def CSL(alphaS, alphaL, K, bkdir):
Ne, Nd = K.shape
H = np.eye((Ne))- np.ones((Ne, Ne))/Ne
K = np.dot(H, K)
for dsafilename1 in glob.iglob(bkdir+"/*.Adjacents_1_*"):
A_local1 = read_bk.dsa(dsafilename1)
for dsafilename2 in glob.iglob(bkdir+"/*.Adjacents_2_*"):
A_local2 = read_bk.dsa(dsafilename2)
#dsafilename1 = bkdir+prefix+'Adjacents_1_'+scenario+'.dsa'
#dsafilename2 = bkdir+prefix+'Adjacents_2_'+scenario+'.dsa'
nD1 = A_local1.shape[0]-1
nD2 = A_local2.shape[0]-1
Nei1 = A_local1[:-1, :-1]
Nei2 = A_local2[:-1, :-1]
r0 = np.concatenate((Nei1, np.zeros((nD1,nD2))), axis=1)
r1 = np.concatenate((np.zeros((nD2,nD1)), Nei2), axis=1)
Neighbor = np.concatenate((r0, r1), axis=0)
B = np.identity(Nd)
for i in range(Nd):
Ni = np.sum(Neighbor[i,:])-1
if Ni > 0:
B[i,:] = -Neighbor[i,:]/Ni
B[i,i] = 1
else:
B[i,:] = -1/(Nd-1)
B[i,i] = 1
svdK = np.linalg.svd(K, compute_uv=False)
svdB = np.linalg.svd(B, compute_uv=False)
condNum = svdK[0]/svdB[0]
#BigK = np.concatenate((K, alpha * B), axis=0)
#KtK = np.dot(BigK.T, BigK)
I = np.identity(Nd)
BigK = np.concatenate((K, alphaS*svdK[0]*I, alphaL*condNum*B), axis=0)
KtK = np.dot(BigK.T, BigK)
T = np.dot(np.linalg.inv(KtK), BigK.T)
Imatrix = T[:, :Ne]
return Imatrix
def tCSL(alphaS, alphaL, alphaT, K, bkdir):#, prefix, scenario):
Ne, Nd = K.shape
H = np.eye((Ne))- np.ones((Ne, Ne))/Ne
K = np.dot(H, K)
for dsafilename1 in glob.iglob(bkdir+"/*.Adjacents_1_*"):
A_local1 = read_bk.dsa(dsafilename1)
for dsafilename2 in glob.iglob(bkdir+"/*.Adjacents_2_*"):
A_local2 = read_bk.dsa(dsafilename2)
#dsafilename1 = bkdir+prefix+'Adjacents_1_'+scenario+'.dsa'
#A_local1 = read_dsa.read_dsa(dsafilename1)
#dsafilename2 = bkdir+prefix+'Adjacents_2_'+scenario+'.dsa'
#A_local2 = read_dsa.read_dsa(dsafilename2)
nD1 = A_local1.shape[0]-1
nD2 = A_local2.shape[0]-1
Nei1 = A_local1[:-1, :-1]
Nei2 = A_local2[:-1, :-1]
r0 = np.concatenate((Nei1, np.zeros((nD1,nD2))), axis=1)
r1 = np.concatenate((np.zeros((nD2,nD1)), Nei2), axis=1)
Neighbor = np.concatenate((r0, r1), axis=0)
B = np.identity(Nd)
for i in range(Nd):
Ni = np.sum(Neighbor[i,:])-1
if Ni > 0:
B[i,:] = -Neighbor[i,:]/Ni
B[i,i] = 1
Nd3 = 3 * Nd
K3 = np.concatenate((np.zeros((Ne,Nd)), K, np.zeros((Ne,Nd))), axis=1)
B3 = np.kron(np.identity(3), B)
I3 = np.identity(Nd3)
Bt = np.concatenate((-np.identity(Nd), 2*np.identity(Nd), -np.identity(Nd)), axis=1)
BigK = np.concatenate((K3, alphaS * I3, alphaL * B3, alphaT * Bt), axis=0)
KtK = np.dot(BigK.T, BigK)
T = np.dot(np.linalg.inv(KtK), BigK.T)
Imatrix = T[Nd:(2*Nd), :Ne]
return Imatrix
def CSL(phi, K, bkdir):
## alphaS
Logalpha = np.arange(-6, 7, 1)
nLcurve = len(Logalpha)
LcurveS = [] # Lcurve Residual L2
for i in Logalpha:
alphai = 10 ** i
Imat = Imatrix.MN(alphai, K)
beta = np.dot(Imat, phi)
phihat = np.dot(K, beta)
phidiff = phi-phihat
Resid2 = np.sqrt(sum(phidiff*phidiff))
L2 = np.sqrt(sum(beta*beta))
LcurveS = np.concatenate((LcurveS, [i, Resid2, L2]), axis=0)
LcurveS = LcurveS.reshape(nLcurve,3)
LcurveS0 = np.array([LcurveS[:,0], LcurveS[:,1]/max(LcurveS[:,1]), LcurveS[:,2]/max(LcurveS[:,2])])
LcurveS = LcurveS0.T
Resid2D1 = np.diff(LcurveS[:,1]); Resid2D2 = np.diff(Resid2D1);
L2D1 = np.diff(LcurveS[:,2]); L2D2 = np.diff(L2D1);
pho = np.array([LcurveS[:,1], np.concatenate((Resid2D1,[0])), np.concatenate((Resid2D2,[0,0]))])
pho = pho.T
eta = np.array([LcurveS[:,2], np.concatenate((L2D1,[0])), np.concatenate((L2D2,[0,0]))])
eta = eta.T
nume =(np.multiply(pho[:,1], eta[:,2]) - np.multiply(pho[:,2], eta[:,1]))
denume = np.power((np.multiply(pho[:,1], pho[:,1]) - np.multiply(eta[:,1],eta[:,1])), 3/2)
kappa = np.array(np.divide(nume,denume))
maxKappa = np.where(abs(kappa) == np.nanmax(abs(kappa)))[0]
logalphaS = LcurveS[maxKappa[0],0]
figLC, axLC = plt.subplots(2,2)
axLC[0,0].plot(LcurveS[:,0], LcurveS[:,1]);
axLC[0,0].set_xlim((Logalpha[0],Logalpha[-1]));
axLC[0,0].set_xlabel('alpha');
axLC[0,0].set_ylabel('Residual')
axLC[0,1].plot(LcurveS[:,0], LcurveS[:,2]);
axLC[0,1].set_xlim((Logalpha[0],Logalpha[-1]));
axLC[0,1].set_xlabel('alpha');
axLC[0,1].set_ylabel('|J|')
axLC[1,0].scatter(LcurveS[:,1], LcurveS[:,2]);
axLC[1,0].set_xlabel('Residual');
axLC[1,0].set_ylabel('|J|')
axLC[1,1].scatter(LcurveS[:,0], kappa);
axLC[1,1].set_xlabel('alpha');
axLC[1,1].set_ylabel('kappa')
fig, ax = plt.subplots()
ax.scatter(LcurveS[:,1],LcurveS[:,2])
plt.xlabel('Residual'); plt.ylabel('|J|')
for i, txt in enumerate(Logalpha):
ax.annotate(txt, (LcurveS[i,1],LcurveS[i,2]), xytext = (5,1), textcoords = 'offset points')
## alphaL
Ne, Nd = K.shape
for dsafilename1 in glob.iglob(bkdir+"/*.Adjacents_1_*"):
A_local1 = read_bk.dsa(dsafilename1)
for dsafilename2 in glob.iglob(bkdir+"/*.Adjacents_2_*"):
A_local2 = read_bk.dsa(dsafilename2)
nD1 = A_local1.shape[0]-1
nD2 = A_local2.shape[0]-1
Nei1 = A_local1[:-1, :-1]
Nei2 = A_local2[:-1, :-1]
r0 = np.concatenate((Nei1, np.zeros((nD1,nD2))), axis=1)
r1 = np.concatenate((np.zeros((nD2,nD1)), Nei2), axis=1)
Neighbor = np.concatenate((r0, r1), axis=0)
B = np.identity(Nd)
for i in range(Nd):
Ni = np.sum(Neighbor[i,:])-1
if Ni > 0:
B[i,:] = -Neighbor[i,:]/Ni
B[i,i] = 1
else:
B[i,:] = -1/(Nd-1)
B[i,i] = 1
alphaS = 10 ** logalphaS
Logalpha = np.arange(-6, 7, 1)
nLcurve = len(Logalpha)
LcurveL = [] # np.zeros((nLcurve, 4))
for i in Logalpha:
alphaLi = 10 ** i
Imat = Imatrix.CSL(alphaS, alphaLi, K, bkdir)
beta = np.dot(Imat, phi)
phihat = np.dot(K, beta)
phidiff = phi-phihat
Resid2 = np.sqrt(sum(phidiff*phidiff))
L2 = np.sqrt(sum(beta * beta))
Bbeta = np.dot(B, beta)
BL2 = np.sqrt(sum(Bbeta * Bbeta))
LcurveL = np.concatenate((LcurveL, [i, Resid2, L2, BL2]), axis=0)
LcurveL = LcurveL.reshape(nLcurve, 4)
LcurveL0 = np.array([LcurveL[:,0], LcurveL[:,1]/max(LcurveL[:,1]), LcurveL[:,2]/max(LcurveL[:,2]), LcurveL[:,3]/max(LcurveL[:,3])])
LcurveL = LcurveL0.T
Resid2D1 = np.diff(LcurveL[:,1]); Resid2D2 = np.diff(Resid2D1);
L2D1 = np.diff(LcurveL[:,3]); L2D2 = np.diff(L2D1);
pho = np.array([LcurveL[:,1], np.concatenate((Resid2D1,[0])), np.concatenate((Resid2D2,[0,0]))])
pho = pho.T
eta = np.array([LcurveL[:,3], np.concatenate((L2D1,[0])), np.concatenate((L2D2,[0,0]))])
eta = eta.T
nume =(np.multiply(pho[:,1], eta[:,2]) - np.multiply(pho[:,2], eta[:,1]))
denume = np.power((np.multiply(pho[:,1], pho[:,1]) - np.multiply(eta[:,1],eta[:,1])), 3/2)
kappa = np.array(np.divide(nume,denume))
maxKappa = np.where(abs(kappa) == np.nanmax(abs(kappa)))[0]
logalphaL = LcurveL[maxKappa[0],0]
figLCL, axLCL = plt.subplots(2,2)
axLCL[0,0].plot(LcurveL[:,0], LcurveL[:,1]);
axLCL[0,0].set_xlim((Logalpha[0],Logalpha[-1]));
axLCL[0,0].set_xlabel('alpha');
axLCL[0,0].set_ylabel('Residual')
axLCL[0,1].plot(LcurveL[:,0], LcurveL[:,3]);
axLCL[0,1].set_xlim((Logalpha[0],Logalpha[-1]));
axLCL[0,1].set_xlabel('alpha');
axLCL[0,1].set_ylabel('|BJ|')
axLCL[1,0].scatter(LcurveL[:,1], LcurveL[:,3]);
axLCL[1,0].set_xlabel('Residual');
axLCL[1,0].set_ylabel('|BJ|')
axLCL[1,1].scatter(LcurveL[:,0], kappa);
axLCL[1,1].set_xlabel('alpha');
axLCL[1,1].set_ylabel('kappa')
fig, ax = plt.subplots()
ax.scatter(LcurveL[:,1],LcurveL[:,3])
plt.xlabel('Residual'); plt.ylabel('|BJ|')
for i, txt in enumerate(Logalpha):
ax.annotate(txt, (LcurveL[i,1],LcurveL[i,3]), xytext = (5,1), textcoords = 'offset points')
logalpha = logalphaS, LcurveS, logalphaL, LcurveL
return logalpha
def CSL(phi, K, bkdir):
## alphaS
Logalpha = np.arange(-6, 7, 1)
nLcurve = len(Logalpha)
LcurveS = [] # Lcurve Residual L2
for i in Logalpha:
alphai = 10**i
Imat = Imatrix.MN(alphai, K)
beta = np.dot(Imat, phi)
phihat = np.dot(K, beta)
phidiff = phi - phihat
Resid2 = np.sqrt(sum(phidiff * phidiff))
L2 = np.sqrt(sum(beta * beta))
LcurveS = np.concatenate((LcurveS, [i, Resid2, L2]), axis=0)
LcurveS = LcurveS.reshape(nLcurve, 3)
LcurveS0 = np.array([
LcurveS[:, 0], LcurveS[:, 1] / max(LcurveS[:, 1]),
LcurveS[:, 2] / max(LcurveS[:, 2])
])
LcurveS = LcurveS0.T
Resid2D1 = np.diff(LcurveS[:, 1])
Resid2D2 = np.diff(Resid2D1)
L2D1 = np.diff(LcurveS[:, 2])
L2D2 = np.diff(L2D1)
pho = np.array([
LcurveS[:, 1],
np.concatenate((Resid2D1, [0])),
np.concatenate((Resid2D2, [0, 0]))
])
pho = pho.T
eta = np.array([
LcurveS[:, 2],
np.concatenate((L2D1, [0])),
np.concatenate((L2D2, [0, 0]))
])
eta = eta.T
nume = (np.multiply(pho[:, 1], eta[:, 2]) -
np.multiply(pho[:, 2], eta[:, 1]))
denume = np.power((np.multiply(pho[:, 1], pho[:, 1]) -
np.multiply(eta[:, 1], eta[:, 1])), 3 / 2)
kappa = np.array(np.divide(nume, denume))
maxKappa = np.where(abs(kappa) == np.nanmax(abs(kappa)))[0]
logalphaS = LcurveS[maxKappa[0], 0]
figLC, axLC = plt.subplots(2, 2)
axLC[0, 0].plot(LcurveS[:, 0], LcurveS[:, 1])
axLC[0, 0].set_xlim((Logalpha[0], Logalpha[-1]))
axLC[0, 0].set_xlabel('alpha')
axLC[0, 0].set_ylabel('Residual')
axLC[0, 1].plot(LcurveS[:, 0], LcurveS[:, 2])
axLC[0, 1].set_xlim((Logalpha[0], Logalpha[-1]))
axLC[0, 1].set_xlabel('alpha')
axLC[0, 1].set_ylabel('|J|')
axLC[1, 0].scatter(LcurveS[:, 1], LcurveS[:, 2])
axLC[1, 0].set_xlabel('Residual')
axLC[1, 0].set_ylabel('|J|')
axLC[1, 1].scatter(LcurveS[:, 0], kappa)
axLC[1, 1].set_xlabel('alpha')
axLC[1, 1].set_ylabel('kappa')
fig, ax = plt.subplots()
ax.scatter(LcurveS[:, 1], LcurveS[:, 2])
plt.xlabel('Residual')
plt.ylabel('|J|')
for i, txt in enumerate(Logalpha):
ax.annotate(txt, (LcurveS[i, 1], LcurveS[i, 2]),
xytext=(5, 1),
textcoords='offset points')
## alphaL
Ne, Nd = K.shape
for dsafilename1 in glob.iglob(bkdir + "/*.Adjacents_1_*"):
A_local1 = read_bk.dsa(dsafilename1)
for dsafilename2 in glob.iglob(bkdir + "/*.Adjacents_2_*"):
A_local2 = read_bk.dsa(dsafilename2)
nD1 = A_local1.shape[0] - 1
nD2 = A_local2.shape[0] - 1
Nei1 = A_local1[:-1, :-1]
Nei2 = A_local2[:-1, :-1]
r0 = np.concatenate((Nei1, np.zeros((nD1, nD2))), axis=1)
r1 = np.concatenate((np.zeros((nD2, nD1)), Nei2), axis=1)
Neighbor = np.concatenate((r0, r1), axis=0)
B = np.identity(Nd)
for i in range(Nd):
Ni = np.sum(Neighbor[i, :]) - 1
if Ni > 0:
B[i, :] = -Neighbor[i, :] / Ni
B[i, i] = 1
else:
B[i, :] = -1 / (Nd - 1)
B[i, i] = 1
alphaS = 10**logalphaS
Logalpha = np.arange(-6, 7, 1)
nLcurve = len(Logalpha)
LcurveL = [] # np.zeros((nLcurve, 4))
for i in Logalpha:
alphaLi = 10**i
Imat = Imatrix.CSL(alphaS, alphaLi, K, bkdir)
beta = np.dot(Imat, phi)
phihat = np.dot(K, beta)
phidiff = phi - phihat
Resid2 = np.sqrt(sum(phidiff * phidiff))
L2 = np.sqrt(sum(beta * beta))
Bbeta = np.dot(B, beta)
BL2 = np.sqrt(sum(Bbeta * Bbeta))
LcurveL = np.concatenate((LcurveL, [i, Resid2, L2, BL2]), axis=0)
LcurveL = LcurveL.reshape(nLcurve, 4)
LcurveL0 = np.array([
LcurveL[:, 0], LcurveL[:, 1] / max(LcurveL[:, 1]),
LcurveL[:, 2] / max(LcurveL[:, 2]), LcurveL[:, 3] / max(LcurveL[:, 3])
])
LcurveL = LcurveL0.T
Resid2D1 = np.diff(LcurveL[:, 1])
Resid2D2 = np.diff(Resid2D1)
L2D1 = np.diff(LcurveL[:, 3])
L2D2 = np.diff(L2D1)
pho = np.array([
LcurveL[:, 1],
np.concatenate((Resid2D1, [0])),
np.concatenate((Resid2D2, [0, 0]))
])
pho = pho.T
eta = np.array([
LcurveL[:, 3],
np.concatenate((L2D1, [0])),
np.concatenate((L2D2, [0, 0]))
])
eta = eta.T
nume = (np.multiply(pho[:, 1], eta[:, 2]) -
np.multiply(pho[:, 2], eta[:, 1]))
denume = np.power((np.multiply(pho[:, 1], pho[:, 1]) -
np.multiply(eta[:, 1], eta[:, 1])), 3 / 2)
kappa = np.array(np.divide(nume, denume))
maxKappa = np.where(abs(kappa) == np.nanmax(abs(kappa)))[0]
logalphaL = LcurveL[maxKappa[0], 0]
figLCL, axLCL = plt.subplots(2, 2)
axLCL[0, 0].plot(LcurveL[:, 0], LcurveL[:, 1])
axLCL[0, 0].set_xlim((Logalpha[0], Logalpha[-1]))
axLCL[0, 0].set_xlabel('alpha')
axLCL[0, 0].set_ylabel('Residual')
axLCL[0, 1].plot(LcurveL[:, 0], LcurveL[:, 3])
axLCL[0, 1].set_xlim((Logalpha[0], Logalpha[-1]))
axLCL[0, 1].set_xlabel('alpha')
axLCL[0, 1].set_ylabel('|BJ|')
axLCL[1, 0].scatter(LcurveL[:, 1], LcurveL[:, 3])
axLCL[1, 0].set_xlabel('Residual')
axLCL[1, 0].set_ylabel('|BJ|')
axLCL[1, 1].scatter(LcurveL[:, 0], kappa)
axLCL[1, 1].set_xlabel('alpha')
axLCL[1, 1].set_ylabel('kappa')
fig, ax = plt.subplots()
ax.scatter(LcurveL[:, 1], LcurveL[:, 3])
plt.xlabel('Residual')
plt.ylabel('|BJ|')
for i, txt in enumerate(Logalpha):
ax.annotate(txt, (LcurveL[i, 1], LcurveL[i, 3]),
xytext=(5, 1),
textcoords='offset points')
logalpha = logalphaS, LcurveS, logalphaL, LcurveL
return logalpha
