python: fix other np.matrix issues

bindings/python/pinocchio/derivative/dcrba.py

@@ -83,8 +83,8 @@ def __call__(self):
 
                     for d in iv(joint_diff):
 
-                        T_iSd = np.matrix(H[:,d,i0:i1])   # this is 0 if d<=i (<=j)
-                        T_jSd = np.matrix(H[:,d,j0:j1])   # this is 0 is d<=j
+                        T_iSd = np.array(H[:,d,i0:i1])   # this is 0 if d<=i (<=j)
+                        T_jSd = np.array(H[:,d,j0:j1])   # this is 0 is d<=j
 
                         '''
                         assert( norm(T_iSd)<1e-6 or not joint_diff<i )  # d<i => TiSd=0
@@ -254,7 +254,7 @@ def __call__(self,q,vq):
                 # CEN ===> Sii' vi x Yi Si = (Sii x vi)' Yi Si
                 C[ii0:ii1,i0:i1] += Sii.T*vxYS
                 # CEN ===> Sii' Si x Yi vi = (Sii x Si)' Yi vi
-                C[ii0:ii1,i0:i1] += np.matrix(td(H[:,i0:i1,ii0:ii1],Yv,[0,0])[:,:,0]).T
+                C[ii0:ii1,i0:i1] += np.array(td(H[:,i0:i1,ii0:ii1],Yv,[0,0])[:,:,0])
 
         return C
 

bindings/python/pinocchio/derivative/lambdas.py

@@ -55,7 +55,7 @@ def setRobotArgs(robot):
 adjdual.__doc__ = "Force pre-cross product adjdual(a) = -adj(a)' "
 
 td = np.tensordot
-quad = lambda H,v: np.matrix(td(td(H,v,[2,0]),v,[1,0])).T
+quad = lambda H,v: np.array(td(td(H,v,[2,0]),v,[1,0]))
 quad.__doc__ = '''Tensor product v'*H*v, with H.shape = [ nop, nv, nv ]'''
 
 def np_prettyprint(sarg = '{: 0.5f}',eps=5e-7):

bindings/python/pinocchio/romeo_wrapper.py

@@ -21,8 +21,6 @@ def __init__(self, filename, package_dirs=None, verbose=False):
             0, 0, 0, 0,                                      # head
             1.5, -0.6, 0.5, 1.05, -0.4, -0.3, -0.2,          # right arm
         ])
-        if pin.getNumpyType()==np.matrix:
-            self.q0 = np.matrix(self.q0).T
 
         self.opCorrespondances = {"lh": "LWristPitch",
                                   "rh": "RWristPitch",

doc/d-practical-exercises/1-directgeom.md

@@ -55,7 +55,7 @@ the following example.
 
 ```py
 import numpy as np
-A = np.matrix([[1, 2, 3, 4], [5, 6, 7, 8]])  # Define a 2x4 matrix
+A = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])  # Define a 2x4 matrix
 b = np.zeros([4, 1])  # Define a 4 vector (ie a 4x1 matrix) initialized with 0
 c = A * b             # Obtain c by multiplying A by b.
 ```

doc/d-practical-exercises/2-invgeom.md

@@ -85,7 +85,7 @@ from a SciPy-like vector to a Pinocchio-like vector using:
 ```py
 import numpy as np
 x = np.array([1.0, 2.0, 3.0])
-q = np.matrix(x).T
+q = np.array(x)
 x = q.getA()[:, 0]
 ```
 

doc/d-practical-exercises/3-invkine.md

@@ -69,7 +69,7 @@ def Rquat(x, y, z, w):
     q.normalize()
     return q.matrix()
 
-Mgoal = pin.SE3(Rquat(.4, .02, -.5, .7), np.matrix([.2, -.4, .7]).T)
+Mgoal = pin.SE3(Rquat(.4, .02, -.5, .7), np.array([.2, -.4, .7]))
 robot.viewer.gui.addXYZaxis('world/framegoal', [1., 0., 0., 1.], .015, 4)
 place('world/framegoal', Mgoal)
 ```

doc/d-practical-exercises/5-planner.md

@@ -29,7 +29,7 @@ below:
 obs = se3.GeometryObject.CreateCapsule(rad, length)  # Pinocchio obstacle object
 obs.name = "obs"                                     # Set object name
 obs.parentJoint = 0                                  # Set object parent = 0 = universe
-obs.placement = se3.SE3(rotate('x', .1) * rotate('y', .1) * rotate('z', .1), np.matrix([.1, .1, .1]).T)  # Set object placement wrt parent
+obs.placement = se3.SE3(rotate('x', .1) * rotate('y', .1) * rotate('z', .1), np.array([.1, .1, .1]))  # Set object placement wrt parent
 robot.collision_model.addGeometryObject(obs, robot.model, False) # Add object to collision model
 robot.visual_model.addGeometryObject(obs, robot.model, False)    # Add object to visual model
 # Also create a geometric object in gepetto viewer, with according name.

doc/d-practical-exercises/6-wpg.md

@@ -27,10 +27,10 @@ verbose output of BFGS. For example, the robot can track a target moving
 vertically using the following example:
 
 ```py
-cost.Mdes = se3.SE3(eye(3), np.matrix([0.2, 0, 0.1 + t / 100.]))  # Reference target at time 0.
+cost.Mdes = se3.SE3(eye(3), np.array([0.2, 0, 0.1 + t / 100.]))  # Reference target at time 0.
 q = np.copy(robot.q0)
 for t in range(100):
-    cost.Mdes.translation = np.matrix([0.2, 0, 0.1 + t / 100.])
+    cost.Mdes.translation = np.array([0.2, 0, 0.1 + t / 100.])
     q = fmin_bfgs(cost, q, maxiter=10, disp=False)
     robot.display(q)
 ```

doc/d-practical-exercises/src/dpendulum.py

@@ -85,11 +85,11 @@ def step(self,iu):
 
     def render(self):
         q = d2cq(self.x[0])
-        self.pendulum.display(np.matrix([q,]))
+        self.pendulum.display(np.array([q,]))
         time.sleep(self.pendulum.DT)
 
     def dynamics(self,ix,iu):
-        x   = np.matrix(d2c (ix)).T
+        x   = np.array(d2c (ix))
         u   = d2cu(iu)
 
         self.xc,_ = self.pendulum.dynamics(x,u)

doc/d-practical-exercises/src/mobilerobot.py

@@ -19,17 +19,17 @@ class MobileRobotWrapper(RobotWrapper):
     def __init__(self, urdf, pkgs):
         self.initFromURDF(urdf, pkgs, pin.JointModelPlanar())
 
-        M0 = pin.SE3(eye(3), np.matrix([.0, .0, .6]).T)
+        M0 = pin.SE3(eye(3), np.array([.0, .0, .6]))
         self.model.jointPlacements[2] = M0 * self.model.jointPlacements[2]
         self.visual_model.geometryObjects[0].placement = M0 * self.visual_model.geometryObjects[0].placement
         self.visual_data.oMg[0] = M0 * self.visual_data.oMg[0]
 
         # Placement of the "mobile" frame wrt basis center.
-        basisMop = pin.SE3(eye(3), np.matrix([.3, .0, .1]).T)
+        basisMop = pin.SE3(eye(3), np.array([.3, .0, .1]))
         self.model.addFrame(pin.Frame('mobile', 1, 1, basisMop, pin.FrameType.OP_FRAME))
 
         # Placement of the tool frame wrt end effector frame (located at the center of the wrist)
-        effMop = pin.SE3(eye(3), np.matrix([.0, .08, .095]).T)
+        effMop = pin.SE3(eye(3), np.maarraytrix([.0, .08, .095]))
         self.model.addFrame(pin.Frame('tool', 6, 6, effMop, pin.FrameType.OP_FRAME))
 
         # Create data again after setting frames

doc/d-practical-exercises/src/pendulum.py

@@ -78,7 +78,7 @@ def createPendulum(self,nbJoint,rootId=0,prefix='',jointPlacement=None):
         length = 1.0
         mass = length
         inertia = pin.Inertia(mass,
-                              np.matrix([0.0,0.0,length/2]).T,
+                              np.array([0.0,0.0,length/2]),
                               mass/5*np.diagflat([ 1e-2,length**2,  1e-2 ]) )
 
         for i in range(nbJoint):
@@ -93,8 +93,8 @@ def createPendulum(self,nbJoint,rootId=0,prefix='',jointPlacement=None):
             try:self.viewer.viewer.gui.addCapsule('world/'+prefix+'arm'+istr, .1,.8*length,color)
             except:pass
             self.visuals.append( Visual('world/'+prefix+'arm'+istr,jointId,
-                                        pin.SE3(eye(3),np.matrix([0.,0.,length/2]))))
-            jointPlacement     = pin.SE3(eye(3),np.matrix([0.0,0.0,length]).T)
+                                        pin.SE3(eye(3),np.array([0.,0.,length/2]))))
+            jointPlacement     = pin.SE3(eye(3),np.array([0.0,0.0,length]))
 
         self.model.addFrame( pin.Frame('tip',jointId,0,jointPlacement,pin.FrameType.OP_FRAME) )
 
@@ -156,7 +156,7 @@ def dynamics(self,x,u,display=False):
         cost = 0.0
         q = modulePi(x[:self.nq])
         v = x[self.nq:]
-        u = np.clip(np.reshape(np.matrix(u),[self.nu,1]),-self.umax,self.umax)
+        u = np.clip(np.reshape(np.array(u),[self.nu,1]),-self.umax,self.umax)
 
 
         DT = self.DT/self.NDT

doc/d-practical-exercises/src/robot_hand.py

@@ -96,10 +96,10 @@ def collision(self, c2, data=None, oMj1=None, oMj2=None):
             wb = pb + ab * r2
 
             # Compute normal matrix
-            x = np.matrix([1., 0, 0]).T
+            x = np.array([1., 0, 0])
             r1 = cross(ab, x)
             if norm(r1) < 1e-2:
-                x = np.matrix([0, 1., 0]).T
+                x = np.array([0, 1., 0])
             r1 = cross(ab, x)
             r1 /= norm(r1)
             r2 = cross(ab, r1)
@@ -158,10 +158,10 @@ def __init__(self):
 
     def createHand(self, root_id=0, prefix='', joint_placement=None):
         def trans(x, y, z):
-            return pin.SE3(eye(3), np.matrix([x, y, z]).T)
+            return pin.SE3(eye(3), np.array([x, y, z]))
 
         def inertia(m, c):
-            return pin.Inertia(m, np.matrix(c, np.double).T, eye(3) * m ** 2)
+            return pin.Inertia(m, np.array(c, np.double), eye(3) * m ** 2)
 
         def joint_name(body):
             return prefix + body + '_joint'
@@ -186,18 +186,18 @@ def body_name(body):
         self.visuals.append(Visual(body_name('wpalmb'), joint_id, pin.SE3(rotate('x', pi / 2), zero(3)), H, W))
 
         self.viewer.viewer.gui.addCapsule(body_name('wpalmt'), H, W, color)
-        pos = pin.SE3(rotate('x', pi / 2), np.matrix([L, 0, 0]).T)
+        pos = pin.SE3(rotate('x', pi / 2), np.array([L, 0, 0]))
         self.visuals.append(Visual(body_name('wpalmt'), joint_id, pos, H, W))
 
         self.viewer.viewer.gui.addCapsule(body_name('wpalml'), H, L, color)
-        pos = pin.SE3(rotate('y', pi / 2), np.matrix([L / 2, -W / 2, 0]).T)
+        pos = pin.SE3(rotate('y', pi / 2), np.array([L / 2, -W / 2, 0]))
         self.visuals.append(Visual(body_name('wpalml'), joint_id, pos, H, L))
 
         self.viewer.viewer.gui.addCapsule(body_name('wpalmr'), H, L, color)
-        pos = pin.SE3(rotate('y', pi / 2), np.matrix([L / 2, +W / 2, 0]).T)
+        pos = pin.SE3(rotate('y', pi / 2), np.array([L / 2, +W / 2, 0]))
         self.visuals.append(Visual(body_name('wpalmr'), joint_id, pos, H, L))
 
-        joint_placement = pin.SE3(eye(3), np.matrix([5 * cm, 0, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([5 * cm, 0, 0]))
         joint_id = self.model.addJoint(joint_id, pin.JointModelRY(), joint_placement, joint_name('palm'))
         self.model.appendBodyToJoint(joint_id, inertia(2, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addCapsule(body_name('palm2'), 1 * cm, W, color)
@@ -206,79 +206,79 @@ def body_name(body):
         FL = 4 * cm
         palmIdx = joint_id
 
-        joint_placement = pin.SE3(eye(3), np.matrix([2 * cm, W / 2, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([2 * cm, W / 2, 0]))
         joint_id = self.model.addJoint(palmIdx, pin.JointModelRY(), joint_placement, joint_name('finger11'))
         self.model.appendBodyToJoint(joint_id, inertia(.5, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addCapsule(body_name('finger11'), H, FL - 2 * H, color)
-        pos = pin.SE3(rotate('y', pi / 2), np.matrix([FL / 2 - H, 0, 0]).T)
+        pos = pin.SE3(rotate('y', pi / 2), np.array([FL / 2 - H, 0, 0]))
         self.visuals.append(Visual(body_name('finger11'), joint_id, pos, H, FL - 2 * H))
 
-        joint_placement = pin.SE3(eye(3), np.matrix([FL, 0, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([FL, 0, 0]))
         joint_id = self.model.addJoint(joint_id, pin.JointModelRY(), joint_placement, joint_name('finger12'))
         self.model.appendBodyToJoint(joint_id, inertia(.5, [0, 0, 0]), pin.SE3.Identity())
 
         self.viewer.viewer.gui.addCapsule(body_name('finger12'), H, FL - 2 * H, color)
-        pos = pin.SE3(rotate('y', pi / 2), np.matrix([FL / 2 - H, 0, 0]).T)
+        pos = pin.SE3(rotate('y', pi / 2), np.array([FL / 2 - H, 0, 0]))
         self.visuals.append(Visual(body_name('finger12'), joint_id, pos, H, FL - 2 * H))
 
-        joint_placement = pin.SE3(eye(3), np.matrix([FL - 2 * H, 0, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([FL - 2 * H, 0, 0]))
         joint_id = self.model.addJoint(joint_id, pin.JointModelRY(), joint_placement, joint_name('finger13'))
         self.model.appendBodyToJoint(joint_id, inertia(.3, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addSphere(body_name('finger13'), H, color)
         self.visuals.append(Visual(body_name('finger13'), joint_id, trans(2 * H, 0, 0), H, 0))
 
-        joint_placement = pin.SE3(eye(3), np.matrix([2 * cm, 0, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([2 * cm, 0, 0]))
         joint_id = self.model.addJoint(palmIdx, pin.JointModelRY(), joint_placement, joint_name('finger21'))
         self.model.appendBodyToJoint(joint_id, inertia(.5, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addCapsule(body_name('finger21'), H, FL - 2 * H, color)
-        pos = pin.SE3(rotate('y', pi / 2), np.matrix([FL / 2 - H, 0, 0]).T)
+        pos = pin.SE3(rotate('y', pi / 2), np.array([FL / 2 - H, 0, 0]))
         self.visuals.append(Visual(body_name('finger21'), joint_id, pos, H, FL - 2 * H))
 
-        joint_placement = pin.SE3(eye(3), np.matrix([FL, 0, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([FL, 0, 0]))
         joint_id = self.model.addJoint(joint_id, pin.JointModelRY(), joint_placement, joint_name('finger22'))
         self.model.appendBodyToJoint(joint_id, inertia(.5, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addCapsule(body_name('finger22'), H, FL - 2 * H, color)
-        pos = pin.SE3(rotate('y', pi / 2), np.matrix([FL / 2 - H, 0, 0]).T)
+        pos = pin.SE3(rotate('y', pi / 2), np.array([FL / 2 - H, 0, 0]))
         self.visuals.append(Visual(body_name('finger22'), joint_id, pos, H, FL - 2 * H))
 
-        joint_placement = pin.SE3(eye(3), np.matrix([FL - H, 0, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([FL - H, 0, 0]))
         joint_id = self.model.addJoint(joint_id, pin.JointModelRY(), joint_placement, joint_name('finger23'))
         self.model.appendBodyToJoint(joint_id, inertia(.3, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addSphere(body_name('finger23'), H, color)
         self.visuals.append(Visual(body_name('finger23'), joint_id, trans(H, 0, 0), H, 0))
 
-        joint_placement = pin.SE3(eye(3), np.matrix([2 * cm, -W / 2, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([2 * cm, -W / 2, 0]))
         joint_id = self.model.addJoint(palmIdx, pin.JointModelRY(), joint_placement, joint_name('finger31'))
         self.model.appendBodyToJoint(joint_id, inertia(.5, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addCapsule(body_name('finger31'), H, FL - 2 * H, color)
-        pos = pin.SE3(rotate('y', pi / 2), np.matrix([FL / 2 - H, 0, 0]).T)
+        pos = pin.SE3(rotate('y', pi / 2), np.array([FL / 2 - H, 0, 0]))
         self.visuals.append(Visual(body_name('finger31'), joint_id, pos, H, FL - 2 * H))
 
-        joint_placement = pin.SE3(eye(3), np.matrix([FL, 0, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([FL, 0, 0]))
         joint_id = self.model.addJoint(joint_id, pin.JointModelRY(), joint_placement, joint_name('finger32'))
         self.model.appendBodyToJoint(joint_id, inertia(.5, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addCapsule(body_name('finger32'), H, FL - 2 * H, color)
-        pos = pin.SE3(rotate('y', pi / 2), np.matrix([FL / 2 - H, 0, 0]).T)
+        pos = pin.SE3(rotate('y', pi / 2), np.array([FL / 2 - H, 0, 0]))
         self.visuals.append(Visual(body_name('finger32'), joint_id, pos, H, FL - 2 * H))
 
-        joint_placement = pin.SE3(eye(3), np.matrix([FL - 2 * H, 0, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([FL - 2 * H, 0, 0]))
         joint_id = self.model.addJoint(joint_id, pin.JointModelRY(), joint_placement, joint_name('finger33'))
         self.model.appendBodyToJoint(joint_id, inertia(.3, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addSphere(body_name('finger33'), H, color)
         self.visuals.append(Visual(body_name('finger33'), joint_id, trans(2 * H, 0, 0), H, 0))
 
-        joint_placement = pin.SE3(eye(3), np.matrix([1 * cm, -W / 2 - H * 1.5, 0]).T)
+        joint_placement = pin.SE3(eye(3), np.array([1 * cm, -W / 2 - H * 1.5, 0]))
         joint_id = self.model.addJoint(1, pin.JointModelRY(), joint_placement, joint_name('thumb1'))
         self.model.appendBodyToJoint(joint_id, inertia(.5, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addCapsule(body_name('thumb1'), H, 2 * cm, color)
-        pos = pin.SE3(rotate('z', pi / 3) * rotate('x', pi / 2), np.matrix([1 * cm, -1 * cm, 0]).T)
+        pos = pin.SE3(rotate('z', pi / 3) * rotate('x', pi / 2), np.array([1 * cm, -1 * cm, 0]))
         self.visuals.append(Visual(body_name('thumb1'), joint_id, pos, 2 * cm))
 
-        joint_placement = pin.SE3(rotate('z', pi / 3) * rotate('x', pi), np.matrix([3 * cm, -1.8 * cm, 0]).T)
+        joint_placement = pin.SE3(rotate('z', pi / 3) * rotate('x', pi), np.array([3 * cm, -1.8 * cm, 0]))
         joint_id = self.model.addJoint(joint_id, pin.JointModelRZ(), joint_placement, joint_name('thumb2'))
         self.model.appendBodyToJoint(joint_id, inertia(.4, [0, 0, 0]), pin.SE3.Identity())
         self.viewer.viewer.gui.addCapsule(body_name('thumb2'), H, FL - 2 * H, color)
-        pos = pin.SE3(rotate('x', pi / 3), np.matrix([-0.7 * cm, .8 * cm, -0.5 * cm]).T)
+        pos = pin.SE3(rotate('x', pi / 3), np.array([-0.7 * cm, .8 * cm, -0.5 * cm]))
         self.visuals.append(Visual(body_name('thumb2'), joint_id, pos, H, FL - 2 * H))
 
         # Prepare some patches to represent collision points. Yet unvisible.

doc/d-practical-exercises/src/ur5x4.py

@@ -31,12 +31,12 @@ def loadRobot(M0, name):
 
 robots = []
 # Load 4 Ur5 robots, placed at 0.3m from origin in the 4 directions x,y,-x,-y.
-Mt = SE3(eye(3), np.matrix([.3, 0, 0]).T)  # First robot is simply translated
+Mt = SE3(eye(3), np.array([.3, 0, 0]))  # First robot is simply translated
 for i in range(4):
     robots.append(loadRobot(SE3(rotate('z', np.pi / 2 * i), zero(3)) * Mt, "robot%d" % i))
 
 # Set up the robots configuration with end effector pointed upward.
-q0 = np.matrix([np.pi / 4, -np.pi / 4, -np.pi / 2, np.pi / 4, np.pi / 2, 0]).T
+q0 = np.array([np.pi / 4, -np.pi / 4, -np.pi / 2, np.pi / 4, np.pi / 2, 0])
 for i in range(4):
     robots[i].display(q0)
 
@@ -45,6 +45,6 @@ def loadRobot(M0, name):
 w, h, d = 0.25, 0.25, 0.005
 color = [red, green, blue, transparency] = [1, 1, 0.78, 1.0]
 gepettoViewer.addBox('world/toolplate', w, h, d, color)
-Mtool = SE3(rotate('z', 1.268), np.matrix([0, 0, .77]).T)
+Mtool = SE3(rotate('z', 1.268), np.array([0, 0, .77]))
 gepettoViewer.applyConfiguration('world/toolplate', se3ToXYZQUATtuple(Mtool))
 gepettoViewer.refresh()

examples/forward-dynamics-derivatives.py

@@ -19,8 +19,8 @@
 model.upperPositionLimit = np.ones((model.nq,1))
 
 q = pin.randomConfiguration(model) # joint configuration
-v = np.matrix(np.random.rand(model.nv,1)) # joint velocity
-tau = np.matrix(np.random.rand(model.nv,1)) # joint acceleration
+v = np.random.rand(model.nv,1) # joint velocity
+tau = np.random.rand(model.nv,1) # joint acceleration
 
 # Evaluate the derivatives
 

models/simple_model.py

@@ -11,7 +11,7 @@
 
 def placement(x=0, y=0, z=0, rx=0, ry=0, rz=0):
     m = pin.SE3.Identity()
-    m.translation = np.matrix([[float(i)] for i in [x, y, z]])
+    m.translation = np.array([x, y, z])
     m.rotation *= rotate('x', rx)
     m.rotation *= rotate('y', ry)
     m.rotation *= rotate('z', rz)

unittest/python/bindings_com_velocity_derivatives.py

@@ -5,8 +5,8 @@
 
 def df_dq(model,func,q,h=1e-9):
     """ Perform df/dq by num_diff. q is in the lie manifold.
-    :params func: function to differentiate f : np.matrix -> np.matrix
-    :params q: configuration value at which f is differentiated. type np.matrix
+    :params func: function to differentiate f : np.array -> np.array
+    :params q: configuration value at which f is differentiated. type np.array
     :params h: eps
     
     :returns df/dq