def smoothing_Laplacian_rx0(MSK, Hobs, rx0max):
"""
This program use Laplacian filter.
The bathymetry is optimized for a given rx0 factor by doing an iterated
sequence of Laplacian filterings.
Usage:
RetBathy = smoothing_Laplacian_rx0(MSK, Hobs, rx0max)
---MSK(eta_rho,xi_rho) is the mask of the grid
1 for sea
0 for land
---Hobs(eta_rho,xi_rho) is the raw depth of the grid
---rx0max is the target rx0 roughness factor
"""
eta_rho, xi_rho = Hobs.shape
ListNeigh = np.array([[1, 0], [0, 1], [-1, 0], [0, -1]])
RetBathy = Hobs.copy()
tol = 0.00001
WeightMatrix = np.zeros((eta_rho, xi_rho))
for iEta in range(eta_rho):
for iXi in range(xi_rho):
WeightSum = 0
for ineigh in range(4):
iEtaN = iEta + ListNeigh[ineigh, 0]
iXiN = iXi + ListNeigh[ineigh, 1]
if (iEtaN <= eta_rho-1 and iEtaN >= 0 and iXiN <= xi_rho-1 \
and iXiN >= 0 and MSK[iEtaN,iXiN] == 1):
WeightSum = WeightSum + 1
WeightMatrix[iEta, iXi] = WeightSum
Iter = 1
NumberDones = np.zeros((eta_rho, xi_rho))
while (True):
RoughMat = bathy_tools.RoughnessMatrix(RetBathy, MSK)
Kbefore = np.where(RoughMat > rx0max)
nbPtBefore = np.size(Kbefore, 1)
realR = RoughMat.max()
TheCorrect = np.zeros((eta_rho, xi_rho))
IsFinished = 1
nbPointMod = 0
AdditionalDone = np.zeros((eta_rho, xi_rho))
for iEta in range(eta_rho):
for iXi in range(xi_rho):
Weight = 0
WeightSum = 0
for ineigh in range(4):
iEtaN = iEta + ListNeigh[ineigh, 0]
iXiN = iXi + ListNeigh[ineigh, 1]
if (iEtaN <= eta_rho-1 and iEtaN >= 0 and iXiN <= xi_rho-1 \
and iXiN >= 0 and MSK[iEtaN,iXiN] == 1):
Weight = Weight + RetBathy[iEtaN, iXiN]
AdditionalDone[iEtaN, iXiN] = AdditionalDone[
iEtaN, iXiN] + NumberDones[iEta, iXi]
TheWeight = WeightMatrix[iEta, iXi]
WeDo = 0
if TheWeight > tol:
if RoughMat[iEta, iXi] > rx0max:
WeDo = 1
if NumberDones[iEta, iXi] > 0:
WeDo = 1
if WeDo == 1:
IsFinished = 0
TheDelta = (Weight - TheWeight * RetBathy[iEta, iXi]) / (
2 * TheWeight)
TheCorrect[iEta, iXi] = TheCorrect[iEta, iXi] + TheDelta
nbPointMod = nbPointMod + 1
NumberDones[iEta, iXi] = 1
NumberDones = NumberDones + AdditionalDone
RetBathy = RetBathy + TheCorrect
NewRoughMat = bathy_tools.RoughnessMatrix(RetBathy, MSK)
Kafter = np.where(NewRoughMat > rx0max)
nbPtAfter = np.size(Kafter, 1)
TheProd = (RoughMat > rx0max) * (NewRoughMat > rx0max)
nbPtInt = TheProd.sum()
if (nbPtInt == nbPtAfter and nbPtBefore == nbPtAfter):
eStr = ' no erase'
else:
eStr = ''
NumberDones = np.zeros((eta_rho, xi_rho))
print 'Iteration #', Iter
print 'current r=', realR, ' nbPointMod=', nbPointMod, eStr
print ' '
Iter = Iter + 1
if (IsFinished == 1):
break
return RetBathy
def LP_smoothing_rx0_heuristic(MSK, Hobs, rx0max, SignConst, AmpConst):
"""
This program perform a linear programming method in order to
optimize the bathymetry for a fixed factor r.
The inequality |H(e)-H(e')| / (H(e)-H(e')) <= r where H(e)=h(e)+dh(e)
can be rewritten as two linear inequalities on dh(e) and dh(e').
The optimal bathymetry is obtain by minimising the perturbation
P = sum_e(|dh(e)| under the above inequalitie constraintes.
In order to reduce the computation time, an heurastic method is
used.
Usage:
NewBathy = LP_smoothing_rx0_heuristic(MSK, Hobs, rx0max, SignConst, AmpConst)
---MSK(eta_rho,xi_rho) is the mask of the grd
1 for sea
0 for land
---Hobs(eta_rho,xi_rho) is the raw depth of the grid
---rx0max is the target rx0 roughness factor
---SignConst(eta_rho,xi_rho) matrix of 0, +1, -1
+1 only bathymetry increase are allowed.
-1 only bathymetry decrease are allowed.
0 increase and decrease are allowed.
(put 0 if you are indifferent)
---AmpConst(eta_rho,xi_rho) matrix of reals.
coefficient alpha such that the new bathymetry should
satisfy to |h^{new} - h^{raw}| <= alpha h^{raw}
(put 10000 if you are indifferent)
"""
# the points that need to be modified
MSKbad = LP_bathy_tools.GetBadPoints(MSK, Hobs, rx0max)
eta_rho, xi_rho = MSK.shape
Kdist = 5
Kbad = np.where(MSKbad == 1)
nbKbad = np.size(Kbad,1)
ListIdx = np.zeros((eta_rho,xi_rho), dtype=np.int)
ListIdx[Kbad] = list(range(nbKbad))
ListEdges = []
nbEdge = 0
for iK in range(nbKbad):
iEta, iXi = Kbad[0][iK], Kbad[1][iK]
ListNeigh = LP_bathy_tools.Neighborhood(MSK, iEta, iXi, 2*Kdist+1)
nbNeigh = np.size(ListNeigh, 0)
for iNeigh in range(nbNeigh):
iEtaN, iXiN = ListNeigh[iNeigh]
if (MSKbad[iEtaN,iXiN] == 1):
idx = ListIdx[iEtaN,iXiN]
if (idx > iK):
nbEdge = nbEdge + 1
ListEdges.append([iK, idx])
ListEdges = np.array(ListEdges)
ListVertexStatus = LP_bathy_tools.ConnectedComponent(ListEdges, nbKbad)
nbColor = ListVertexStatus.max()
NewBathy = Hobs.copy()
for iColor in range(1,nbColor+1):
print('---------------------------------------------------------------')
MSKcolor = np.zeros((eta_rho, xi_rho))
K = np.where(ListVertexStatus == iColor)
nbK = np.size(K,1)
print('iColor = ', iColor, ' nbK = ', nbK)
for iVertex in range(nbKbad):
if (ListVertexStatus[iVertex,0] == iColor):
iEta, iXi = Kbad[0][iVertex], Kbad[1][iVertex]
MSKcolor[iEta, iXi] = 1
ListNeigh = LP_bathy_tools.Neighborhood(MSK, iEta, iXi, Kdist)
nbNeigh = np.size(ListNeigh, 0)
for iNeigh in range(nbNeigh):
iEtaN, iXiN = ListNeigh[iNeigh]
MSKcolor[iEtaN,iXiN] = 1
K = np.where(MSKcolor == 1)
MSKHobs = np.zeros((eta_rho, xi_rho))
MSKHobs[K] = Hobs[K].copy()
TheNewBathy = LP_smoothing_rx0(MSKcolor, MSKHobs, rx0max, SignConst, AmpConst)
NewBathy[K] = TheNewBathy[K].copy()
print('Final obtained bathymetry')
RMat = bathy_tools.RoughnessMatrix(NewBathy, MSK)
MaxRx0 = RMat.max()
print('rx0max = ', rx0max, ' MaxRx0 = ', MaxRx0)
return NewBathy
hgrd.lat_rho,
checkbounds=False,
masked=False,
order=0)
# Save raw bathymetry.
hraw = h.copy()
# ROMS depth is positive.
hh = -h
# Depth deeper than hmin.
h = np.where(hh < hmin, hmin, hh)
# Smooth the raw bathy using the direct iterative method from Martinho and Batteen (2006).
RoughMat = bathy_tools.RoughnessMatrix(h, hgrd.mask_rho)
print('Currently, the max roughness value is: ', RoughMat.max())
h = bathy_smoothing.smoothing_Positive_rx0(hgrd.mask_rho, h, rmax)
h = bathy_smoothing.smoothing_Laplacian_rx0(hgrd.mask_rho, h, rmax)
RoughMat = bathy_tools.RoughnessMatrix(h, hgrd.mask_rho)
print(('After the filters, the max roughness value is: ', RoughMat.max()))
hgrd.h = h
# Vertical levels.
vgrd = pyroms.vgrid.s_coordinate_4(h, theta_b, theta_s, Tcline, N, hraw=hraw)
# ROMS grid.
grd = pyroms.grid.ROMS_Grid(grd_name, hgrd, vgrd)
# Write grid to netcdf file.
pyroms.grid.write_ROMS_grid(grd, grd_final)
def LP_smoothing_rx0(MSK, Hobs, rx0max, SignConst, AmpConst):
"""
This program perform a linear programming method in order to
optimize the bathymetry for a fixed factor r.
The inequality |H(e)-H(e')| / (H(e)-H(e')) <= r where H(e)=h(e)+dh(e)
can be rewritten as two linear inequalities on dh(e) and dh(e').
The optimal bathymetry is obtain by minimising the perturbation
P = sum_e(|dh(e)| under the above inequalitie constraintes.
Usage:
NewBathy = LP_smoothing_rx0(MSK, Hobs, rx0max, SignConst, AmpConst)
---MSK(eta_rho,xi_rho) is the mask of the grd
1 for sea
0 for land
---Hobs(eta_rho,xi_rho) is the raw depth of the grid
---rx0max is the target rx0 roughness factor
---SignConst(eta_rho,xi_rho) matrix of 0, +1, -1
+1 only bathymetry increase are allowed.
-1 only bathymetry decrease are allowed.
0 increase and decrease are allowed.
(put 0 if you are indifferent)
---AmpConst(eta_rho,xi_rho) matrix of reals.
coefficient alpha such that the new bathymetry should
satisfy to |h^{new} - h^{raw}| <= alpha h^{raw}
(put 10000 if you are indifferent)
"""
eta_rho, xi_rho = MSK.shape
iList, jList, sList, Constant = LP_bathy_tools.GetIJS_rx0(MSK, Hobs, rx0max)
iListApp, jListApp, sListApp, ConstantApp = LP_bathy_tools.GetIJS_maxamp(MSK, Hobs, AmpConst)
iList, jList, sList, Constant = LP_bathy_tools.MergeIJS_listings(iList, jList, sList, Constant, iListApp, jListApp, sListApp, ConstantApp)
iListApp, jListApp, sListApp, ConstantApp = LP_bathy_tools.GetIJS_signs(MSK, SignConst)
iList, jList, sList, Constant = LP_bathy_tools.MergeIJS_listings(iList, jList, sList, Constant, iListApp, jListApp, sListApp, ConstantApp)
TotalNbVert = int(MSK.sum())
ObjectiveFct = np.zeros((2*TotalNbVert,1))
for iVert in range(TotalNbVert):
ObjectiveFct[TotalNbVert+iVert,0] = 1
ValueFct, ValueVar, testfeasibility = LP_tools.SolveLinearProgram(iList, jList, sList, Constant, ObjectiveFct)
if (testfeasibility == 0):
NewBathy = NaN * np.ones((eta_rho,xi_rho))
raise ValueError('Feasibility test failed. testfeasibility = 0.')
correctionBathy = np.zeros((eta_rho,xi_rho))
nbVert = 0
for iEta in range(eta_rho):
for iXi in range(xi_rho):
if (MSK[iEta,iXi] == 1):
correctionBathy[iEta,iXi] = ValueVar[nbVert]
nbVert = nbVert + 1
NewBathy = Hobs + correctionBathy
RMat = bathy_tools.RoughnessMatrix(NewBathy, MSK)
MaxRx0 = RMat.max()
print('rx0max = ', rx0max, ' MaxRx0 = ', MaxRx0)
return NewBathy
