819]),\n",
+    " np.array([ 1.54391907, -1.58254265,  1.93724031, -1.53335868]),\n",
+    " np.array([ 1.51479801, -1.53731134, -0.58242123,  0.90462621]),\n",
+    " np.array([ 1.44800478, -1.46329318, -1.33586448,  1.48036335]),\n",
+    " np.array([ 1.40542619, -1.41846823, -0.85157192,  0.89649887]),\n",
+    " np.array([ 1.36151447, -1.37544602, -0.8782344 ,  0.86044414]),\n",
+    " np.array([ 1.29170425, -1.29740573, -1.39620442,  1.56080594]),\n",
+    " np.array([ 1.21684746, -1.2021926 , -1.49713579,  1.90426261]),\n",
+    " np.array([ 1.16579769, -1.13015334, -1.02099531,  1.44078521]),\n",
+    " np.array([ 1.18899947, -1.18593751,  0.4640355 , -1.11568352]),\n",
+    " np.array([ 1.18923678, -1.19305194,  0.00474629, -0.14228851]),\n",
+    " np.array([ 1.18450234, -1.19285596, -0.09468873,  0.00391948]),\n",
+    " np.array([ 1.16938901, -1.17758861, -0.30226665,  0.30534706]),\n",
+    " np.array([ 1.14860889, -1.1556876 , -0.41560239,  0.43802026]),\n",
+    " np.array([ 1.12381992, -1.12905946, -0.49577947,  0.53256269]),\n",
+    " np.array([ 1.09763939, -1.10139022, -0.5236106 ,  0.55338486]),\n",
+    " np.array([ 1.07129065, -1.07415824, -0.52697478,  0.54463952]),\n",
+    " np.array([ 1.04520189, -1.04775071, -0.52177524,  0.52815074]),\n",
+    " np.array([ 1.01925473, -1.02176134, -0.51894314,  0.51978733]),\n",
+    " np.array([ 0.99326029, -0.99576573, -0.51988888,  0.51991216]),\n",
+    " np.array([ 0.96713226, -0.96957085, -0.52256045,  0.52389762]),\n",
+    " np.array([ 0.94089059, -0.94318632, -0.52483347,  0.52769065]),\n",
+    " np.array([ 0.91460743, -0.91671151, -0.52566331,  0.52949614]),\n",
+    " np.array([ 0.88836448, -0.89025679, -0.52485899,  0.52909444]),\n",
+    " np.array([ 0.8622333 , -0.86391161, -0.52262358,  0.52690367]),\n",
+    " np.array([ 0.83627113, -0.83774103, -0.51924341,  0.52341162]),\n",
+    " np.array([ 0.81052314, -0.81179221, -0.51495979,  0.51897629]),\n",
+    " np.array([ 0.78502583, -0.7861013 , -0.50994604,  0.51381814]),\n",
+    " np.array([ 0.75980973, -0.76069794, -0.50432205,  0.50806732]),\n",
+    " np.array([ 0.73490108, -0.73560765, -0.49817305,  0.50180573]),\n",
+    " np.array([ 0.71032295, -0.71085309, -0.49156268,  0.49509113]),\n",
+    " np.array([ 0.68609592, -0.68645468, -0.48454062,  0.48796838]),\n",
+    " np.array([ 0.66223857, -0.66243097, -0.4771469 ,  0.48047417]),\n",
+    " np.array([ 0.63876784, -0.638799  , -0.46941458,  0.47263926]),\n",
+    " np.array([ 0.61569926, -0.61557451, -0.46137163,  0.46448992]),\n",
+    " np.array([ 0.59304714, -0.59277205, -0.45304233,  0.45604915]),\n",
+    " np.array([ 0.57082472, -0.57040516, -0.44444851,  0.44733776]),\n",
+    " np.array([ 0.5490442 , -0.5484864 , -0.43561042,  0.43837527]),\n",
+    " np.array([ 0.52771682, -0.52702737, -0.42654753,  0.42918064]),\n",
+    " np.array([ 0.50685287, -0.50603872, -0.41727905,  0.41977288]),\n",
+    " np.array([ 0.48646165, -0.48553015, -0.40782438,  0.41017143]),\n",
+    " np.array([ 0.46655148, -0.46551033, -0.39820344,  0.40039651]),\n",
+    " np.array([ 0.44712963, -0.44598686, -0.38843682,  0.39046924]),\n",
+    " np.array([ 0.42820234, -0.42696627, -0.37854593,  0.38041178]),\n",
+    " np.array([ 0.40977469, -0.40845391, -0.36855301,  0.37024729]),\n",
+    " np.array([ 0.39185063, -0.39045392, -0.35848111,  0.35999991]),\n",
+    " np.array([ 0.37443293, -0.37296918, -0.34835401,  0.34969464]),\n",
+    " np.array([ 0.35752313, -0.35600132, -0.33819611,  0.33935717]),\n",
+    " np.array([ 0.34112151, -0.33955064, -0.32803223,  0.32901368]),\n",
+    " np.array([ 0.32522714, -0.32361611, -0.31788744,  0.31869062]),\n",
+    " np.array([ 0.3098378 , -0.30819539, -0.30778687,  0.30841447]),\n",
+    " np.array([ 0.29495002, -0.29328481, -0.29775549,  0.29821151]),\n",
+    " np.array([ 0.28055913, -0.27887943, -0.28781785,  0.28810754]),\n",
+    " np.array([ 0.26665924, -0.26497305, -0.27799791,  0.27812764]),\n",
+    " np.array([ 0.2532433 , -0.25155825, -0.26831881,  0.26829597]),\n",
+    " np.array([ 0.24030316, -0.23862648, -0.25880271,  0.25863553]),\n",
+    " np.array([ 0.22782963, -0.22616808, -0.24947056,  0.249168  ]),\n",
+    " np.array([ 0.21581253, -0.2141724 , -0.240342  ,  0.23991356]),\n",
+    " np.array([ 0.20424077, -0.20262786, -0.23143524,  0.23089078]),\n",
+    " np.array([ 0.19310242, -0.19152203, -0.22276693,  0.22211657]),\n",
+    " np.array([ 0.18238482, -0.18084173, -0.21435216,  0.21360604]),\n",
+    " np.array([ 0.1720746 , -0.1705731 , -0.20620435,  0.20537255]),\n",
+    " np.array([ 0.16215783, -0.16070172, -0.1983353 ,  0.19742769]),\n",
+    " np.array([ 0.15262007, -0.15121265, -0.19075521,  0.18978131]),\n",
+    " np.array([ 0.14344644, -0.14209057, -0.18347268,  0.1824416 ]),\n",
+    " np.array([ 0.1346217 , -0.13331981, -0.17649481,  0.17541513]),\n",
+    " np.array([ 0.12613034, -0.12488446, -0.16982728,  0.16870702]),\n",
+    " np.array([ 0.11795661, -0.11676841, -0.16347443,  0.162321  ]),\n",
+    " np.array([ 0.11008464, -0.10895544, -0.1574394 ,  0.15625955]),\n",
+    " np.array([ 0.10249843, -0.10142923, -0.1517242 ,  0.15052409]),\n",
+    " np.array([ 0.09518194, -0.09417348, -0.14632985,  0.14511507]),\n",
+    " np.array([ 0.08811912, -0.08717187, -0.14125652,  0.14003219]),\n",
+    " np.array([ 0.08129394, -0.08040814, -0.13650357,  0.13527455]),\n",
+    " np.array([ 0.07469045, -0.0738661 , -0.13206966,  0.13084086]),\n",
+    " np.array([ 0.06829281, -0.06752961, -0.12795279,  0.12672967]),\n",
+    " np.array([ 0.0620853 , -0.06138263, -0.12415021,  0.12293963]),\n",
+    " np.array([ 0.05605239, -0.05540914, -0.12065827,  0.11946986]),\n",
+    " np.array([ 0.05017879, -0.04959312, -0.11747205,  0.11632045]),\n",
+    " np.array([ 0.04444955, -0.04391845, -0.11458473,  0.11349339]),\n",
+    " np.array([ 0.03885023, -0.03836872, -0.11198653,  0.11099465]),\n",
+    " np.array([ 0.03336706, -0.03292676, -0.10966334,  0.10883912]),\n",
+    " np.array([ 0.02798731, -0.02757362, -0.10759493,  0.10706279]),\n",
+    " np.array([ 0.02269973, -0.02228629, -0.10575156,  0.10574658]),\n",
+    " np.array([ 0.01749586, -0.01703493, -0.10407742,  0.10502727]),\n",
+    " np.array([ 0.01237456, -0.01178555, -0.10242597,  0.10498748]),\n",
+    " np.array([ 0.00735098, -0.00651136, -0.10047168,  0.10548388]),\n",
+    " np.array([ 0.00245966, -0.00117719, -0.09782643,  0.10668329]),\n",
+    " np.array([-0.00194355,  0.0032169 , -0.08806415,  0.08788188])]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 70,
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
-      "   0  8.22722e+02  1.53608e-07  2.85796e-11  1.00000e-09  1.00000e-09   1.0000     1\n",
-      "   1  7.82866e+02  1.64964e+07  1.64366e+03  1.00000e-09  1.00000e-09   0.1250     1\n",
-      "   2  7.74377e+02  1.59686e+07  1.55226e+03  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "   3  7.65439e+02  1.66619e+07  1.51114e+03  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "   4  7.46728e+02  1.71219e+07  1.47746e+03  1.00000e-09  1.00000e-09   0.0625     1\n",
-      "   5  6.73463e+02  1.67466e+07  1.42448e+03  1.00000e-09  1.00000e-09   0.1250     1\n",
-      "   6  5.15004e+02  1.34686e+07  1.34587e+03  1.00000e-09  1.00000e-09   0.2500     1\n",
-      "   7  2.06038e+02  1.11691e+07  9.69961e+02  1.00000e-09  1.00000e-09   0.5000     1\n",
-      "   8  2.00761e+02  4.14994e+06  4.06760e+02  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "   9  1.47211e+02  3.94685e+06  3.53679e+02  1.00000e-09  1.00000e-09   0.2500     1\n",
+      "   0  1.23861e-01  1.86586e+02  -1.56928e+06  1.00000e+02  1.00000e+02   0.0312     0\n",
+      "   1  2.87954e-01  1.72339e+03  -1.52928e+06  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "   2  5.39916e-01  3.56269e+03  -1.49132e+06  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "   3  8.96508e-01  7.01725e+03  -1.45873e+06  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "   4  1.37132e+00  1.33917e+04  -1.43153e+06  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "   5  1.96286e+00  2.45857e+04  -1.40971e+06  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "   6  2.63553e+00  4.20907e+04  -1.39320e+06  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "   7  3.31405e+00  6.44937e+04  -1.38188e+06  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "   8  4.61426e+00  8.64758e+04  -1.33121e+06  1.00000e+02  1.00000e+02   0.0312     0\n",
+      "   9  4.32704e+00  1.36846e+05  -1.46865e+06  1.00000e+02  1.00000e+02   0.0156     0\n",
       "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
-      "  10  1.45307e+02  3.07307e+06  2.93457e+02  1.00000e-09  1.00000e-09   0.0625     1\n",
-      "  11  1.43810e+02  2.95843e+06  2.80205e+02  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "  12  1.31407e+02  3.12254e+06  2.61558e+02  1.00000e-09  1.00000e-09   0.0625     1\n",
-      "  13  1.30515e+02  2.71872e+06  2.55405e+02  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "  14  1.18786e+02  2.87331e+06  2.45170e+02  1.00000e-09  1.00000e-09   0.0625     1\n",
-      "  15  1.06145e+02  2.56880e+06  2.14438e+02  1.00000e-09  1.00000e-09   0.0625     1\n",
-      "  16  9.25951e+01  2.37605e+06  1.97031e+02  1.00000e-09  1.00000e-09   0.2500     1\n",
-      "  17  8.30065e+01  2.11979e+06  1.83576e+02  1.00000e-09  1.00000e-09   0.2500     1\n",
-      "  18  8.16102e+01  1.74436e+06  1.63244e+02  1.00000e-09  1.00000e-09   0.0625     1\n",
-      "  19  3.81373e+01  8.63706e+06  1.59411e+02  1.00000e-09  1.00000e-09   0.5000     1\n",
+      "  10  4.17093e+00  1.36816e+05  -1.52823e+06  1.00000e+02  1.00000e+02   0.0078     0\n",
+      "  11  3.97099e+00  1.38023e+05  -1.47497e+06  1.00000e+02  1.00000e+02   0.0078     0\n",
+      "  12  3.95794e+00  1.43984e+05  -1.45162e+06  1.00000e+02  1.00000e+02   0.0078     0\n",
+      "  13  4.65072e+00  1.33650e+05  -1.44111e+06  1.00000e+02  1.00000e+02   0.0078     0\n",
+      "  14  4.76588e+00  1.58157e+05  -1.40792e+06  1.00000e+02  1.00000e+02   0.0078     0\n",
+      "  15  4.87966e+00  1.58820e+05  -1.36980e+06  1.00000e+02  1.00000e+02   0.0078     0\n",
+      "  16  5.09447e+00  1.59441e+05  -1.29127e+06  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "  17  5.54177e+00  1.61417e+05  -1.15753e+06  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "  18  5.81175e+00  1.71170e+05  -9.70149e+05  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "  19  5.98966e+00  1.74643e+05  -8.08422e+05  1.00000e+02  1.00000e+02   0.0156     0\n",
       "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
-      "  20  3.76670e+01  7.76821e+05  7.41861e+01  1.00000e-09  1.00000e-09   0.0625     1\n",
-      "  21  3.64285e+01  6.99766e+05  7.11054e+01  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  22  3.39374e+01  2.99123e+06  6.26298e+01  1.00000e-09  1.00000e-09   0.1250     1\n",
-      "  23  3.36298e+01  6.43193e+05  6.04564e+01  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "  24  3.33496e+01  6.69338e+05  5.79480e+01  1.00000e-09  1.00000e-09   0.0078     1\n",
-      "  25  3.14735e+01  1.10352e+06  5.58016e+01  1.00000e-09  1.00000e-09   0.0625     1\n",
-      "  26  3.12530e+01  6.91668e+05  4.73205e+01  1.00000e-09  1.00000e-09   0.0078     1\n",
-      "  27  2.78995e+01  1.67839e+06  4.56223e+01  1.00000e-09  1.00000e-09   0.2500     1\n",
-      "  28  2.72211e+01  6.11993e+05  4.80125e+01  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "  29  2.28130e+01  8.76072e+05  4.70907e+01  1.00000e-09  1.00000e-09   0.1250     1\n",
+      "  20  6.16152e+00  1.76037e+05  -6.72795e+05  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "  21  6.42863e+00  1.77806e+05  -5.61106e+05  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "  22  6.73548e+00  1.83311e+05  -4.69909e+05  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "  23  6.95229e+00  1.90390e+05  -3.94696e+05  1.00000e+02  1.00000e+02   0.0156     0\n",
+      "  24  7.31945e+00  1.94028e+05  -3.21455e+05  1.00000e+02  1.00000e+02   0.0312     0\n",
+      "  25  7.40508e+00  2.02550e+05  -2.29037e+05  1.00000e+02  1.00000e+02   0.0312     0\n",
+      "  26  7.63842e+00  2.02480e+05  -1.66189e+05  1.00000e+02  1.00000e+02   0.0312     0\n",
+      "  27  7.96976e+00  2.04366e+05  -1.23731e+05  1.00000e+02  1.00000e+02   0.0312     0\n",
+      "  28  8.23922e+00  2.10523e+05  -9.44868e+04  1.00000e+02  1.00000e+02   0.0312     0\n",
+      "  29  8.98672e+00  2.14750e+05  -6.88851e+04  1.00000e+02  1.00000e+02   0.0625     0\n",
       "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
-      "  30  2.25688e+01  5.26996e+05  2.87922e+01  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "  31  2.22231e+01  5.34503e+05  2.65264e+01  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  32  2.21574e+01  3.32318e+05  3.37833e+01  1.00000e-09  1.00000e-09   0.0078     1\n",
-      "  33  2.19798e+01  3.88303e+05  2.83477e+01  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  34  2.15549e+01  6.01611e+05  4.21262e+01  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  35  2.13188e+01  5.70678e+05  2.82849e+01  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  36  2.09601e+01  4.95414e+05  2.56437e+01  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  37  2.06580e+01  5.11630e+05  2.49112e+01  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  38  2.03268e+01  4.84106e+05  2.42919e+01  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  39  2.00539e+01  4.87820e+05  2.34225e+01  1.00000e-09  1.00000e-09   0.0312     1\n",
+      "  30  9.22857e+00  2.32228e+05  -4.50699e+04  1.00000e+02  1.00000e+02   0.0625     0\n",
+      "  31  9.39012e+00  2.33438e+05  -3.13395e+04  1.00000e+02  1.00000e+02   0.0625     0\n",
+      "  32  9.60129e+00  2.33613e+05  -1.97340e+04  1.00000e+02  1.00000e+02   0.1250     0\n",
+      "  33  9.61976e+00  2.33014e+05  -8.01319e+03  1.00000e+02  1.00000e+02   0.2500     0\n",
+      "  34  9.86093e+00  2.25240e+05  8.37669e-03  1.00000e+02  1.00000e+02   0.5000     0\n",
+      "  35  9.92731e+00  2.19184e+05  -9.94228e+02  1.00000e+02  1.00000e+02   0.2500     0\n",
+      "  36  9.76790e+00  2.16211e+05  7.23548e-03  1.00000e+02  1.00000e+02   0.5000     0\n",
+      "  37  9.79297e+00  2.02314e+05  1.26367e-01  1.00000e+02  1.00000e+02   0.5000     0\n",
+      "  38  9.75768e+00  1.93974e+05  1.17514e-01  1.00000e+02  1.00000e+02   0.5000     0\n",
+      "  39  9.71158e+00  1.85253e+05  1.12120e-01  1.00000e+02  1.00000e+02   0.5000     0\n",
       "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
-      "  40  1.98552e+01  4.55520e+05  2.32399e+01  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "  41  1.29691e+01  4.04156e+05  1.89734e+01  1.00000e-09  1.00000e-09   1.0000     1\n",
-      "  42  1.28452e+01  3.29528e+05  1.98127e+01  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "  43  1.26077e+01  3.40873e+05  1.86347e+01  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "  44  1.24248e+01  3.09126e+05  1.68829e+01  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "  45  1.21672e+01  2.77048e+05  1.51092e+01  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  46  1.19678e+01  1.54374e+05  9.19618e+00  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  47  1.14039e+01  7.31306e+04  4.50704e+00  1.00000e-09  1.00000e-09   0.2500     1\n",
-      "  48  1.13527e+01  2.32491e+05  1.85320e+01  1.00000e-09  1.00000e-09   0.0039     1\n",
-      "  49  1.12639e+01  1.00167e+05  6.47902e+00  1.00000e-09  1.00000e-09   0.0625     1\n",
+      "  40  9.66298e+00  1.76815e+05  1.07005e-01  1.00000e+02  1.00000e+02   0.5000     0\n",
+      "  41  9.61461e+00  1.68674e+05  1.02097e-01  1.00000e+02  1.00000e+02   0.5000     0\n",
+      "  42  9.56752e+00  1.60855e+05  9.74035e-02  1.00000e+02  1.00000e+02   0.5000     0\n",
+      "  43  9.47799e+00  1.53372e+05  1.74671e-01  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  44  9.39568e+00  1.39259e+05  8.44952e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  45  9.32081e+00  1.26418e+05  7.68473e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  46  9.25268e+00  1.14764e+05  6.99156e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  47  9.19065e+00  1.04188e+05  6.36339e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  48  9.13416e+00  9.45950e+04  5.79420e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  49  9.08269e+00  8.58949e+04  5.27850e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
       "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
-      "  50  1.12175e+01  1.58071e+05  5.61753e+00  1.00000e-09  1.00000e-09   0.0156     1\n",
-      "  51  1.11446e+01  9.74140e+04  3.05637e+00  1.00000e-09  1.00000e-09   0.0625     1\n",
-      "  52  1.10797e+01  6.36989e+04  3.71029e+00  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  53  1.08488e+01  5.33516e+04  1.88867e+00  1.00000e-09  1.00000e-09   0.2500     1\n",
-      "  54  1.07958e+01  9.80265e+04  5.78745e+00  1.00000e-09  1.00000e-09   0.0312     1\n",
-      "  55  1.07894e+01  1.98524e+04  1.63667e+00  1.00000e-09  1.00000e-09   0.0039     1\n",
-      "  56  1.07906e+01  1.95905e+04  1.61528e+00  1.00000e-08  1.00000e-08   0.0020     1\n",
-      "  57  1.07906e+01  1.95880e+04  1.61494e+00  1.00000e-07  1.00000e-07   0.0020     1\n",
-      "  58  1.07906e+01  1.95632e+04  1.61153e+00  1.00000e-06  1.00000e-06   0.0020     1\n",
-      "  59  1.07900e+01  1.93589e+04  1.58081e+00  1.00000e-05  1.00000e-05   0.0020     1\n",
+      "  50  9.03577e+00  7.80067e+04  4.81132e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  51  8.99296e+00  7.08562e+04  4.38813e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  52  8.95388e+00  6.43758e+04  4.00482e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  53  8.91818e+00  5.85038e+04  3.65766e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  54  8.88553e+00  5.31841e+04  3.34326e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  55  8.85566e+00  4.83657e+04  3.05855e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  56  8.82831e+00  4.40020e+04  2.80073e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  57  8.80322e+00  4.00507e+04  2.56728e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  58  8.78019e+00  3.64735e+04  2.35589e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  59  8.75903e+00  3.32353e+04  2.16450e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
       "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
-      "  60  1.07879e+01  1.90422e+04  1.42054e+00  1.00000e-04  1.00000e-04   0.0020     1\n",
-      "  61  1.02103e+01  2.98240e+04  1.10740e+00  1.00000e-05  1.00000e-05   1.0000     1\n",
-      "  62  1.01981e+01  8.72589e+04  4.89501e+00  1.00000e-05  1.00000e-05   0.0039     1\n",
-      "  63  1.01948e+01  7.21877e+04  4.09142e+00  1.00000e-05  1.00000e-05   0.0078     1\n",
-      "  64  1.01577e+01  4.55547e+04  2.65963e+00  1.00000e-05  1.00000e-05   0.0312     1\n",
-      "  65  1.01547e+01  4.53278e+03  3.03044e-01  1.00000e-05  1.00000e-05   0.0156     1\n",
-      "  66  1.00715e+01  4.45681e+03  2.69529e-01  1.00000e-06  1.00000e-06   1.0000     1\n",
-      "  67  1.00615e+01  4.86969e+04  3.84934e+00  1.00000e-06  1.00000e-06   0.0039     1\n",
-      "  68  1.00290e+01  3.87853e+04  3.45709e+00  1.00000e-06  1.00000e-06   0.0312     1\n",
-      "  69  1.00273e+01  8.13921e+03  5.75614e-01  1.00000e-06  1.00000e-06   0.0156     1\n",
+      "  60  8.73955e+00  3.03045e+04  1.99122e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  61  8.72160e+00  2.76522e+04  1.83433e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  62  8.70503e+00  2.52524e+04  1.69229e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  63  8.68972e+00  2.30811e+04  1.56369e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  64  8.67554e+00  2.11170e+04  1.44726e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  65  8.66239e+00  1.93405e+04  1.34186e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  66  8.65016e+00  1.77339e+04  1.24643e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  67  8.63878e+00  1.62811e+04  1.16003e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  68  8.62816e+00  1.49675e+04  1.08182e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  69  8.61823e+00  1.37799e+04  1.01100e-02  1.00000e+01  1.00000e+01   1.0000     1\n",
       "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
-      "  70  9.90109e+00  6.61931e+03  4.95109e-01  1.00000e-06  1.00000e-06   0.5000     1\n",
-      "  71  9.87496e+00  3.85419e+04  2.16375e+00  1.00000e-06  1.00000e-06   0.0312     1\n",
-      "  72  9.85083e+00  1.04511e+04  7.01008e-01  1.00000e-06  1.00000e-06   0.0625     1\n",
-      "  73  9.83419e+00  1.65326e+04  9.76490e-01  1.00000e-06  1.00000e-06   0.0312     1\n",
-      "  74  9.81900e+00  7.15274e+03  5.06347e-01  1.00000e-06  1.00000e-06   0.1250     1\n",
-      "  75  9.79734e+00  3.63683e+04  2.22425e+00  1.00000e-06  1.00000e-06   0.0312     1\n",
-      "  76  9.79187e+00  6.94897e+03  4.35140e-01  1.00000e-06  1.00000e-06   0.0625     1\n",
-      "  77  9.78163e+00  1.49202e+04  8.83738e-01  1.00000e-06  1.00000e-06   0.0312     1\n",
-      "  78  9.77308e+00  5.07870e+03  3.13076e-01  1.00000e-06  1.00000e-06   0.0625     1\n",
-      "  79  9.76524e+00  9.18986e+03  5.38885e-01  1.00000e-06  1.00000e-06   0.0312     1\n",
+      "  70  8.60893e+00  1.27065e+04  9.46882e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  71  8.60019e+00  1.17363e+04  8.88830e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  72  8.59196e+00  1.08595e+04  8.36267e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  73  8.58420e+00  1.00673e+04  7.88673e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  74  8.57686e+00  9.35153e+03  7.45576e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  75  8.56989e+00  8.70497e+03  7.06549e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  76  8.56327e+00  8.12098e+03  6.71206e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  77  8.55697e+00  7.59359e+03  6.39197e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  78  8.55094e+00  7.11738e+03  6.10205e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  79  8.54518e+00  6.68745e+03  5.83945e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
       "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
-      "  80  9.75879e+00  4.07717e+03  2.47685e-01  1.00000e-06  1.00000e-06   0.1250     1\n",
-      "  81  9.74569e+00  2.27846e+04  1.39813e+00  1.00000e-06  1.00000e-06   0.0156     1\n",
-      "  82  9.74030e+00  5.15182e+03  2.97725e-01  1.00000e-06  1.00000e-06   0.0625     1\n",
-      "  83  9.73264e+00  9.41877e+03  5.59391e-01  1.00000e-06  1.00000e-06   0.0312     1\n",
-      "  84  9.72719e+00  3.69964e+03  2.10082e-01  1.00000e-06  1.00000e-06   0.1250     1\n",
-      "  85  9.71550e+00  1.88164e+04  1.09219e+00  1.00000e-06  1.00000e-06   0.0312     1\n",
-      "  86  9.70972e+00  4.11346e+03  2.28018e-01  1.00000e-06  1.00000e-06   0.0625     1\n",
-      "  87  9.70378e+00  6.68727e+03  3.92024e-01  1.00000e-06  1.00000e-06   0.0312     1\n",
-      "  88  9.69636e+00  3.09346e+03  1.70084e-01  1.00000e-06  1.00000e-06   0.1250     1\n",
-      "  89  9.68786e+00  1.31137e+04  7.60712e-01  1.00000e-06  1.00000e-06   0.0312     1\n"
+      "  80  8.53964e+00  6.29936e+03  5.60156e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  81  8.53431e+00  5.94911e+03  5.38604e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  82  8.52918e+00  5.63305e+03  5.19075e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  83  8.52421e+00  5.34789e+03  5.01379e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  84  8.51941e+00  5.09067e+03  4.85341e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  85  8.51474e+00  4.85868e+03  4.70803e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  86  8.51020e+00  4.64950e+03  4.57623e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  87  8.50578e+00  4.46091e+03  4.45672e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  88  8.50147e+00  4.29093e+03  4.34832e-03  1.00000e+01  1.00000e+01   1.0000     1\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "  89  8.49725e+00  4.13776e+03  4.24999e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
+      "  90  8.49312e+00  3.99976e+03  4.16077e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  91  8.48907e+00  3.87546e+03  4.07979e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  92  8.48508e+00  3.76352e+03  4.00626e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  93  8.48117e+00  3.66274e+03  3.93949e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  94  8.47731e+00  3.57204e+03  3.87882e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  95  8.47351e+00  3.49042e+03  3.82368e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  96  8.46975e+00  3.41700e+03  3.77354e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  97  8.46604e+00  3.35096e+03  3.72793e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  98  8.46238e+00  3.29159e+03  3.68642e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "  99  8.45874e+00  3.23822e+03  3.64861e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
+      " 100  8.45514e+00  3.19026e+03  3.61416e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 101  8.45158e+00  3.14717e+03  3.58274e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 102  8.44804e+00  3.10847e+03  3.55407e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 103  8.44452e+00  3.07371e+03  3.52789e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 104  8.44103e+00  3.04251e+03  3.50396e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 105  8.43756e+00  3.01451e+03  3.48207e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 106  8.43411e+00  2.98938e+03  3.46202e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 107  8.43068e+00  2.96682e+03  3.44363e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 108  8.42726e+00  2.94659e+03  3.42676e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 109  8.42386e+00  2.92843e+03  3.41125e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
       "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
-      "  90  9.68266e+00  3.39338e+03  1.86600e-01  1.00000e-06  1.00000e-06   0.0625     1\n",
-      "  91  9.67773e+00  5.36183e+03  3.10928e-01  1.00000e-06  1.00000e-06   0.0312     1\n",
-      "  92  9.66189e+00  2.90718e+03  1.72239e-01  1.00000e-06  1.00000e-06   0.2500     1\n",
-      "  93  9.64225e+00  2.91833e+04  1.69669e+00  1.00000e-06  1.00000e-06   0.0312     1\n",
-      "  94  9.63974e+00  3.81247e+03  2.09775e-01  1.00000e-06  1.00000e-06   0.0625     1\n",
-      "  95  9.63921e+00  7.92591e+03  4.91333e-01  1.00000e-05  1.00000e-05   0.0020     1\n",
-      "  96  9.63659e+00  6.15321e+03  3.70180e-01  1.00000e-05  1.00000e-05   0.0078     1\n",
-      "  97  9.63661e+00  4.43899e+03  2.76598e-01  1.00000e-04  1.00000e-04   0.0020     1\n",
-      "  98  9.63637e+00  3.23573e+03  1.68842e-01  1.00000e-03  1.00000e-03   0.0020     1\n",
-      "  99  9.60595e+00  2.74333e+03  5.91110e-02  1.00000e-04  1.00000e-04   1.0000     1\n"
+      " 110  8.42047e+00  2.91214e+03  3.39698e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 111  8.41710e+00  2.89752e+03  3.38383e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 112  8.41374e+00  2.88439e+03  3.37170e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 113  8.41039e+00  2.87260e+03  3.36048e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 114  8.40705e+00  2.86201e+03  3.35009e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 115  8.40372e+00  2.85249e+03  3.34045e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 116  8.40039e+00  2.84391e+03  3.33149e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 117  8.39708e+00  2.83619e+03  3.32315e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 118  8.39377e+00  2.82922e+03  3.31536e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 119  8.39047e+00  2.82292e+03  3.30808e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
+      " 120  8.38718e+00  2.81721e+03  3.30125e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 121  8.38389e+00  2.81202e+03  3.29484e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 122  8.38061e+00  2.80730e+03  3.28881e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 123  8.37734e+00  2.80298e+03  3.28311e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 124  8.37407e+00  2.79902e+03  3.27772e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 125  8.37080e+00  2.79538e+03  3.27261e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 126  8.36754e+00  2.79200e+03  3.26774e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 127  8.36429e+00  2.78886e+03  3.26311e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 128  8.36104e+00  2.78593e+03  3.25868e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 129  8.35779e+00  2.78316e+03  3.25445e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
+      " 130  8.35455e+00  2.78055e+03  3.25038e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 131  8.35131e+00  2.77806e+03  3.24646e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 132  8.34807e+00  2.77567e+03  3.24268e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 133  8.34484e+00  2.77337e+03  3.23903e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 134  8.34161e+00  2.77113e+03  3.23549e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 135  8.33839e+00  2.76895e+03  3.23206e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 136  8.33517e+00  2.76681e+03  3.22872e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 137  8.33195e+00  2.76470e+03  3.22547e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 138  8.32873e+00  2.76261e+03  3.22229e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 139  8.32552e+00  2.76052e+03  3.21918e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
+      " 140  8.32231e+00  2.75844e+03  3.21614e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 141  8.31911e+00  2.75635e+03  3.21315e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 142  8.31590e+00  2.75425e+03  3.21022e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 143  8.31270e+00  2.75213e+03  3.20733e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 144  8.30951e+00  2.74999e+03  3.20449e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 145  8.30631e+00  2.74782e+03  3.20169e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 146  8.30312e+00  2.74562e+03  3.19892e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 147  8.29993e+00  2.74339e+03  3.19618e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 148  8.29674e+00  2.74112e+03  3.19348e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 149  8.29356e+00  2.73882e+03  3.19080e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
+      " 150  8.29038e+00  2.73648e+03  3.18815e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 151  8.28720e+00  2.73409e+03  3.18552e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 152  8.28402e+00  2.73167e+03  3.18290e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 153  8.28085e+00  2.72920e+03  3.18031e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 154  8.27768e+00  2.72669e+03  3.17774e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 155  8.27451e+00  2.72413e+03  3.17518e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 156  8.27134e+00  2.72153e+03  3.17263e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 157  8.26818e+00  2.71889e+03  3.17010e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 158  8.26502e+00  2.71620e+03  3.16758e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 159  8.26186e+00  2.71347e+03  3.16507e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
+      " 160  8.25871e+00  2.71070e+03  3.16257e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 161  8.25555e+00  2.70788e+03  3.16008e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 162  8.25240e+00  2.70503e+03  3.15760e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 163  8.24925e+00  2.70213e+03  3.15512e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 164  8.24611e+00  2.69919e+03  3.15266e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 165  8.24296e+00  2.69621e+03  3.15020e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 166  8.23982e+00  2.69319e+03  3.14774e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 167  8.23669e+00  2.69013e+03  3.14530e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 168  8.23355e+00  2.68704e+03  3.14285e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 169  8.23042e+00  2.68391e+03  3.14042e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
+      " 170  8.22728e+00  2.68075e+03  3.13799e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 171  8.22415e+00  2.67755e+03  3.13556e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 172  8.22103e+00  2.67431e+03  3.13313e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 173  8.21790e+00  2.67105e+03  3.13071e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 174  8.21478e+00  2.66775e+03  3.12830e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 175  8.21166e+00  2.66442e+03  3.12589e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 176  8.20855e+00  2.66107e+03  3.12348e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 177  8.20543e+00  2.65768e+03  3.12107e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 178  8.20232e+00  2.65427e+03  3.11867e-03  1.00000e+01  1.00000e+01   1.0000     1\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      " 179  8.19921e+00  2.65083e+03  3.11627e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
+      " 180  8.19610e+00  2.64737e+03  3.11387e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 181  8.19300e+00  2.64388e+03  3.11148e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 182  8.18989e+00  2.64037e+03  3.10909e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 183  8.18679e+00  2.63683e+03  3.10670e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 184  8.18370e+00  2.63328e+03  3.10431e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 185  8.18060e+00  2.62970e+03  3.10193e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 186  8.17751e+00  2.62611e+03  3.09954e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 187  8.17442e+00  2.62249e+03  3.09716e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 188  8.17133e+00  2.61886e+03  3.09479e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 189  8.16824e+00  2.61521e+03  3.09241e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      "iter \t cost \t      stop \t    grad \t  xreg \t      ureg \t step \t feas\n",
+      " 190  8.16516e+00  2.61155e+03  3.09004e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 191  8.16208e+00  2.60787e+03  3.08766e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 192  8.15900e+00  2.60418e+03  3.08529e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 193  8.15592e+00  2.60047e+03  3.08292e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 194  8.15285e+00  2.59675e+03  3.08056e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 195  8.14978e+00  2.59302e+03  3.07819e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 196  8.14671e+00  2.58927e+03  3.07583e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 197  8.14364e+00  2.58552e+03  3.07347e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 198  8.14057e+00  2.58176e+03  3.07111e-03  1.00000e+01  1.00000e+01   1.0000     1\n",
+      " 199  8.13751e+00  2.57798e+03  3.06875e-03  1.00000e+01  1.00000e+01   1.0000     1\n"
      ]
     },
     {
      "data": {
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-       "  array([-0.06500669,  0.05565112,  0.53261783, -1.81064785]),\n",
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-       "  array([-0.02777722,  0.02583974, -0.05883449, -0.41103367]),\n",
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-       "  array([-0.02599902,  0.02627106,  0.12426707, -0.10460939]),\n",
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-       "  array([-1.24294444e-03, -5.58053665e-03,  3.76727050e-01, -1.85384633e+00]),\n",
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-       "  array([ 0.00106432, -0.00022673, -0.04411862,  0.01773411]),\n",
-       "  array([ 6.60498153e-04, -5.22579516e-05, -4.03820501e-02,  1.74473308e-02]),\n",
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-       "  array([ 7.63120643e-05, -1.21393142e-07, -2.43466316e-02, -2.70744739e-02])],\n",
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-       "  array([ 0.00505131, -0.02061498]),\n",
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-       "  array([ 0.00410653, -0.01100935]),\n",
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-       "  array([ 0.00327164, -0.01583679]),\n",
-       "  array([0.00374192, 0.01572243]),\n",
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-       "  array([0.00277776, 0.00637701]),\n",
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-       "  array([0.00261952, 0.0031665 ]),\n",
-       "  array([0.00247602, 0.00309112]),\n",
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-       "  array([0.00204913, 0.00250989]),\n",
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-       "  array([ 0.00181241, -0.00136566]),\n",
-       "  array([ 0.0017519 , -0.00164286]),\n",
-       "  array([ 0.00168072, -0.00166064]),\n",
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-       "  array([ 0.00148501, -0.00133774]),\n",
-       "  array([ 0.00143259, -0.00124103]),\n",
-       "  array([ 0.00138695, -0.00118182]),\n",
-       "  array([ 0.00134574, -0.00112911]),\n",
-       "  array([ 0.00131417, -0.00118104]),\n",
-       "  array([0.00127332, 0.00098092]),\n",
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-       "  array([0.00121884, 0.00077885]),\n",
-       "  array([ 0.00119889, -0.00104467]),\n",
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-       "  array([ 0.00115702, -0.00025267]),\n",
-       "  array([0.00114045, 0.00026378]),\n",
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-       "  array([1.00017228e-03, 2.74865484e-05]),\n",
-       "  array([1.00016177e-03, 3.01461957e-05]),\n",
-       "  array([1.00018110e-03, 3.03899067e-05]),\n",
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-       "  array([1.00031215e-03, 3.32925301e-05]),\n",
-       "  array([1.00042553e-03, 3.71435397e-05]),\n",
-       "  array([1.00057211e-03, 3.42757779e-05]),\n",
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-       "  array([-9.99948052e-04, -3.98666926e-05]),\n",
-       "  array([-8.34998757e-04, -3.83462283e-05]),\n",
-       "  array([-4.33343683e-04, -2.03126144e-05]),\n",
-       "  array([-1.24132527e-04, -4.99066334e-06]),\n",
-       "  array([3.75674851e-05, 2.82131419e-06]),\n",
-       "  array([9.45901732e-05, 9.20707568e-06]),\n",
-       "  array([ 8.03317879e-05, -6.59839394e-06])],\n",
+       "([array([3.14, 0.  , 0.  , 0.  ]),\n",
+       "  array([  3.71059542,  -2.05541894,  11.41190835, -41.10837881]),\n",
+       "  array([  3.76668242,  -2.83395101,   1.12174006, -15.5706414 ]),\n",
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+       "  array([ 3.71635446, -3.12552479, -3.48419748, -2.57923624]),\n",
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+       "  array([  2.92679904,  -2.97209156, -11.95299728,  -0.92496958]),\n",
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+       "  array([ 1.51479801, -1.53731134, -0.58242123,  0.90462621]),\n",
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+       "  array([ 1.40542619, -1.41846823, -0.85157192,  0.89649887]),\n",
+       "  array([ 1.36151447, -1.37544602, -0.8782344 ,  0.86044414]),\n",
+       "  array([ 1.29170425, -1.29740573, -1.39620442,  1.56080594]),\n",
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+       "  array([ 1.18923678, -1.19305194,  0.00474629, -0.14228851]),\n",
+       "  array([ 1.18450234, -1.19285596, -0.09468873,  0.00391948]),\n",
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+       "  array([ 0.71032295, -0.71085309, -0.49156268,  0.49509113]),\n",
+       "  array([ 0.68609592, -0.68645468, -0.48454062,  0.48796838]),\n",
+       "  array([ 0.66223857, -0.66243097, -0.4771469 ,  0.48047417]),\n",
+       "  array([ 0.63876784, -0.638799  , -0.46941458,  0.47263926]),\n",
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+       "  array([ 0.59304714, -0.59277205, -0.45304233,  0.45604915]),\n",
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+       "  array([ 0.52771682, -0.52702737, -0.42654753,  0.42918064]),\n",
+       "  array([ 0.50685287, -0.50603872, -0.41727905,  0.41977288]),\n",
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+       "  array([ 0.46655148, -0.46551033, -0.39820344,  0.40039651]),\n",
+       "  array([ 0.44712963, -0.44598686, -0.38843682,  0.39046924]),\n",
+       "  array([ 0.42820234, -0.42696627, -0.37854593,  0.38041178]),\n",
+       "  array([ 0.40977469, -0.40845391, -0.36855301,  0.37024729]),\n",
+       "  array([ 0.39185063, -0.39045392, -0.35848111,  0.35999991]),\n",
+       "  array([ 0.37443293, -0.37296918, -0.34835401,  0.34969464]),\n",
+       "  array([ 0.35752313, -0.35600132, -0.33819611,  0.33935717]),\n",
+       "  array([ 0.34112151, -0.33955064, -0.32803223,  0.32901368]),\n",
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+       "  array([ 0.3098378 , -0.30819539, -0.30778687,  0.30841447]),\n",
+       "  array([ 0.29495002, -0.29328481, -0.29775549,  0.29821151]),\n",
+       "  array([ 0.28055913, -0.27887943, -0.28781785,  0.28810754]),\n",
+       "  array([ 0.26665924, -0.26497305, -0.27799791,  0.27812764]),\n",
+       "  array([ 0.2532433 , -0.25155825, -0.26831881,  0.26829597]),\n",
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+       "  array([ 0.21581253, -0.2141724 , -0.240342  ,  0.23991356]),\n",
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+       "  array([ 0.15262007, -0.15121265, -0.19075521,  0.18978131]),\n",
+       "  array([ 0.14344644, -0.14209057, -0.18347268,  0.1824416 ]),\n",
+       "  array([ 0.1346217 , -0.13331981, -0.17649481,  0.17541513]),\n",
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+       "  array([ 0.09518194, -0.09417348, -0.14632985,  0.14511507]),\n",
+       "  array([ 0.08811912, -0.08717187, -0.14125652,  0.14003219]),\n",
+       "  array([ 0.08129394, -0.08040814, -0.13650357,  0.13527455]),\n",
+       "  array([ 0.07469045, -0.0738661 , -0.13206966,  0.13084086]),\n",
+       "  array([ 0.06829281, -0.06752961, -0.12795279,  0.12672967]),\n",
+       "  array([ 0.0620853 , -0.06138263, -0.12415021,  0.12293963]),\n",
+       "  array([ 0.05605239, -0.05540914, -0.12065827,  0.11946986]),\n",
+       "  array([ 0.05017879, -0.04959312, -0.11747205,  0.11632045]),\n",
+       "  array([ 0.04444955, -0.04391845, -0.11458473,  0.11349339]),\n",
+       "  array([ 0.03885023, -0.03836872, -0.11198653,  0.11099465]),\n",
+       "  array([ 0.03336706, -0.03292676, -0.10966334,  0.10883912]),\n",
+       "  array([ 0.02798731, -0.02757362, -0.10759493,  0.10706279]),\n",
+       "  array([ 0.02269973, -0.02228629, -0.10575156,  0.10574658]),\n",
+       "  array([ 0.01749586, -0.01703493, -0.10407742,  0.10502727]),\n",
+       "  array([ 0.01237456, -0.01178555, -0.10242597,  0.10498748]),\n",
+       "  array([ 0.00735098, -0.00651136, -0.10047168,  0.10548388]),\n",
+       "  array([ 0.00245966, -0.00117719, -0.09782643,  0.10668329]),\n",
+       "  array([-0.00194355,  0.0032169 , -0.08806415,  0.08788188])],\n",
+       " [array([0.4866609]),\n",
+       "  array([-0.16534915]),\n",
+       "  array([0.19685077]),\n",
+       "  array([-0.13141714]),\n",
+       "  array([0.09778713]),\n",
+       "  array([-0.31548976]),\n",
+       "  array([-0.0881419]),\n",
+       "  array([-0.05118947]),\n",
+       "  array([-0.09959294]),\n",
+       "  array([-0.16997898]),\n",
+       "  array([-0.80757709]),\n",
+       "  array([0.13825521]),\n",
+       "  array([-0.17131604]),\n",
+       "  array([-0.39017407]),\n",
+       "  array([-0.57631949]),\n",
+       "  array([-0.4394058]),\n",
+       "  array([-0.34153197]),\n",
+       "  array([-0.37870836]),\n",
+       "  array([-0.41298379]),\n",
+       "  array([-0.37387454]),\n",
+       "  array([-0.32108156]),\n",
+       "  array([-0.24198414]),\n",
+       "  array([-0.38692992]),\n",
+       "  array([-0.36172493]),\n",
+       "  array([-0.36918615]),\n",
+       "  array([-0.36005173]),\n",
+       "  array([-0.35433378]),\n",
+       "  array([-0.34641826]),\n",
+       "  array([-0.34012226]),\n",
+       "  array([-0.33475816]),\n",
+       "  array([-0.33002287]),\n",
+       "  array([-0.32520387]),\n",
+       "  array([-0.32001327]),\n",
+       "  array([-0.31442664]),\n",
+       "  array([-0.3085249]),\n",
+       "  array([-0.30238686]),\n",
+       "  array([-0.29606381]),\n",
+       "  array([-0.28958512]),\n",
+       "  array([-0.28296947]),\n",
+       "  array([-0.27623222]),\n",
+       "  array([-0.26938846]),\n",
+       "  array([-0.26245374]),\n",
+       "  array([-0.2554439]),\n",
+       "  array([-0.24837482]),\n",
+       "  array([-0.24126222]),\n",
+       "  array([-0.23412157]),\n",
+       "  array([-0.22696801]),\n",
+       "  array([-0.21981632]),\n",
+       "  array([-0.21268086]),\n",
+       "  array([-0.20557555]),\n",
+       "  array([-0.19851381]),\n",
+       "  array([-0.19150853]),\n",
+       "  array([-0.184572]),\n",
+       "  array([-0.17771589]),\n",
+       "  array([-0.17095119]),\n",
+       "  array([-0.16428818]),\n",
+       "  array([-0.15773637]),\n",
+       "  array([-0.15130451]),\n",
+       "  array([-0.14500052]),\n",
+       "  array([-0.13883148]),\n",
+       "  array([-0.13280362]),\n",
+       "  array([-0.12692232]),\n",
+       "  array([-0.12119208]),\n",
+       "  array([-0.11561656]),\n",
+       "  array([-0.11019856]),\n",
+       "  array([-0.10494009]),\n",
+       "  array([-0.09984231]),\n",
+       "  array([-0.09490565]),\n",
+       "  array([-0.09012982]),\n",
+       "  array([-0.08551381]),\n",
+       "  array([-0.08105598]),\n",
+       "  array([-0.0767541]),\n",
+       "  array([-0.0726054]),\n",
+       "  array([-0.06860661]),\n",
+       "  array([-0.06475399]),\n",
+       "  array([-0.06104345]),\n",
+       "  array([-0.05747052]),\n",
+       "  array([-0.05403043]),\n",
+       "  array([-0.05071818]),\n",
+       "  array([-0.04752854]),\n",
+       "  array([-0.0444561]),\n",
+       "  array([-0.04149531]),\n",
+       "  array([-0.03864052]),\n",
+       "  array([-0.035886]),\n",
+       "  array([-0.03322594]),\n",
+       "  array([-0.03065453]),\n",
+       "  array([-0.0281659]),\n",
+       "  array([-0.02575419]),\n",
+       "  array([-0.02341353]),\n",
+       "  array([-0.02113806]),\n",
+       "  array([-0.0189219]),\n",
+       "  array([-0.01675918]),\n",
+       "  array([-0.01464397]),\n",
+       "  array([-0.0125703]),\n",
+       "  array([-0.01053193]),\n",
+       "  array([-0.00852156]),\n",
+       "  array([-0.00652851]),\n",
+       "  array([-0.00453919]),\n",
+       "  array([-0.00254965]),\n",
+       "  array([-0.00030361])],\n",
        " False)"
       ]
      },
-     "execution_count": 112,
+     "execution_count": 70,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "runningModel = IntegratedActionModelEuler(DifferentialActionModelFullyActuated(robot.model, runningCostModel))\n",
-    "terminalModel = IntegratedActionModelEuler(DifferentialActionModelFullyActuated(robot.model, terminalCostModel))\n",
-    "\n",
-    "# Defining the time duration for running action models and the terminal one\n",
-    "dt = 1e-2\n",
-    "runningModel.timeStep = dt\n",
-    "\n",
-    "# For this optimal control problem, we define 250 knots (or running action\n",
-    "# models) plus a terminal knot\n",
-    "T = 100\n",
-    "q0 = [-1.57, 2]\n",
-    "x0 = np.hstack([q0, np.zeros(robot.model.nv)])\n",
-    "problem = ShootingProblem(x0, [runningModel] * T, terminalModel)\n",
-    "\n",
     "# Creating the DDP solver for this OC problem, defining a logger\n",
-    "ddp = SolverDDP(problem)\n",
+    "ddp = SolverFDDP(problem)\n",
     "ddp.callback = [CallbackDDPVerbose()]\n",
     "ddp.callback.append(CallbackDDPLogger())\n",
     "\n",
@@ -444,133 +4763,184 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 108,
+   "execution_count": 71,
    "metadata": {},
    "outputs": [],
    "source": [
-    "from crocoddyl.diagnostic import displayTrajectory\n",
-    "\n",
     "displayTrajectory(robot, ddp.xs, runningModel.timeStep)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 109,
+   "execution_count": 72,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[array([3.14, 0.  , 0.  , 0.  ]),\n",
+       " array([  3.71059542,  -2.05541894,  11.41190835, -41.10837881]),\n",
+       " array([  3.76668242,  -2.83395101,   1.12174006, -15.5706414 ]),\n",
+       " array([ 3.89056434, -2.99656298,  2.47763835, -3.25223937]),\n",
+       " array([ 3.71635446, -3.12552479, -3.48419748, -2.57923624]),\n",
+       " array([ 3.5244489 , -2.92584309, -3.83811128,  3.99363411]),\n",
+       " array([  2.92679904,  -2.97209156, -11.95299728,  -0.92496958]),\n",
+       " array([  2.338523  ,  -2.87566759, -11.76552081,   1.92847956]),\n",
+       " array([ 1.95375756, -2.56138768, -7.69530875,  6.28559803]),\n",
+       " array([ 1.77584689, -2.1567364 , -3.55821333,  8.09302574]),\n",
+       " array([ 1.72344537, -1.86560016, -1.04803039,  5.82272469]),\n",
+       " array([ 1.367794  , -1.5842915 , -7.11302751,  5.62617331]),\n",
+       " array([ 1.34280047, -1.42985981, -0.49987048,  3.08863373]),\n",
+       " array([ 1.44705705, -1.50587472,  2.08513161, -1.52029819]),\n",
+       " array([ 1.54391907, -1.58254265,  1.93724031, -1.53335868]),\n",
+       " array([ 1.51479801, -1.53731134, -0.58242123,  0.90462621]),\n",
+       " array([ 1.44800478, -1.46329318, -1.33586448,  1.48036335]),\n",
+       " array([ 1.40542619, -1.41846823, -0.85157192,  0.89649887]),\n",
+       " array([ 1.36151447, -1.37544602, -0.8782344 ,  0.86044414]),\n",
+       " array([ 1.29170425, -1.29740573, -1.39620442,  1.56080594]),\n",
+       " array([ 1.21684746, -1.2021926 , -1.49713579,  1.90426261]),\n",
+       " array([ 1.16579769, -1.13015334, -1.02099531,  1.44078521]),\n",
+       " array([ 1.18899947, -1.18593751,  0.4640355 , -1.11568352]),\n",
+       " array([ 1.18923678, -1.19305194,  0.00474629, -0.14228851]),\n",
+       " array([ 1.18450234, -1.19285596, -0.09468873,  0.00391948]),\n",
+       " array([ 1.16938901, -1.17758861, -0.30226665,  0.30534706]),\n",
+       " array([ 1.14860889, -1.1556876 , -0.41560239,  0.43802026]),\n",
+       " array([ 1.12381992, -1.12905946, -0.49577947,  0.53256269]),\n",
+       " array([ 1.09763939, -1.10139022, -0.5236106 ,  0.55338486]),\n",
+       " array([ 1.07129065, -1.07415824, -0.52697478,  0.54463952]),\n",
+       " array([ 1.04520189, -1.04775071, -0.52177524,  0.52815074]),\n",
+       " array([ 1.01925473, -1.02176134, -0.51894314,  0.51978733]),\n",
+       " array([ 0.99326029, -0.99576573, -0.51988888,  0.51991216]),\n",
+       " array([ 0.96713226, -0.96957085, -0.52256045,  0.52389762]),\n",
+       " array([ 0.94089059, -0.94318632, -0.52483347,  0.52769065]),\n",
+       " array([ 0.91460743, -0.91671151, -0.52566331,  0.52949614]),\n",
+       " array([ 0.88836448, -0.89025679, -0.52485899,  0.52909444]),\n",
+       " array([ 0.8622333 , -0.86391161, -0.52262358,  0.52690367]),\n",
+       " array([ 0.83627113, -0.83774103, -0.51924341,  0.52341162]),\n",
+       " array([ 0.81052314, -0.81179221, -0.51495979,  0.51897629]),\n",
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+       " array([ 0.63876784, -0.638799  , -0.46941458,  0.47263926]),\n",
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+       " array([ 0.44712963, -0.44598686, -0.38843682,  0.39046924]),\n",
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+       " array([ 0.3098378 , -0.30819539, -0.30778687,  0.30841447]),\n",
+       " array([ 0.29495002, -0.29328481, -0.29775549,  0.29821151]),\n",
+       " array([ 0.28055913, -0.27887943, -0.28781785,  0.28810754]),\n",
+       " array([ 0.26665924, -0.26497305, -0.27799791,  0.27812764]),\n",
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+       " array([ 0.22782963, -0.22616808, -0.24947056,  0.249168  ]),\n",
+       " array([ 0.21581253, -0.2141724 , -0.240342  ,  0.23991356]),\n",
+       " array([ 0.20424077, -0.20262786, -0.23143524,  0.23089078]),\n",
+       " array([ 0.19310242, -0.19152203, -0.22276693,  0.22211657]),\n",
+       " array([ 0.18238482, -0.18084173, -0.21435216,  0.21360604]),\n",
+       " array([ 0.1720746 , -0.1705731 , -0.20620435,  0.20537255]),\n",
+       " array([ 0.16215783, -0.16070172, -0.1983353 ,  0.19742769]),\n",
+       " array([ 0.15262007, -0.15121265, -0.19075521,  0.18978131]),\n",
+       " array([ 0.14344644, -0.14209057, -0.18347268,  0.1824416 ]),\n",
+       " array([ 0.1346217 , -0.13331981, -0.17649481,  0.17541513]),\n",
+       " array([ 0.12613034, -0.12488446, -0.16982728,  0.16870702]),\n",
+       " array([ 0.11795661, -0.11676841, -0.16347443,  0.162321  ]),\n",
+       " array([ 0.11008464, -0.10895544, -0.1574394 ,  0.15625955]),\n",
+       " array([ 0.10249843, -0.10142923, -0.1517242 ,  0.15052409]),\n",
+       " array([ 0.09518194, -0.09417348, -0.14632985,  0.14511507]),\n",
+       " array([ 0.08811912, -0.08717187, -0.14125652,  0.14003219]),\n",
+       " array([ 0.08129394, -0.08040814, -0.13650357,  0.13527455]),\n",
+       " array([ 0.07469045, -0.0738661 , -0.13206966,  0.13084086]),\n",
+       " array([ 0.06829281, -0.06752961, -0.12795279,  0.12672967]),\n",
+       " array([ 0.0620853 , -0.06138263, -0.12415021,  0.12293963]),\n",
+       " array([ 0.05605239, -0.05540914, -0.12065827,  0.11946986]),\n",
+       " array([ 0.05017879, -0.04959312, -0.11747205,  0.11632045]),\n",
+       " array([ 0.04444955, -0.04391845, -0.11458473,  0.11349339]),\n",
+       " array([ 0.03885023, -0.03836872, -0.11198653,  0.11099465]),\n",
+       " array([ 0.03336706, -0.03292676, -0.10966334,  0.10883912]),\n",
+       " array([ 0.02798731, -0.02757362, -0.10759493,  0.10706279]),\n",
+       " array([ 0.02269973, -0.02228629, -0.10575156,  0.10574658]),\n",
+       " array([ 0.01749586, -0.01703493, -0.10407742,  0.10502727]),\n",
+       " array([ 0.01237456, -0.01178555, -0.10242597,  0.10498748]),\n",
+       " array([ 0.00735098, -0.00651136, -0.10047168,  0.10548388]),\n",
+       " array([ 0.00245966, -0.00117719, -0.09782643,  0.10668329]),\n",
+       " array([-0.00194355,  0.0032169 , -0.08806415,  0.08788188])]"
+      ]
+     },
+     "execution_count": 72,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ddp.xs"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "[array([ 0.03434323, -0.00174103]),\n",
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-       " array([0.02866946, 0.0004568 ]),\n",
-       " array([2.60434255e-02, 5.76080344e-05]),\n",
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-       " array([0.01062994, 0.00022519]),\n",
-       " array([0.009389  , 0.00021008]),\n",
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-       " array([5.63949851e-03, 5.51275868e-05]),\n",
-       " array([4.95734605e-03, 1.46062335e-05]),\n",
-       " array([ 4.35882837e-03, -2.01188236e-05]),\n",
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-       " array([-1.22997939e-05, -6.76895006e-07]),\n",
-       " array([-9.49414836e-06, -5.20512588e-07]),\n",
-       " array([-6.44875500e-06, -3.58389148e-07]),\n",
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-       " array([-1.75043220e-06, -1.16259446e-07]),\n",
-       " array([-3.54928263e-07, -4.63188419e-08]),\n",
-       " array([ 4.97444614e-07, -4.47770519e-09]),\n",
-       " array([9.43867321e-07, 1.67324153e-08]),\n",
-       " array([1.11822224e-06, 2.43586848e-08]),\n",
-       " array([1.13075756e-06, 2.40830464e-08]),\n",
-       " array([1.06202328e-06, 1.99848461e-08]),\n",
-       " array([9.64788912e-07, 1.46882720e-08]),\n",
-       " array([8.69552669e-07, 9.67391624e-09]),\n",
-       " array([7.90904233e-07, 5.61950936e-09]),\n",
-       " array([7.33261449e-07, 2.69903777e-09]),\n",
-       " array([6.95360548e-07, 8.12476831e-10]),\n",
-       " array([ 6.73401220e-07, -2.56030771e-10]),\n",
-       " array([ 6.63018301e-07, -7.40896901e-10]),\n",
-       " array([ 6.60354040e-07, -8.43626453e-10]),\n",
-       " array([ 6.62506960e-07, -7.12548348e-10]),\n",
-       " array([ 6.67585083e-07, -4.41944575e-10]),\n",
-       " array([ 6.74525619e-07, -8.23506490e-11]),\n",
-       " array([6.82779843e-07, 3.42849843e-10]),\n",
-       " array([6.91911700e-07, 8.16791999e-10]),\n",
-       " array([7.01127444e-07, 1.30508142e-09]),\n",
-       " array([7.08745180e-07, 1.72848388e-09]),\n",
-       " array([7.11630984e-07, 1.93336819e-09]),\n",
-       " array([7.04676293e-07, 1.66330694e-09]),\n",
-       " array([6.8047287e-07, 5.3907942e-10]),\n",
-       " array([ 6.29457551e-07, -1.94447535e-09]),\n",
-       " array([ 5.40946189e-07, -6.44393291e-09]),\n",
-       " array([ 4.05664486e-07, -1.41542129e-08]),\n",
-       " array([ 2.20335752e-07, -2.15210389e-08])]"
+       "3.7"
       ]
      },
-     "execution_count": 109,
+     "execution_count": 58,
      "metadata": {},
      "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fa29910df50>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
     }
    ],
    "source": [
-    "ddp.us"
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "control = np.vstack(ddp.us)\n",
+    "t = np.arange(0,T*dt, dt)\n",
+    "fig, axs = plt.subplots(1,2, figsize=(15,10))\n",
+    "fig.suptitle('Motor torques')\n",
+    "# axs[0].plot(t,control[:,0], t,control[:,1])\n",
+    "axs[0].plot(t,control[:,0])\n",
+    "axs[0].set_title('Moments')\n",
+    "axs[0].legend(['M1','M2'])\n",
+    "\n",
+    "t_state = t\n",
+    "t_state[-1]"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -589,7 +4959,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython2",
-   "version": "2.7.16"
+   "version": "2.7.12"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/cartpole_swing_up_sol.ipynb b/examples/notebooks/cartpole_swing_up_sol.ipynb
index aff3ed461015fc379e84754b387930fc58c8b690..00f97328697d9512e15f2be3ddd99285cc213f68 100644
--- a/examples/notebooks/cartpole_swing_up_sol.ipynb
+++ b/examples/notebooks/cartpole_swing_up_sol.ipynb
@@ -400,7 +400,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython2",
-   "version": "2.7.15+"
+   "version": "2.7.12"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/kinton_fixed_base.ipynb b/examples/notebooks/kinton_fixed_base.ipynb
index fbbcc39e3b0df2a8b673a363db7e04bced267472..df79af6a9602d6fb0a9628cd187e9db746229e4c 100644
--- a/examples/notebooks/kinton_fixed_base.ipynb
+++ b/examples/notebooks/kinton_fixed_base.ipynb
@@ -169,7 +169,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython2",
-   "version": "2.7.16"
+   "version": "2.7.12"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/kinton_flying_ee.ipynb b/examples/notebooks/kinton_flying_ee.ipynb
index d20bf6f4096afcbb1794b4903cec27b1b077efe6..23d6c63a4ee2a57ccc27f65ec48bb9d768d6a80b 100644
--- a/examples/notebooks/kinton_flying_ee.ipynb
+++ b/examples/notebooks/kinton_flying_ee.ipynb
@@ -499,7 +499,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython2",
-   "version": "2.7.16"
+   "version": "2.7.12"
   }
  },
  "nbformat": 4,