def setupImplicitFunction(operAlpha, An, geom):
#setup function to obtain B and RHS for the Fourier series calc
def getBandRHS(alphaiLoc):
alphaLoc = geom.alphaGeometric(operAlpha) - alphaiLoc
clLoc = geom.clLoc(alphaLoc)
RHS = clLoc*geom.chordLoc
B = numpy.sin(numpy.outer(geom.thetaLoc, geom.sumN))*(4.0*geom.bref)
return (B,RHS)
alphaiLoc = []
for i in range(geom.n):
alphaiLoc.append(
C.inner_prod(geom.sumN*numpy.sin(geom.sumN*geom.thetaLoc[i])/numpy.sin(geom.thetaLoc[i]), An))
alphaiLoc = C.veccat(alphaiLoc)
(B,RHS) = getBandRHS(alphaiLoc)
makeMeZero = RHS - C.mul(B, An)
CL = An[0]*numpy.pi*geom.AR
CDi = 0.0
for i in range(geom.n):
k = geom.sumN[i]
CDi += k * An[i]**2 / An[0]**2
CDi *= numpy.pi*geom.AR*An[0]**2
return (makeMeZero, alphaiLoc, CL, CDi)
def test_MX(self):
x = MX.sym("x", 2)
y = MX.sym("y", 2, 2)
f1 = MXFunction("f1", [x, y], [x + y[0, 0], mul(y, x)])
f2 = MXFunction("f2", [x, y], [mul(MX.zeros(0, 2), x)])
f3 = MXFunction("f3", [x, y], [MX.zeros(0, 0), mul(y, x)])
f4 = MXFunction("f4", [x, y], [MX.zeros(0, 2), mul(y, x)])
ndir = 2
in1 = [x, y]
v1 = [DMatrix([1.1, 1.3]), DMatrix([[0.7, 1.5], [2.1, 0.9]])]
w = x[:]
w[1] *= 2
w2 = x[:]
w2[1] *= x[0]
ww = x[:]
ww[[0, 1]] *= x
wwf = x[:]
wwf[[1, 0]] *= x
wwr = x[:]
wwr[[0, 0, 1, 1]] *= 2
yy = y[:, :]
yy[:, 0] = x
yy2 = y[:, :]
yy2[:, 0] = x**2
yyy = y[:, :]
yyy[[1, 0], 0] = x
yyy2 = y[:, :]
yyy2[[1, 0], 0] = x**2
def remove_first(x):
ret = DMatrix(x)
if ret.numel() > 0:
ret[0, 0] = DMatrix(1, 1)
return ret
else:
return ret
def remove_last(x):
ret = DMatrix(x)
if ret.nnz() > 0:
ret[ret.sparsity().row()[-1],
ret.sparsity().getCol()[-1]] = DMatrix(1, 1)
return ret
else:
return x
spmods = [lambda x: x, remove_first, remove_last]
# TODO: sparse seeding
for inputs, values, out, jac in [
(in1, v1, x, DMatrix.eye(2)),
(in1, v1, x.T, DMatrix.eye(2)),
(in1, v1, x**2, 2 * c.diag(x)),
(in1, v1, (x**2).attachAssert(True), 2 * c.diag(x)),
(in1, v1, (x**2).T, 2 * c.diag(x)),
(in1, v1, c.reshape(x, (1, 2)), DMatrix.eye(2)),
(in1, v1, c.reshape(x**2, (1, 2)), 2 * c.diag(x)),
(in1, v1, x + y.nz[0], DMatrix.eye(2)),
(in1, v1, x + y[0, 0], DMatrix.eye(2)),
(in1, v1, x + x, 2 * DMatrix.eye(2)),
(in1, v1, x**2 + x, 2 * c.diag(x) + DMatrix.eye(2)),
(in1, v1, x * x, 2 * c.diag(x)),
(in1, v1, x * y.nz[0], DMatrix.eye(2) * y.nz[0]),
(in1, v1, x * y[0, 0], DMatrix.eye(2) * y[0, 0]),
(in1, v1, x[0], DMatrix.eye(2)[0, :]),
(in1, v1, (x**2)[0], horzcat([2 * x[0], MX(1, 1)])),
(in1, v1, x[0] + x[1], DMatrix.ones(1, 2)),
(in1, v1, sin(repmat(x**2, 1, 3)),
repmat(cos(c.diag(x**2)) * 2 * c.diag(x), 3, 1)),
(in1, v1, sin(repsum((x**2).T, 1,
2)), cos(x[0]**2 + x[1]**2) * 2 * x.T),
(in1, v1, vertcat([x[1], x[0]]), sparsify(DMatrix([[0, 1], [1,
0]]))),
(in1, v1, vertsplit(x, [0, 1, 2])[1], sparsify(DMatrix([[0, 1]]))),
(in1, v1, vertcat([x[1]**2, x[0]**2]),
blockcat([[MX(1, 1), 2 * x[1]], [2 * x[0], MX(1, 1)]])),
(in1, v1, vertsplit(x**2,
[0, 1, 2])[1], blockcat([[MX(1, 1),
2 * x[1]]])),
(in1, v1, vertsplit(x**2, [0, 1, 2])[1]**3,
blockcat([[MX(1, 1), 6 * x[1]**5]])),
(in1, v1, horzcat([x[1],
x[0]]).T, sparsify(DMatrix([[0, 1], [1, 0]]))),
(in1, v1, horzcat([x[1]**2, x[0]**2]).T,
blockcat([[MX(1, 1), 2 * x[1]], [2 * x[0], MX(1, 1)]])),
(in1, v1, diagcat([x[1]**2, y, x[0]**2]),
blockcat([[MX(1, 1), 2 * x[1]]] + ([[MX(1, 1), MX(1, 1)]] * 14) +
[[2 * x[0], MX(1, 1)]])),
(in1, v1, horzcat([x[1]**2, x[0]**2]).T,
blockcat([[MX(1, 1), 2 * x[1]], [2 * x[0], MX(1, 1)]])),
(in1, v1, x[[0, 1]], sparsify(DMatrix([[1, 0], [0, 1]]))),
(in1, v1, (x**2)[[0, 1]], 2 * c.diag(x)),
(in1, v1, x[[0, 0, 1, 1]],
sparsify(DMatrix([[1, 0], [1, 0], [0, 1], [0, 1]]))),
(in1, v1, (x**2)[[0, 0, 1, 1]],
blockcat([[2 * x[0], MX(1, 1)], [2 * x[0], MX(1, 1)],
[MX(1, 1), 2 * x[1]], [MX(1, 1), 2 * x[1]]])),
(in1, v1, wwr, sparsify(DMatrix([[2, 0], [0, 2]]))),
(in1, v1, x[[1, 0]], sparsify(DMatrix([[0, 1], [1, 0]]))),
(in1, v1, x[[1, 0], 0], sparsify(DMatrix([[0, 1], [1, 0]]))),
(in1, v1, w, sparsify(DMatrix([[1, 0], [0, 2]]))),
(in1, v1, w2, blockcat([[1, MX(1, 1)], [x[1], x[0]]])),
(in1, v1, ww, 2 * c.diag(x)),
(in1, v1, wwf, vertcat([x[[1, 0]].T, x[[1, 0]].T])),
(in1, v1, yy[:, 0], DMatrix.eye(2)),
(in1, v1, yy2[:, 0], 2 * c.diag(x)),
(in1, v1, yyy[:, 0], sparsify(DMatrix([[0, 1], [1, 0]]))),
(in1, v1, mul(y, x), y),
(in1, v1, mul(x.T, y.T), y),
(in1, v1, mac(y, x, DMatrix.zeros(Sparsity.triplet(2, 1, [1],
[0]))),
y[Sparsity.triplet(2, 2, [1, 1], [0, 1])]),
(in1, v1,
mac(x.T, y.T, DMatrix.zeros(Sparsity.triplet(2, 1, [1], [0]).T)),
y[Sparsity.triplet(2, 2, [1, 1], [0, 1])]),
(in1, v1, mul(y[Sparsity.triplet(2, 2, [0, 1, 1], [0, 0, 1])],
x), y[Sparsity.triplet(2, 2, [0, 1, 1], [0, 0, 1])]),
(in1, v1,
mul(x.T, y[Sparsity.triplet(2, 2, [0, 1, 1], [0, 0, 1])].T),
y[Sparsity.triplet(2, 2, [0, 1, 1], [0, 0, 1])]),
(in1, v1, mul(y, x**2), y * 2 * vertcat([x.T, x.T])),
(in1, v1, sin(x), c.diag(cos(x))),
(in1, v1, sin(x**2), c.diag(cos(x**2) * 2 * x)),
(in1, v1, x * y[:, 0], c.diag(y[:, 0])),
(in1, v1, x * y.nz[[0, 1]], c.diag(y.nz[[0, 1]])),
(in1, v1, x * y.nz[[1, 0]], c.diag(y.nz[[1, 0]])),
(in1, v1, x * y[[0, 1], 0], c.diag(y[[0, 1], 0])),
(in1, v1, x * y[[1, 0], 0], c.diag(y[[1, 0], 0])),
(in1, v1, inner_prod(x, x), (2 * x).T),
(in1, v1, inner_prod(x**2, x), (3 * x**2).T),
#(in1,v1,c.det(horzcat([x,DMatrix([1,2])])),DMatrix([-1,2])), not implemented
(in1, v1, f1.call(in1)[1], y),
(in1, v1, f1.call([x**2, y])[1], y * 2 * vertcat([x.T, x.T])),
(in1, v1, f2.call(in1)[0], DMatrix.zeros(0, 2)),
(in1, v1, f2.call([x**2, y])[0], DMatrix.zeros(0, 2)),
(in1, v1, f3.call(in1)[0], DMatrix.zeros(0, 2)),
(in1, v1, f3.call([x**2, y])[0], DMatrix.zeros(0, 2)),
(in1, v1, f4.call(in1)[0], DMatrix.zeros(0, 2)),
(in1, v1, f4.call([x**2, y])[0], DMatrix.zeros(0, 2)),
#(in1,v1,f1.call([x**2,[]])[1],DMatrix.zeros(2,2)),
#(in1,v1,f1.call([[],y])[1],DMatrix.zeros(2,2)),
(in1, v1, vertcat([x, DMatrix(0, 1)]), DMatrix.eye(2)),
(in1, v1, (x**2).project(sparsify(DMatrix([0, 1])).sparsity()),
blockcat([[MX(1, 1), MX(1, 1)], [MX(1, 1), 2 * x[1]]])),
(in1, v1, c.inner_prod(x, y[:, 0]), y[:, 0].T),
(in1, v1, x.nz[IMatrix([[1, 0]])].T * y.nz[IMatrix([[0, 2]])],
blockcat([[MX(1, 1), y.nz[0]], [y.nz[2], MX(1, 1)]])),
(in1, v1, x.nz[c.diag([1, 0])] * y.nz[c.diag([0, 2])],
blockcat([[MX(1, 1), y.nz[0]], [MX(1, 1), MX(1, 1)],
[MX(1, 1), MX(1, 1)], [y.nz[2], MX(1, 1)]])),
]:
print out
fun = MXFunction("fun", inputs, [out, jac])
funsx = fun.expand()
funsx.init()
for i, v in enumerate(values):
fun.setInput(v, i)
funsx.setInput(v, i)
fun.evaluate()
funsx.evaluate()
self.checkarray(fun.getOutput(0), funsx.getOutput(0))
self.checkarray(fun.getOutput(1), funsx.getOutput(1))
self.check_codegen(fun)
J_ = fun.getOutput(1)
def vec(l):
ret = []
for i in l:
ret.extend(i)
return ret
storage2 = {}
storage = {}
vf_mx = None
for f in [fun, fun.expand()]:
f.init()
d1 = f.derForward(ndir)
d1.init()
d2 = f.derReverse(ndir)
d2.init()
num_in = f.nIn()
num_out = f.nOut()
"""# Fwd and Adjoint AD
for i,v in enumerate(values):
f.setInput(v,i)
d.setInput(v,i)
for d in range(ndir):
f.setInput(DMatrix(inputs[0].sparsity(),random.random(inputs[0].nnz())),num_in+d*num_in + d)
f.setAdjSeed(DMatrix(out.sparsity(),random.random(out.nnz())),num_in+d*num_in + 0)
f.setFwdSeed(0,1,d)
f.setAdjSeed(0,1,d)
f.evaluate()
for d in range(ndir):
seed = array(f.getFwdSeed(0,d)).ravel()
sens = array(f.getFwdSens(0,d)).ravel()
self.checkarray(sens,mul(J_,seed),"Fwd %d %s" % (d,str(type(f))))
seed = array(f.getAdjSeed(0,d)).ravel()
sens = array(f.getAdjSens(0,d)).ravel()
self.checkarray(sens,mul(J_.T,seed),"Adj %d" %d)
"""
# evalThings
for sym, Function in [(MX.sym, MXFunction),
(SX.sym, SXFunction)]:
if isinstance(f, MXFunction) and Function is SXFunction:
continue
if isinstance(f, SXFunction) and Function is MXFunction:
continue
# dense
for spmod, spmod2 in itertools.product(spmods, repeat=2):
fseeds = [[
sym("f",
spmod(f.getInput(i)).sparsity())
for i in range(f.nIn())
] for d in range(ndir)]
aseeds = [[
sym("a",
spmod2(f.getOutput(i)).sparsity())
for i in range(f.nOut())
] for d in range(ndir)]
inputss = [
sym("i",
f.getInput(i).sparsity())
for i in range(f.nIn())
]
with internalAPI():
res = f.call(inputss, True)
fwdsens = f.callForward(inputss, res, fseeds, True)
adjsens = f.callReverse(inputss, res, aseeds, True)
fseed = [
DMatrix(fseeds[d][0].sparsity(),
random.random(fseeds[d][0].nnz()))
for d in range(ndir)
]
aseed = [
DMatrix(aseeds[d][0].sparsity(),
random.random(aseeds[d][0].nnz()))
for d in range(ndir)
]
vf = Function(
"vf", inputss +
vec([fseeds[i] + aseeds[i] for i in range(ndir)]),
list(res) + vec([
list(fwdsens[i]) + list(adjsens[i])
for i in range(ndir)
]))
for i, v in enumerate(values):
vf.setInput(v, i)
offset = len(inputss)
for d in range(ndir):
vf.setInput(fseed[d], offset + 0)
for i in range(len(values) - 1):
vf.setInput(0, offset + i + 1)
offset += len(inputss)
vf.setInput(aseed[d], offset + 0)
vf.setInput(0, offset + 1)
offset += 2
assert (offset == vf.nIn())
vf.evaluate()
self.check_codegen(vf)
offset = len(res)
for d in range(ndir):
seed = array(fseed[d].T).ravel()
sens = array(vf.getOutput(offset + 0).T).ravel()
offset += len(inputss)
self.checkarray(
sens, mul(J_, seed), "eval Fwd %d %s" %
(d, str(type(f)) + str(sym)))
seed = array(aseed[d].T).ravel()
sens = array(vf.getOutput(offset + 0).T).ravel()
offset += len(inputss)
self.checkarray(
sens, mul(J_.T, seed), "eval Adj %d %s" %
(d,
str([
vf.getOutput(i) for i in range(vf.nOut())
])))
assert (offset == vf.nOut())
# Complete random seeding
random.seed(1)
for i in range(vf.nIn()):
vf.setInput(
DMatrix(
vf.getInput(i).sparsity(),
random.random(vf.getInput(i).nnz())), i)
vf.evaluate()
self.check_codegen(vf)
storagekey = (spmod, spmod2)
if not (storagekey in storage):
storage[storagekey] = []
storage[storagekey].append(
[vf.getOutput(i) for i in range(vf.nOut())])
# Added to make sure that the same seeds are used for SX and MX
if Function is MXFunction:
vf_mx = vf
# Second order sensitivities
for sym2, Function2 in [(MX.sym, MXFunction),
(SX.sym, SXFunction)]:
if isinstance(vf,
MXFunction) and Function2 is SXFunction:
continue
if isinstance(vf,
SXFunction) and Function2 is MXFunction:
continue
for spmod_2, spmod2_2 in itertools.product(spmods,
repeat=2):
fseeds2 = [[
sym2("f",
vf_mx.getInput(i).sparsity())
for i in range(vf.nIn())
] for d in range(ndir)]
aseeds2 = [[
sym2("a",
vf_mx.getOutput(i).sparsity())
for i in range(vf.nOut())
] for d in range(ndir)]
inputss2 = [
sym2("i",
vf_mx.getInput(i).sparsity())
for i in range(vf.nIn())
]
with internalAPI():
res2 = vf.call(inputss2, True)
fwdsens2 = vf.callForward(
inputss2, res2, fseeds2, True)
adjsens2 = vf.callReverse(
inputss2, res2, aseeds2, True)
vf2 = Function2(
"vf2", inputss2 + vec([
fseeds2[i] + aseeds2[i]
for i in range(ndir)
]),
list(res2) + vec([
list(fwdsens2[i]) + list(adjsens2[i])
for i in range(ndir)
]))
random.seed(1)
for i in range(vf2.nIn()):
vf2.setInput(
DMatrix(
vf2.getInput(i).sparsity(),
random.random(vf2.getInput(i).nnz())),
i)
vf2.evaluate()
self.check_codegen(vf2)
storagekey = (spmod, spmod2)
if not (storagekey in storage2):
storage2[storagekey] = []
storage2[storagekey].append(
[vf2.getOutput(i) for i in range(vf2.nOut())])
# Remainder of eval testing
for store, order in [(storage, "first-order"),
(storage2, "second-order")]:
for stk, st in store.items():
for i in range(len(st) - 1):
for k, (a, b) in enumerate(zip(st[0], st[i + 1])):
if b.numel() == 0 and sparsify(a).nnz() == 0:
continue
if a.numel() == 0 and sparsify(b).nnz() == 0:
continue
self.checkarray(sparsify(a), sparsify(b),
("%s, output(%d)" % (order, k)) +
str(vf2.getInput(0)))
for f in [fun.expand(), fun]:
# jacobian()
for mode in ["forward", "reverse"]:
f.setOption("ad_weight", 0 if mode == 'forward' else 1)
f.setOption("ad_weight_sp", 0 if mode == 'forward' else 1)
f.init()
Jf = f.jacobian(0, 0)
Jf.init()
for i, v in enumerate(values):
Jf.setInput(v, i)
Jf.evaluate()
self.check_codegen(Jf)
self.checkarray(Jf.getOutput(), J_)
self.checkarray(DMatrix.ones(Jf.getOutput().sparsity()),
DMatrix.ones(J_.sparsity()),
str(out) + str(mode))
self.checkarray(DMatrix.ones(f.jacSparsity()),
DMatrix.ones(J_.sparsity()))
# Scalarized
if out.isempty(): continue
s_i = out.sparsity().row()[0]
s_j = out.sparsity().getCol()[0]
s_k = s_i * out.size2() + s_j
fun = MXFunction("fun", inputs, [out[s_i, s_j], jac[s_k, :].T])
for i, v in enumerate(values):
fun.setInput(v, i)
fun.evaluate()
J_ = fun.getOutput(1)
for f in [fun, fun.expand()]:
# gradient()
for mode in ["forward", "reverse"]:
f.setOption("ad_weight", 0 if mode == 'forward' else 1)
f.setOption("ad_weight_sp", 0 if mode == 'forward' else 1)
f.init()
Gf = f.gradient(0, 0)
Gf.init()
for i, v in enumerate(values):
Gf.setInput(v, i)
Gf.evaluate()
self.check_codegen(Gf)
self.checkarray(Gf.getOutput(),
J_,
failmessage=("mode: %s" % mode))
#self.checkarray(DMatrix(Gf.getOutput().sparsity(),1),DMatrix(J_.sparsity(),1),str(mode)+str(out)+str(type(fun)))
H_ = None
for f in [fun, fun.expand()]:
# hessian()
for mode in ["forward", "reverse"]:
f.setOption("ad_weight", 0 if mode == 'forward' else 1)
f.setOption("ad_weight_sp", 0 if mode == 'forward' else 1)
f.init()
Hf = f.hessian(0, 0)
Hf.init()
for i, v in enumerate(values):
Hf.setInput(v, i)
Hf.evaluate()
self.check_codegen(Hf)
if H_ is None:
H_ = Hf.getOutput()
self.checkarray(Hf.getOutput(),
H_,
failmessage=("mode: %s" % mode))
def test_MX(self):
x = MX.sym("x",2)
y = MX.sym("y",2,2)
f1 = MXFunction([x,y],[x+y[0,0],mul(y,x)])
f1.init()
f2 = MXFunction([x,y],[mul(MX.zeros(0,2),x)])
f2.init()
f3 = MXFunction([x,y],[MX.zeros(0,0),mul(y,x)])
f3.init()
f4 = MXFunction([x,y],[MX.zeros(0,2),mul(y,x)])
f4.init()
ndir = 2
in1 = [x,y]
v1 = [DMatrix([1.1,1.3]),DMatrix([[0.7,1.5],[2.1,0.9]])]
w=x[:]
w[1]*=2
w2=x[:]
w2[1]*=x[0]
ww=x[:]
ww[[0,1]]*=x
wwf=x[:]
wwf[[1,0]]*=x
wwr=x[:]
wwr[[0,0,1,1]]*=2
yy=y[:,:]
yy[:,0] = x
yy2=y[:,:]
yy2[:,0] = x**2
yyy=y[:,:]
yyy[[1,0],0] = x
yyy2=y[:,:]
yyy2[[1,0],0] = x**2
def remove_first(x):
ret = DMatrix(x)
if ret.numel()>0:
ret[0,0] = DMatrix.sparse(1,1)
return ret
else:
return ret
def remove_last(x):
ret = DMatrix(x)
if ret.size()>0:
ret[ret.sparsity().row()[-1],ret.sparsity().getCol()[-1]] = DMatrix.sparse(1,1)
return ret
else:
return x
spmods = [lambda x: x , remove_first, remove_last]
# TODO: sparse seeding
for inputs,values,out, jac in [
(in1,v1,x,DMatrix.eye(2)),
(in1,v1,x.T,DMatrix.eye(2)),
(in1,v1,x**2,2*c.diag(x)),
(in1,v1,(x**2).attachAssert(True),2*c.diag(x)),
(in1,v1,(x**2).T,2*c.diag(x)),
(in1,v1,c.reshape(x,(1,2)),DMatrix.eye(2)),
(in1,v1,c.reshape(x**2,(1,2)),2*c.diag(x)),
(in1,v1,x+y.nz[0],DMatrix.eye(2)),
(in1,v1,x+y[0,0],DMatrix.eye(2)),
(in1,v1,x+x,2*DMatrix.eye(2)),
(in1,v1,x**2+x,2*c.diag(x)+DMatrix.eye(2)),
(in1,v1,x*x,2*c.diag(x)),
(in1,v1,x*y.nz[0],DMatrix.eye(2)*y.nz[0]),
(in1,v1,x*y[0,0],DMatrix.eye(2)*y[0,0]),
(in1,v1,x[0],DMatrix.eye(2)[0,:]),
(in1,v1,(x**2)[0],horzcat([2*x[0],MX.sparse(1,1)])),
(in1,v1,x[0]+x[1],DMatrix.ones(1,2)),
(in1,v1,vertcat([x[1],x[0]]),sparse(DMatrix([[0,1],[1,0]]))),
(in1,v1,vertsplit(x,[0,1,2])[1],sparse(DMatrix([[0,1]]))),
(in1,v1,vertcat([x[1]**2,x[0]**2]),blockcat([[MX.sparse(1,1),2*x[1]],[2*x[0],MX.sparse(1,1)]])),
(in1,v1,vertsplit(x**2,[0,1,2])[1],blockcat([[MX.sparse(1,1),2*x[1]]])),
(in1,v1,vertsplit(x**2,[0,1,2])[1]**3,blockcat([[MX.sparse(1,1),6*x[1]**5]])),
(in1,v1,horzcat([x[1],x[0]]).T,sparse(DMatrix([[0,1],[1,0]]))),
(in1,v1,horzcat([x[1]**2,x[0]**2]).T,blockcat([[MX.sparse(1,1),2*x[1]],[2*x[0],MX.sparse(1,1)]])),
(in1,v1,diagcat([x[1]**2,y,x[0]**2]),
blockcat( [[MX.sparse(1,1),2*x[1]]] + ([[MX.sparse(1,1),MX.sparse(1,1)]]*14) + [[2*x[0],MX.sparse(1,1)]] )
),
(in1,v1,horzcat([x[1]**2,x[0]**2]).T,blockcat([[MX.sparse(1,1),2*x[1]],[2*x[0],MX.sparse(1,1)]])),
(in1,v1,x[[0,1]],sparse(DMatrix([[1,0],[0,1]]))),
(in1,v1,(x**2)[[0,1]],2*c.diag(x)),
(in1,v1,x[[0,0,1,1]],sparse(DMatrix([[1,0],[1,0],[0,1],[0,1]]))),
(in1,v1,(x**2)[[0,0,1,1]],blockcat([[2*x[0],MX.sparse(1,1)],[2*x[0],MX.sparse(1,1)],[MX.sparse(1,1),2*x[1]],[MX.sparse(1,1),2*x[1]]])),
(in1,v1,wwr,sparse(DMatrix([[2,0],[0,2]]))),
(in1,v1,x[[1,0]],sparse(DMatrix([[0,1],[1,0]]))),
(in1,v1,x[[1,0],0],sparse(DMatrix([[0,1],[1,0]]))),
(in1,v1,w,sparse(DMatrix([[1,0],[0,2]]))),
(in1,v1,w2,blockcat([[1,MX.sparse(1,1)],[x[1],x[0]]])),
(in1,v1,ww,2*c.diag(x)),
(in1,v1,wwf,vertcat([x[[1,0]].T,x[[1,0]].T])),
(in1,v1,yy[:,0],DMatrix.eye(2)),
(in1,v1,yy2[:,0],2*c.diag(x)),
(in1,v1,yyy[:,0],sparse(DMatrix([[0,1],[1,0]]))),
(in1,v1,mul(y,x),y),
(in1,v1,mul(x.T,y.T),y),
(in1,v1,mul(y,x,DMatrix.zeros(Sparsity.triplet(2,1,[1],[0]))),y[Sparsity.triplet(2,2,[1,1],[0,1])]),
(in1,v1,mul(x.T,y.T,DMatrix.zeros(Sparsity.triplet(2,1,[1],[0]).T)),y[Sparsity.triplet(2,2,[1,1],[0,1])]),
(in1,v1,mul(y[Sparsity.triplet(2,2,[0,1,1],[0,0,1])],x),y[Sparsity.triplet(2,2,[0,1,1],[0,0,1])]),
(in1,v1,mul(x.T,y[Sparsity.triplet(2,2,[0,1,1],[0,0,1])].T),y[Sparsity.triplet(2,2,[0,1,1],[0,0,1])]),
(in1,v1,mul(y,x**2),y*2*vertcat([x.T,x.T])),
(in1,v1,sin(x),c.diag(cos(x))),
(in1,v1,sin(x**2),c.diag(cos(x**2)*2*x)),
(in1,v1,x*y[:,0],c.diag(y[:,0])),
(in1,v1,x*y.nz[[0,1]],c.diag(y.nz[[0,1]])),
(in1,v1,x*y.nz[[1,0]],c.diag(y.nz[[1,0]])),
(in1,v1,x*y[[0,1],0],c.diag(y[[0,1],0])),
(in1,v1,x*y[[1,0],0],c.diag(y[[1,0],0])),
(in1,v1,inner_prod(x,x),(2*x).T),
(in1,v1,inner_prod(x**2,x),(3*x**2).T),
#(in1,v1,c.det(horzcat([x,DMatrix([1,2])])),DMatrix([-1,2])), not implemented
(in1,v1,f1.call(in1)[1],y),
(in1,v1,f1.call([x**2,y])[1],y*2*vertcat([x.T,x.T])),
(in1,v1,f2.call(in1)[0],DMatrix.zeros(0,2)),
(in1,v1,f2.call([x**2,y])[0],DMatrix.zeros(0,2)),
(in1,v1,f3.call(in1)[0],DMatrix.zeros(0,2)),
(in1,v1,f3.call([x**2,y])[0],DMatrix.zeros(0,2)),
(in1,v1,f4.call(in1)[0],DMatrix.zeros(0,2)),
(in1,v1,f4.call([x**2,y])[0],DMatrix.zeros(0,2)),
#(in1,v1,f1.call([x**2,[]])[1],DMatrix.zeros(2,2)),
#(in1,v1,f1.call([[],y])[1],DMatrix.zeros(2,2)),
(in1,v1,vertcat([x,DMatrix.sparse(0,1)]),DMatrix.eye(2)),
(in1,v1,(x**2).setSparse(sparse(DMatrix([0,1])).sparsity()),blockcat([[MX.sparse(1,1),MX.sparse(1,1)],[MX.sparse(1,1),2*x[1]]])),
(in1,v1,c.inner_prod(x,y[:,0]),y[:,0].T),
(in1,v1,x.nz[IMatrix([[1,0]])]*y.nz[IMatrix([[0,2]])],blockcat([[MX.sparse(1,1),y.nz[0]],[y.nz[2],MX.sparse(1,1)]])),
(in1,v1,x.nz[c.diag([1,0])]*y.nz[c.diag([0,2])],blockcat([[MX.sparse(1,1),y.nz[0]],[MX.sparse(1,1),MX.sparse(1,1)],[MX.sparse(1,1),MX.sparse(1,1)],[y.nz[2],MX.sparse(1,1)]])),
]:
print out
fun = MXFunction(inputs,[out,jac])
fun.init()
funsx = fun.expand()
funsx.init()
for i,v in enumerate(values):
fun.setInput(v,i)
funsx.setInput(v,i)
fun.evaluate()
funsx.evaluate()
self.checkarray(fun.getOutput(0),funsx.getOutput(0))
self.checkarray(fun.getOutput(1),funsx.getOutput(1))
J_ = fun.getOutput(1)
def vec(l):
ret = []
for i in l:
ret.extend(i)
return ret
storage2 = {}
storage = {}
vf_mx = None
for f in [fun,fun.expand()]:
f.init()
d = f.derivative(ndir,ndir)
d.init()
num_in = f.getNumInputs()
num_out = f.getNumOutputs()
"""# Fwd and Adjoint AD
for i,v in enumerate(values):
f.setInput(v,i)
d.setInput(v,i)
for d in range(ndir):
f.setInput(DMatrix(inputs[0].sparsity(),random.random(inputs[0].size())),num_in+d*num_in + d)
f.setAdjSeed(DMatrix(out.sparsity(),random.random(out.size())),num_in+d*num_in + 0)
f.setFwdSeed(0,1,d)
f.setAdjSeed(0,1,d)
f.evaluate()
for d in range(ndir):
seed = array(f.getFwdSeed(0,d)).ravel()
sens = array(f.getFwdSens(0,d)).ravel()
self.checkarray(sens,mul(J_,seed),"Fwd %d %s" % (d,str(type(f))))
seed = array(f.getAdjSeed(0,d)).ravel()
sens = array(f.getAdjSens(0,d)).ravel()
self.checkarray(sens,mul(J_.T,seed),"Adj %d" %d)
"""
# evalThings
for sym, Function in [(MX.sym,MXFunction),(SX.sym,SXFunction)]:
if isinstance(f, MXFunction) and Function is SXFunction: continue
if isinstance(f, SXFunction) and Function is MXFunction: continue
# dense
for spmod,spmod2 in itertools.product(spmods,repeat=2):
fseeds = [[sym("f",spmod(f.getInput(i)).sparsity()) for i in range(f.getNumInputs())] for d in range(ndir)]
aseeds = [[sym("a",spmod2(f.getOutput(i)).sparsity()) for i in range(f.getNumOutputs())] for d in range(ndir)]
inputss = [sym("i",f.input(i).sparsity()) for i in range(f.getNumInputs())]
with internalAPI():
res,fwdsens,adjsens = f.callDerivative(inputss,fseeds,aseeds,True)
fseed = [DMatrix(fseeds[d][0].sparsity(),random.random(fseeds[d][0].size())) for d in range(ndir) ]
aseed = [DMatrix(aseeds[d][0].sparsity(),random.random(aseeds[d][0].size())) for d in range(ndir) ]
vf = Function(inputss+vec([fseeds[i]+aseeds[i] for i in range(ndir)]),list(res) + vec([list(fwdsens[i])+list(adjsens[i]) for i in range(ndir)]))
vf.init()
for i,v in enumerate(values):
vf.setInput(v,i)
offset = len(inputss)
for d in range(ndir):
vf.setInput(fseed[d],offset+0)
for i in range(len(values)-1):
vf.setInput(0,offset+i+1)
offset += len(inputss)
vf.setInput(aseed[d],offset+0)
vf.setInput(0,offset+1)
offset+=2
assert(offset==vf.getNumInputs())
vf.evaluate()
offset = len(res)
for d in range(ndir):
seed = array(fseed[d]).ravel()
sens = array(vf.getOutput(offset+0)).ravel()
offset+=len(inputss)
self.checkarray(sens,mul(J_,seed),"eval Fwd %d %s" % (d,str(type(f))+str(sym)))
seed = array(aseed[d]).ravel()
sens = array(vf.getOutput(offset+0)).ravel()
offset+=len(inputss)
self.checkarray(sens,mul(J_.T,seed),"eval Adj %d %s" % (d,str([vf.getOutput(i) for i in range(vf.getNumOutputs())])))
assert(offset==vf.getNumOutputs())
# Complete random seeding
random.seed(1)
for i in range(vf.getNumInputs()):
vf.setInput(DMatrix(vf.input(i).sparsity(),random.random(vf.input(i).size())),i)
vf.evaluate()
storagekey = (spmod,spmod2)
if not(storagekey in storage):
storage[storagekey] = []
storage[storagekey].append([vf.getOutput(i) for i in range(vf.getNumOutputs())])
# Added to make sure that the same seeds are used for SX and MX
if Function is MXFunction:
vf_mx = vf
# Second order sensitivities
for sym2, Function2 in [(MX.sym,MXFunction),(SX.sym,SXFunction)]:
if isinstance(vf, MXFunction) and Function2 is SXFunction: continue
if isinstance(vf, SXFunction) and Function2 is MXFunction: continue
for spmod_2,spmod2_2 in itertools.product(spmods,repeat=2):
fseeds2 = [[sym2("f",vf_mx.input(i).sparsity()) for i in range(vf.getNumInputs())] for d in range(ndir)]
aseeds2 = [[sym2("a",vf_mx.output(i).sparsity()) for i in range(vf.getNumOutputs()) ] for d in range(ndir)]
inputss2 = [sym2("i",vf_mx.input(i).sparsity()) for i in range(vf.getNumInputs())]
with internalAPI():
res2,fwdsens2,adjsens2 = vf.callDerivative(inputss2,fseeds2,aseeds2,True)
vf2 = Function2(inputss2+vec([fseeds2[i]+aseeds2[i] for i in range(ndir)]),list(res2) + vec([list(fwdsens2[i])+list(adjsens2[i]) for i in range(ndir)]))
vf2.init()
random.seed(1)
for i in range(vf2.getNumInputs()):
vf2.setInput(DMatrix(vf2.input(i).sparsity(),random.random(vf2.input(i).size())),i)
vf2.evaluate()
storagekey = (spmod,spmod2)
if not(storagekey in storage2):
storage2[storagekey] = []
storage2[storagekey].append([vf2.getOutput(i) for i in range(vf2.getNumOutputs())])
# Remainder of eval testing
for store,order in [(storage,"first-order"),(storage2,"second-order")]:
for stk,st in store.items():
for i in range(len(st)-1):
for k,(a,b) in enumerate(zip(st[0],st[i+1])):
if b.numel()==0 and sparse(a).size()==0: continue
if a.numel()==0 and sparse(b).size()==0: continue
self.checkarray(sparse(a),sparse(b),("%s, output(%d)" % (order,k))+str(vf2.getInput(0)))
for f in [fun.expand(),fun]:
# jacobian()
for mode in ["forward","reverse"]:
f.setOption("ad_mode",mode)
f.init()
Jf=f.jacobian(0,0)
Jf.init()
for i,v in enumerate(values):
Jf.setInput(v,i)
Jf.evaluate()
self.checkarray(Jf.getOutput(),J_)
self.checkarray(DMatrix(Jf.output().sparsity(),1),DMatrix(J_.sparsity(),1),str(out)+str(mode))
self.checkarray(DMatrix(f.jacSparsity(),1),DMatrix(J_.sparsity(),1))
# Scalarized
if out.isEmpty(): continue
s_i = out.sparsity().row()[0]
s_j = out.sparsity().getCol()[0]
s_k = s_i*out.size2()+s_j
fun = MXFunction(inputs,[out[s_i,s_j],jac[s_k,:].T])
fun.init()
for i,v in enumerate(values):
fun.setInput(v,i)
fun.evaluate()
J_ = fun.getOutput(1)
for f in [fun,fun.expand()]:
# gradient()
for mode in ["forward","reverse"]:
f.setOption("ad_mode",mode)
f.init()
Gf=f.gradient(0,0)
Gf.init()
for i,v in enumerate(values):
Gf.setInput(v,i)
Gf.evaluate()
self.checkarray(Gf.getOutput(),J_,failmessage=("mode: %s" % mode))
#self.checkarray(DMatrix(Gf.output().sparsity(),1),DMatrix(J_.sparsity(),1),str(mode)+str(out)+str(type(fun)))
H_ = None
for f in [fun,fun.expand()]:
# hessian()
for mode in ["forward","reverse"]:
f.setOption("ad_mode",mode)
f.init()
Hf=f.hessian(0,0)
Hf.init()
for i,v in enumerate(values):
Hf.setInput(v,i)
Hf.evaluate()
if H_ is None:
H_ = Hf.getOutput()
self.checkarray(Hf.getOutput(),H_,failmessage=("mode: %s" % mode))