def createReducedMatrices(U_POD,U_DEIM,PT,p,path):
''' creates 12 matrices for the reduced system with V as basis and saves them
Parameters
-------
U_POD : 2-D array
pod base vectors
U_DEIM : 2-D array
deim base vectors
PT : 2-D array
DEIM index matrix
p : array
DEIM indices
path : str
path to directory to save the base matrices
Returns
-------
saves the base matrices in the path directory
'''
np.save(path + "U_POD_truncated.npy",U_POD)
np.save(path + "U_DEIM_truncated.npy",U_DEIM)
np.save(path + "PT.npy",PT)
np.save(path + "p.npy",p)
P = np.dot(U_DEIM,la.inv(np.dot(PT.T,U_DEIM)))
for i in range(0,12):
Ai = io.read_PETSc_mat('data/TMM/2.8/Transport/Matrix5_4/1dt/Ai_'+str(i).zfill(2)+'.petsc')
Ae = io.read_PETSc_mat('data/TMM/2.8/Transport/Matrix5_4/1dt/Ae_'+str(i).zfill(2)+'.petsc')
#Ai = sp.sparse.block_diag((Ai,Ai))y
#Ae = sp.sparse.block_diag((Ae,Ae))
Ar = U_POD.T.dot(Ai.dot(Ae.dot(U_POD)))
Pr = U_POD.T.dot(Ai.dot(P))
np.save(path + 'reduced_A' +str(i).zfill(2), Ar)
np.save(path + 'reduced_P' +str(i).zfill(2), Pr)
def test(self,nspinup,ntimestep):
y = np.ones(52749,dtype=np.float_) * 2.17
#load high dim matrices
Ae = []
Ai = []
print("load matrices")
for i in range(12):
print(i)
Ai.append(io.read_PETSc_mat('data/TMM/2.8/Transport/Matrix5_4/1dt/Ai_'+str(i).zfill(2)+'.petsc'))
Ae.append(io.read_PETSc_mat('data/TMM/2.8/Transport/Matrix5_4/1dt/Ae_'+str(i).zfill(2)+'.petsc'))
#check if q is zero in fortran routine
q = np.zeros(52749,dtype=np.float_)
t = 0
#q_select = np.zeros(p.shape[0],dtype=np.float_)
starttime =time.time()
for spin in range(nspinup):
for step in range(ntimestep):
t = np.fmod(0 + step*self.dt, 1.0);
counter = 0
for i in range(4448):
self.bc[0] = self.lat[i]
self.bc[1] = self.interpolation_a[step]*self.fice[i,self.interpolation_j[step]] + self.interpolation_b[step]*self.fice[i,self.interpolation_k[step]]
q[self.J[i]:self.J[i+1]] = modeln.metos3dbgc(self.dt,t,y[self.J[i]:self.J[i+1]],self.u,self.bc,self.dc[self.J[i]:self.J[i+1],:])[:,0]
#print("q:", q[self.J[i]:self.J[i+1]])
Aiint = self.interpolation_a[step]*Ai[self.interpolation_j[step]] + self.interpolation_b[step]*Ai[self.interpolation_k[step]]
Aeint = self.interpolation_a[step]*Ae[self.interpolation_j[step]] + self.interpolation_b[step]*Ae[self.interpolation_k[step]]
#Aey = io.read_PETSc_vec("simulation/compare/Aey_sp%.4dts%.4dN.petsc" % (spin,step))
#Aeq = io.read_PETSc_vec("simulation/compare/Ae+q_sp%.4dts%.4dN.petsc" % (spin,step))
#q_v = io.read_PETSc_vec("simulation/compare/q_sp%.4dts%.4dN.petsc" % (spin,step))
#Aiint_metos = io.read_PETSc_mat("simulation/compare/A%.4d.petsc" % (step))
#print("norm A interplaton: ", (Aiint-Aiint_metos))
ye = Aeint.dot(y)
yeq = ye +q
#io.write_PETSc_vec(yeq,"yeqts%.4dN.petsc" % step)
# A_saved = io.read_PETSc_mat("Ai_interpolatedts%.4d.petsc" % step)
y_j = Aiint.dot(yeq)
#print("q:", np.linalg.norm(q_v-q))
#print("before Ai:", np.linalg.norm(Aeq-yeq))
#print(step,spin)
if(step == 2879):
v = io.read_PETSc_vec("simulation/POD_DEIM/sp%.4dts%.4dN.petsc" % (spin,step))
print("time: ", time.time() - starttime ,spin,step,np.linalg.norm(y-v))
io.write_PETSc_vec(y_j,"simulation/compare/exp01/sp%.4dts%.4dN.petsc" % (spin,step))
starttime = time.time()
#io.write_PETSc_mat(Aiint,"Ai%.4dN.petsc" % step)
# print(Aiint-A_saved.T)
y = y_j
def Init(self):
#boundary and domain condition
self.lat = io.read_PETSc_vec(self.config["-Metos3DBoundaryConditionInputDirectory"][0] + self.config["-Metos3DLatitudeFileFormat"][0])
dz = io.read_PETSc_vec(self.config["-Metos3DDomainConditionInputDirectory"][0] + self.config["-Metos3DLayerHeightFileFormat"][0])
z = io.read_PETSc_vec(self.config["-Metos3DDomainConditionInputDirectory"][0] + self.config["-Metos3DLayerDepthFileFormat"][0])
self.lsm = io.read_PETSc_mat(self.config["-Metos3DProfileInputDirectory"][0] + self.config["-Metos3DProfileMaskFile"][0])
self.fice = np.zeros((self.profiles,np.int_(self.config["-Metos3DIceCoverCount"][0])),dtype=np.float_)
for i in range(np.int_(self.config["-Metos3DIceCoverCount"][0])):
self.fice[:,i] = io.read_PETSc_vec(self.config["-Metos3DBoundaryConditionInputDirectory"][0] + (self.config["-Metos3DIceCoverFileFormat"][0] % i))
self.bc = np.zeros(2,dtype=np.float_)
self.dc = np.zeros((self.ny,2),dtype=np.float_)
self.dc[:,0] = z
self.dc[:,1] = dz
self.u = np.array(self.config["-Metos3DParameterValue"],dtype=np.float_)
self.dt = np.float_(self.config["-Metos3DTimeStep"][0])
self.nspinup = np.int_(self.config["-Metos3DSpinupCount"][0])
self.ntimestep = np.int_(self.config["-Metos3DTimeStepCount"][0])
self.matrixCount = np.int_(self.config["-Metos3DMatrixCount"][0])
self.U_PODN = np.load(self.config["-Metos3DMatrixInputDirectory"][0] +'N/'+ self.config["-Metos3DMatrixPODFileFormat"][0])
self.U_PODDOP = np.load(self.config["-Metos3DMatrixInputDirectory"][0] +'DOP/'+ self.config["-Metos3DMatrixPODFileFormat"][0])
self.U_DEIMN = np.load(self.config["-Metos3DMatrixInputDirectory"][0] +'N/'+ self.config["-Metos3DMatrixDEIMFileFormat"][0])
self.U_DEIMDOP = np.load(self.config["-Metos3DMatrixInputDirectory"][0] +'DOP/'+ self.config["-Metos3DMatrixDEIMFileFormat"][0])
self.DEIM_IndicesN = np.load(self.config["-Metos3DMatrixInputDirectory"][0] +'N/'+ self.config["-Metos3DDEIMIndicesFileFormat"][0])
self.DEIM_IndicesDOP = np.load(self.config["-Metos3DMatrixInputDirectory"][0] +'DOP/'+ self.config["-Metos3DDEIMIndicesFileFormat"][0])
self.AN = np.ndarray(shape=(self.matrixCount,self.U_PODN.shape[1],self.U_PODN.shape[1]), dtype=np.float_, order='C')
self.ADOP = np.ndarray(shape=(self.matrixCount,self.U_PODDOP.shape[1],self.U_PODDOP.shape[1]), dtype=np.float_, order='C')
for i in range(0,self.matrixCount):
self.AN[i] = np.load(self.config["-Metos3DMatrixInputDirectory"][0] +'N/'+ self.config["-Metos3DMatrixReducedFileFormat"][0] % i)
self.ADOP[i] = np.load(self.config["-Metos3DMatrixInputDirectory"][0] +'DOP/'+ self.config["-Metos3DMatrixReducedFileFormat"][0] % i)
self.PN = np.ndarray(shape=(self.matrixCount,self.U_PODN.shape[1],self.U_DEIMN.shape[1]), dtype=np.float_, order='C')
self.PDOP = np.ndarray(shape=(self.matrixCount,self.U_PODDOP.shape[1],self.U_DEIMDOP.shape[1]), dtype=np.float_, order='C')
for i in range(0,self.matrixCount):
self.PN[i] = np.load(self.config["-Metos3DMatrixInputDirectory"][0] +'N/'+ self.config["-Metos3DMatrixReducedDEINFileFormat"][0] % i)
self.PDOP[i] = np.load(self.config["-Metos3DMatrixInputDirectory"][0] +'DOP/'+ self.config["-Metos3DMatrixReducedDEINFileFormat"][0] % i)
#precomputin the interplaton indices for a year
[self.interpolation_a,self.interpolation_b,self.interpolation_j,self.interpolation_k] = util.linearinterpolation(2880,12,0.0003472222222222)
self.yN = np.ones(self.ny,dtype=np.float_) * np.float_(self.config["-Metos3DTracerInitValue"])[0]
self.yDOP = np.ones(self.ny,dtype=np.float_) * np.float_(self.config["-Metos3DTracerInitValue"])[1]
self.y_redN = np.dot(self.U_PODN.T,self.yN)
self.y_redDOP = np.dot(self.U_PODDOP.T,self.yDOP)
self.qN = np.zeros(self.DEIM_IndicesN.shape[0],dtype=np.float_)
self.qDOP = np.zeros(self.DEIM_IndicesDOP.shape[0],dtype=np.float_)
self.J,self.PJ = util.generateIndicesForNonlinearFunction(self.lsm,self.profiles,self.ny)
self.out_pathN = self.config["-Metos3DTracerOutputDirectory"][0] +self.config["-Metos3DSpinupMonitorFileFormatPrefix"][0] + self.config["-Metos3DSpinupMonitorFileFormatPrefix"][1] +self.config["-Metos3DTracerOutputFile"][0]
self.out_pathDOP = self.config["-Metos3DTracerOutputDirectory"][0] +self.config["-Metos3DSpinupMonitorFileFormatPrefix"][0] + self.config["-Metos3DSpinupMonitorFileFormatPrefix"][1] +self.config["-Metos3DTracerOutputFile"][1]
self.monitor_path = self.config["-Metos3DTracerMointorDirectory"][0] +self.config["-Metos3DSpinupMonitorFileFormatPrefix"][0] + self.config["-Metos3DSpinupMonitorFileFormatPrefix"][1] +self.config["-Metos3DTracerOutputFile"][0]
def Init(self):
#boundary and domain condition
self.lat = io.read_PETSc_vec(self.config["-Metos3DBoundaryConditionInputDirectory"][0] + self.config["-Metos3DLatitudeFileFormat"][0])
dz = io.read_PETSc_vec(self.config["-Metos3DDomainConditionInputDirectory"][0] + self.config["-Metos3DLayerHeightFileFormat"][0])
z = io.read_PETSc_vec(self.config["-Metos3DDomainConditionInputDirectory"][0] + self.config["-Metos3DLayerDepthFileFormat"][0])
self.lsm = io.read_PETSc_mat(self.config["-Metos3DProfileInputDirectory"][0] + self.config["-Metos3DProfileMaskFile"][0])
self.fice = np.zeros((self.profiles,np.int_(self.config["-Metos3DIceCoverCount"][0])),dtype=np.float_)
for i in range(np.int_(self.config["-Metos3DIceCoverCount"][0])):
self.fice[:,i] = io.read_PETSc_vec(self.config["-Metos3DBoundaryConditionInputDirectory"][0] + (self.config["-Metos3DIceCoverFileFormat"][0] % i))
self.bc = np.zeros(2,dtype=np.float_)
self.dc = np.zeros((self.ny,2),dtype=np.float_)
self.dc[:,0] = z
self.dc[:,1] = dz
self.u = np.array(self.config["-Metos3DParameterValue"],dtype=np.float_)
self.dt = np.float_(self.config["-Metos3DTimeStep"][0])
self.nspinup = np.int_(self.config["-Metos3DSpinupCount"][0])
self.ntimestep = np.int_(self.config["-Metos3DTimeStepCount"][0])
self.matrixCount = np.int_(self.config["-Metos3DMatrixCount"][0])
self.U_POD = np.load(self.config["-Metos3DMatrixInputDirectory"][0] + self.config["-Metos3DMatrixPODFileFormat"][0])
self.U_DEIM = np.load(self.config["-Metos3DMatrixInputDirectory"][0] + self.config["-Metos3DMatrixDEIMFileFormat"][0])
self.DEIM_Indices = np.load(self.config["-Metos3DMatrixInputDirectory"][0] + self.config["-Metos3DDEIMIndicesFileFormat"][0])
self.A = np.ndarray(shape=(self.matrixCount,self.U_POD.shape[1],self.U_POD.shape[1]), dtype=np.float_, order='C')
for i in range(0,self.matrixCount):
self.A[i] = np.load(self.config["-Metos3DMatrixInputDirectory"][0] + self.config["-Metos3DMatrixReducedFileFormat"][0] % i)
self.P = np.ndarray(shape=(self.matrixCount,self.U_POD.shape[1],self.U_DEIM.shape[1]), dtype=np.float_, order='C')
for i in range(0,self.matrixCount):
self.P[i] = np.load(self.config["-Metos3DMatrixInputDirectory"][0] + self.config["-Metos3DMatrixReducedDEINFileFormat"][0] % i)
#precomputin the interplaton indices for a year
[self.interpolation_a,self.interpolation_b,self.interpolation_j,self.interpolation_k] = util.linearinterpolation(2880,12,0.0003472222222222)
self.y = np.ones(self.ny,dtype=np.float_) * np.float_(self.config["-Metos3DTracerInitValue"])[0]
self.y_red = np.dot(self.U_POD.T,self.y)
self.q = np.zeros(self.DEIM_Indices.shape[0],dtype=np.float_)
self.J,self.PJ = util.generateIndicesForNonlinearFunction(self.lsm,self.profiles,self.ny)
self.out_path = self.config["-Metos3DTracerOutputDirectory"][0] +self.config["-Metos3DSpinupMonitorFileFormatPrefix"][0] + self.config["-Metos3DSpinupMonitorFileFormatPrefix"][1] +self.config["-Metos3DTracerOutputFile"][0]
self.monitor_path = self.config["-Metos3DTracerMointorDirectory"][0] +self.config["-Metos3DSpinupMonitorFileFormatPrefix"][0] + self.config["-Metos3DSpinupMonitorFileFormatPrefix"][1] +self.config["-Metos3DTracerOutputFile"][0]