def AofT(time,T, ai, taui):
    return ai*np.exp(-time/taui)/(1.+np.exp(-T/(2*taui)))

from SimPEG import *
import sys
sys.path.append("./DoubleLog/")
from plotting import mapDat

class LinearSurvey(Survey.BaseSurvey):
    nD = None
    def __init__(self, time, **kwargs): 
        self.time = time
        self.nD = time.size
        
    def projectFields(self, u):
        return u

class LinearProblem(Problem.BaseProblem):

    surveyPair = LinearSurvey

    def __init__(self, mesh, G, **kwargs):
        Problem.BaseProblem.__init__(self, mesh, **kwargs)
        self.G = G

    def fields(self, m, u=None):
        return self.G.dot(m)

    def Jvec(self, m, v, u=None):
        return self.G.dot(v)

    def Jtvec(self, m, v, u=None):
        return self.G.T.dot(v)


"""
Explanation: $$A(t,T) = \Sigma_i A_i P(dI/dt (t)\otimes e^{-t/\tau_i}/\tau_i)$$
End of explanation
"""


time = np.cumsum(np.r_[0., 1e-5*np.ones(10), 5e-5*np.ones(10), 1e-4*np.ones(10), 5e-4*np.ones(10), 1e-3*np.ones(10)])
# time = np.cumsum(np.r_[0., 1e-5*np.ones(10), 5e-5*np.ones(10),1e-4*np.ones(5)])
M = 41
tau = np.logspace(-4.1, -1, M)

from SimPEG import Mesh
from simpegem1d.Waveform import SineFun, SineFunDeriv, CausalConv
dt = 1e-5
t0 = 0.003
meshtime = Mesh.TensorMesh([np.ones(2**12-1)*dt], x0="0")
P = meshtime.getInterpolationMat(time+t0, 'N')
time_conv = meshtime.gridN
currentderiv = SineFunDeriv(time_conv, t0)
current = SineFun(time_conv, t0)

temp = np.exp(-time_conv/1e-2)/1e-2
out = CausalConv(temp, currentderiv, time_conv)
plt.plot(time_conv, currentderiv)

plt.plot(time_conv, out)

actind = time_conv>t0

plt.plot(time_conv[actind]-t0, -out[actind])
plt.plot(time, -P*out, '.')

time_conv.min(), time_conv.max()

N = time.size
A = np.zeros((N, M))
for j in range(M):
    A[:,j] = P*(CausalConv(np.exp(-time_conv/tau[j]), -currentderiv, time_conv))

mtrue = np.zeros(M)

np.random.seed(1)
inds = np.random.random_integers(0, 41, size=5)
mtrue[inds] = np.r_[0.1, 2, 1, 4, 5]

out = np.dot(A,mtrue)

fig = plt.figure(figsize=(6,4.5))
ax = plt.subplot(111)

for i, ind in enumerate(inds):
    temp, dum, dum = mapDat(mtrue[inds][i]*np.exp(-time/tau[ind]), 1e-5, stretch=2)
    plt.semilogx(time, temp, 'k', alpha = 0.5)    
outmap, ticks, tickLabels = mapDat(out, 1e-5, stretch=2)    
ax.semilogx(time, outmap, 'k', lw=2)
ax.set_yticks(ticks)
ax.set_yticklabels(tickLabels)
# ax.set_ylim(ticks.min(), ticks.max())
ax.set_ylim(ticks.min(), ticks.max())
ax.set_xlim(time.min(), time.max())
ax.grid(True)

# from pymatsolver import MumpsSolver

mesh = Mesh.TensorMesh([M])
prob = LinearProblem(mesh, A)
survey = LinearSurvey(time)
survey.pair(prob)
survey.makeSyntheticData(mtrue, std=0.01)
# survey.dobs = out
reg = Regularization.BaseRegularization(mesh)
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = 1./(0.05*abs(survey.dobs)+0.05*1e-2)
opt = Optimization.ProjectedGNCG(maxIter=20)
# opt = Optimization.InexactGaussNewton(maxIter=20)
opt.lower = -1e-10
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.beta = 1e-4
beta = Directives.BetaSchedule()
beta.coolingFactor = 2
target = Directives.TargetMisfit()
inv = Inversion.BaseInversion(invProb, directiveList=[beta, target])
m0 = np.zeros_like(survey.mtrue)
mrec = inv.run(m0)

plt.semilogx(tau, mtrue, '.')
plt.semilogx(tau, mrec, '.')

fig = plt.figure(figsize=(6,4.5))
ax = plt.subplot(111)
obsmap, ticks, tickLabels = mapDat(survey.dobs, 1e0, stretch=2)    
predmap, dum, dum = mapDat(invProb.dpred, 1e0, stretch=2)    
ax.loglog(time, survey.dobs, 'k', lw=2)
ax.loglog(time, invProb.dpred, 'k.', lw=2)
# ax.set_yticks(ticks)
# ax.set_yticklabels(tickLabels)
# ax.set_ylim(ticks.min(), ticks.max())
# ax.set_ylim(ticks.min(), ticks.max())
ax.set_xlim(time.min(), time.max())
ax.grid(True)

"""
Explanation: Simple exponential basis
$$ \mathbf{A}\mathbf{\alpha} = \mathbf{d}$$
End of explanation
"""


