def testDenseGET():
"""
Simple test of denseGETRF and denseGETRS to solve a linear system
"""
N = 2
A = np.array([[4.0, 6.0], [3.0, 3.0]], dtype=np.float64, order='F')
A_sp = np.ascontiguousarray(A)
P = np.arange(N, dtype=np.int32)
b = np.ones(N, dtype=np.float64)
b_sp = linalg.lu_solve(linalg.lu_factor(A_sp), b)
ret = denseGETRF(A, P)
assert ret == 0
denseGETRS(A, P, b)
assert_allclose(b, b_sp)
assert ret == 0
def testDenseGET():
"""
Simple test of denseGETRF and denseGETRS to solve a linear system
"""
N = 2
A = np.array( [[4.0,6.0],[3.0,3.0]], dtype=np.float64, order='F')
A_sp = np.ascontiguousarray(A)
P = np.arange( N, dtype=np.int32 )
b = np.ones( N, dtype=np.float64 )
b_sp = linalg.lu_solve(linalg.lu_factor(A_sp), b)
ret = denseGETRF(A, P)
assert ret == 0
denseGETRS(A, P, b)
assert_allclose(b, b_sp)
assert ret == 0
def SpilsPrecSetup(self, t, c, fc, jok, jcurPtr, gamma, vtemp1, vtemp2,
vtemp3):
"""
This routine generates the block-diagonal part of the Jacobian
corresponding to the interaction rates, multiplies by -gamma, adds
the identity matrix, and calls denseGETRF to do the LU decomposition of
each diagonal block. The computation of the diagonal blocks uses
the preset block and grouping information. One block per group is
computed. The Jacobian elements are generated by difference
quotients using calls to the routine fblock.
This routine can be regarded as a prototype for the general case
of a block-diagonal preconditioner. The blocks are of size mp, and
there are ngrp=ngx*ngy blocks computed in the block-grouping scheme.
"""
cdata = c.data
rewt = self.rewt
self.errWeights(rewt)
rewtdata = rewt.data
uround = UNIT_ROUNDOFF
P = self.P
pivot = self.pivot
jxr = self.jxr
jyr = self.jyr
mp = self.mp
srur = self.srur
#ngrp = self.ngrp
ngx = self.ngx
ngy = self.ngy
#mxmp = self.mxmp
fsave = self.fsave
"""
Make mp calls to fblock to approximate each diagonal block of Jacobian.
Here, fsave contains the base value of the rate vector and
r0 is a minimum increment factor for the difference quotient.
"""
f1 = vtemp1.data
fac = fc.WrmsNorm(rewt)
r0 = 1000.0 * np.abs(gamma) * uround * NEQ * fac
if (r0 == ZERO): r0 = ONE
for igy in range(ngy):
jy = jyr[igy]
#if00 = jy*mxmp
for igx in range(ngx):
jx = jxr[igx]
#if0 = if00 + jx*mp
#ig = igx + igy*ngx
# Generate ig-th diagonal block
for j in range(mp):
# Generate the jth column as a difference quotient
#jj = if0 + j
save = cdata[:, igx, igy]
r = np.max(srur * np.abs(save), r0 / rewtdata[:, igx, igy])
cdata[:, igx, igy] += r
fac = -gamma / r
self.fblock(t, cdata, jx, jy, f1)
for i in range(mp):
P[igx, igy, j, i] = (f1[i] - fsave[i, jx, jy]) * fac
cdata[j, jx, jy] = save
# Add identity matrix and do LU decompositions on blocks.
for igy in range(ngy):
for igx in range(ngx):
denseAddIdentity(P[igx, igy, ...])
ier = denseGETRF(P[igx, igy, ...], pivot[igx, igy, ...])
if (ier != 0): return 1
jcurPtr = True
return 0
def SpilsPrecSetup(self, tn, u, fu, jok, gamma, vtemp1, vtemp2, vtemp3):
"""
Preconditioner setup routine. Generate and preprocess P.
"""
# Make local copies of pointers in user_data, and of pointer to u's data
P = self.P
Jbd = self.Jbd
pivot = self.pivot
udata = u.data
if jok:
# jok = TRUE: Copy Jbd to P
for jy in range(MY):
for jx in range(MX):
P[jx, jy, ...] = Jbd[jx, jy, ...]
jcurPtr = False
else:
# jok = FALSE: Generate Jbd from scratch and copy to P
# Make local copies of problem variables, for efficiency.
q4coef = self.q4
dely = self.dy
verdco = self.vdco
hordco = self.hdco
# Compute 2x2 diagonal Jacobian blocks (using q4 values
# computed on the last f call). Load into P.
for jy in range(MY):
ydn = YMIN + (jy - 0.5) * dely
yup = ydn + dely
cydn = verdco * np.exp(0.2 * ydn)
cyup = verdco * np.exp(0.2 * yup)
diag = -(cydn + cyup + TWO * hordco)
for jx in range(MX):
c1 = udata[jx, jy, 0]
c2 = udata[jx, jy, 1]
Jbd[jx, jy, 0, 0] = (-Q1 * C3 - Q2 * c2) + diag
# Transposed in Python
Jbd[jx, jy, 1, 0] = -Q2 * c1 + q4coef
Jbd[jx, jy, 0, 1] = Q1 * C3 - Q2 * c2
Jbd[jx, jy, 1, 1] = (-Q2 * c1 - q4coef) + diag
P[jx, jy, ...] = Jbd[jx, jy, ...]
jcurPtr = True
# Scale by -gamma
for jy in range(MY):
for jx in range(MX):
P[jx, jy, ...] *= -gamma
# Add identity matrix and do LU decompositions on blocks in place.
for jy in range(MY):
for jx in range(MX):
P[jx, jy, ...] += np.eye(NUM_SPECIES)
ier = denseGETRF(P[jx, jy, ...], pivot[jx, jy, ...])
# print ier, P[jx,jy,...]
if ier != 0: return 1, jcurPtr
return 0, jcurPtr
def SpilsPrecSetup(self, tn, u, fu, jok, gamma, vtemp1, vtemp2, vtemp3):
"""
Preconditioner setup routine. Generate and preprocess P.
"""
# Make local copies of pointers in user_data, and of pointer to u's data
P = self.P
Jbd = self.Jbd
pivot = self.pivot
udata = u.data
if jok:
# jok = TRUE: Copy Jbd to P
for jy in range(MY):
for jx in range(MX):
P[jx,jy,...] = Jbd[jx,jy,...]
jcurPtr = False
else:
# jok = FALSE: Generate Jbd from scratch and copy to P
# Make local copies of problem variables, for efficiency.
q4coef = self.q4;
dely = self.dy;
verdco = self.vdco;
hordco = self.hdco;
# Compute 2x2 diagonal Jacobian blocks (using q4 values
# computed on the last f call). Load into P.
for jy in range(MY):
ydn = YMIN + (jy - 0.5)*dely;
yup = ydn + dely;
cydn = verdco*np.exp(0.2*ydn);
cyup = verdco*np.exp(0.2*yup);
diag = -(cydn + cyup + TWO*hordco);
for jx in range(MX):
c1 = udata[jx,jy,0]
c2 = udata[jx,jy,1]
Jbd[jx,jy,0,0] = (-Q1*C3 - Q2*c2) + diag
# Transposed in Python
Jbd[jx,jy,1,0] = -Q2*c1 + q4coef
Jbd[jx,jy,0,1] = Q1*C3 - Q2*c2
Jbd[jx,jy,1,1] = (-Q2*c1 - q4coef) + diag
P[jx,jy,...] = Jbd[jx,jy,...]
jcurPtr = True
# Scale by -gamma
for jy in range(MY):
for jx in range(MX):
P[jx,jy,...] *= -gamma
# Add identity matrix and do LU decompositions on blocks in place.
for jy in range(MY):
for jx in range(MX):
P[jx,jy,...] += np.eye(NUM_SPECIES)
ier = denseGETRF(P[jx,jy,...], pivot[jx,jy,...] )
# print ier, P[jx,jy,...]
if ier != 0: return 1, jcurPtr
return 0, jcurPtr
