def sparse_rc_xam() :
#
import numpy
import cppad_py
#
# initialize return variable
ok = True
# ---------------------------------------------------------------------
#
# create an empty sparsity pattern
pattern = cppad_py.sparse_rc()
ok = ok and pattern.nr() == 0
ok = ok and pattern.nc() == 0
ok = ok and pattern.nnz() == 0
#
# resize
nr = 6
nc = 5
nnz = 4
pattern.resize(nr, nc, nnz)
ok = ok and pattern.nr() == nr
ok = ok and pattern.nc() == nc
ok = ok and pattern.nnz() == nnz
#
# indices corresponding to upper-diagonal
for k in range( nnz ) :
pattern.put(k, k, k+1)
#
#
# row and column indices
row = pattern.row()
col = pattern.col()
#
# check row and column indices
for k in range( nnz ) :
ok = ok and row[k] == k
ok = ok and col[k] == k+1
#
#
# For this case, row_major and col_major order are same as original order
row_major = pattern.row_major()
col_major = pattern.col_major()
for k in range( nnz ) :
ok = ok and row_major[k] == k
ok = ok and col_major[k] == k
#
#
return( ok )
def sparse_rcv_xam():
#
import numpy
import cppad_py
#
# initialize return variable
ok = True
# ---------------------------------------------------------------------
# create an empty matrix
matrix = cppad_py.sparse_rcv()
ok = ok and matrix.nr() == 0
ok = ok and matrix.nc() == 0
ok = ok and matrix.nnz() == 0
#
# create sparsity pattern for n by n identity matrix
pattern = cppad_py.sparse_rc()
n = 5
pattern.resize(n, n, n)
for k in range(n):
pattern.put(k, k, k)
#
# create n by n sparse representation of identity matrix
matrix.pat(pattern)
for k in range(n):
matrix.put(k, 1.0)
#
# row, column indices
row = matrix.row()
col = matrix.col()
val = matrix.val()
#
# check results
for k in range(n):
ok = ok and row[k] == k
ok = ok and col[k] == k
ok = ok and val[k] == 1.0
#
# For this case, row_major and col_major order are same as original order
row_major = matrix.row_major()
col_major = matrix.col_major()
for k in range(n):
ok = ok and row_major[k] == k
ok = ok and col_major[k] == k
#
#
return (ok)
def sparse_jac_xam():
#
import numpy
import cppad_py
#
# initialize return variable
ok = True
# ---------------------------------------------------------------------
# number of dependent and independent variables
n = 3
# one
aone = cppad_py.a_double(1.0)
#
# create the independent variables ax
x = numpy.empty(n, dtype=float)
for i in range(n):
x[i] = i + 2.0
#
ax = cppad_py.independent(x)
#
# create dependent variables ay with ay[i] = (j+1) * ax[j]
# where i = mod(j + 1, n)
ay = numpy.empty(n, dtype=cppad_py.a_double)
for j in range(n):
i = j + 1
if i >= n:
i = i - n
#
aj = cppad_py.a_double(j)
ay_i = (aj + aone) * ax[j]
ay[i] = ay_i
#
#
# define af corresponding to f(x)
f = cppad_py.d_fun(ax, ay)
#
# sparsity pattern for identity matrix
pat_eye = cppad_py.sparse_rc()
pat_eye.resize(n, n, n)
for k in range(n):
pat_eye.put(k, k, k)
#
#
# sparsity pattern for the Jacobian
pat_jac = cppad_py.sparse_rc()
f.for_jac_sparsity(pat_eye, pat_jac)
#
# loop over forward and reverse mode
for mode in range(2):
# compute all possibly non-zero entries in Jacobian
subset = cppad_py.sparse_rcv(pat_jac)
# work space used to save time for multiple calls
work = cppad_py.sparse_jac_work()
if mode == 0:
f.sparse_jac_for(subset, x, pat_jac, work)
#
if mode == 1:
f.sparse_jac_rev(subset, x, pat_jac, work)
#
#
# check result
ok = ok and n == subset.nnz()
col_major = subset.col_major()
row = subset.row()
col = subset.col()
val = subset.val()
for k in range(n):
ell = col_major[k]
r = row[ell]
c = col[ell]
v = val[ell]
i = c + 1
if i >= n:
i = i - n
#
ok = ok and c == k
ok = ok and r == i
ok = ok and v == c + 1.0
#
#
#
return (ok)
def sparse_hes_xam():
#
import numpy
import cppad_py
#
# initialize return variable
ok = True
# ---------------------------------------------------------------------
# number of dependent and independent variables
n = 3
#
# create the independent variables ax
x = numpy.empty(n, dtype=float)
for i in range(n):
x[i] = i + 2.0
#
ax = cppad_py.independent(x)
#
# ay[i] = j * ax[j] * ax[i]
# where i = mod(j + 1, n)
ay = numpy.empty(n, dtype=cppad_py.a_double)
for j in range(n):
i = j + 1
if i >= n:
i = i - n
#
aj = cppad_py.a_double(j)
ax_j = ax[j]
ax_i = ax[i]
ay[i] = aj * ax_j * ax_i
#
#
# define af corresponding to f(x)
f = cppad_py.d_fun(ax, ay)
#
# Set select_d (domain) to all true,
# initial select_r (range) to all false
# initialize r to all zeros
select_d = numpy.empty(n, dtype=bool)
select_r = numpy.empty(n, dtype=bool)
r = numpy.empty(n, dtype=float)
for i in range(n):
select_d[i] = True
select_r[i] = False
r[i] = 0.0
#
#
# only select component n-1 of the range function
# f_0 (x) = (n-1) * x_{n-1} * x_0
select_r[0] = True
r[0] = 1.0
#
# sparisty pattern for Hessian
pattern = cppad_py.sparse_rc()
f.for_hes_sparsity(select_d, select_r, pattern)
#
# compute all possibly non-zero entries in Hessian
# (should only compute lower triangle becuase matrix is symmetric)
subset = cppad_py.sparse_rcv(pattern)
#
# work space used to save time for multiple calls
work = cppad_py.sparse_hes_work()
#
f.sparse_hes(subset, x, r, pattern, work)
#
# check that result is sparsity pattern for Hessian of f_0 (x)
ok = ok and subset.nnz() == 2
row = subset.row()
col = subset.col()
val = subset.val()
for k in range(2):
i = row[k]
j = col[k]
v = val[k]
if i <= j:
ok = ok and i == 0
ok = ok and j == n - 1
#
if i >= j:
ok = ok and i == n - 1
ok = ok and j == 0
#
ok = ok and v == n - 1
#
#
return (ok)
def sparse_jac_pattern_xam():
#
import numpy
import cppad_py
#
# initialize return variable
ok = True
# ---------------------------------------------------------------------
# number of dependent and independent variables
n = 3
#
# create the independent variables ax
x = numpy.empty(n, dtype=float)
for i in range(n):
x[i] = i + 2.0
#
ax = cppad_py.independent(x)
#
# create dependent variables ay with ay[i] = ax[j]
# where i = mod(j + 1, n)
ay = numpy.empty(n, dtype=cppad_py.a_double)
for j in range(n):
i = j + 1
if i >= n:
i = i - n
#
ay_i = ax[j]
ay[i] = ay_i
#
#
# define af corresponding to f(x)
f = cppad_py.d_fun(ax, ay)
#
# sparsity pattern for identity matrix
pat_in = cppad_py.sparse_rc()
pat_in.resize(n, n, n)
for k in range(n):
pat_in.put(k, k, k)
#
#
# loop over forward and reverse mode
for mode in range(2):
pat_out = cppad_py.sparse_rc()
if mode == 0:
f.for_jac_sparsity(pat_in, pat_out)
#
if mode == 1:
f.rev_jac_sparsity(pat_in, pat_out)
#
#
# check that result is sparsity pattern for Jacobian
ok = ok and n == pat_out.nnz()
col_major = pat_out.col_major()
row = pat_out.row()
col = pat_out.col()
for k in range(n):
ell = col_major[k]
r = row[ell]
c = col[ell]
i = c + 1
if i >= n:
i = i - n
#
ok = ok and c == k
ok = ok and r == i
#
#
#
return (ok)
def sparse_hes_pattern_xam():
#
import numpy
import cppad_py
#
# initialize return variable
ok = True
# ---------------------------------------------------------------------
# number of dependent and independent variables
n = 3
#
# create the independent variables ax
x = numpy.empty(n, dtype=float)
for i in range(n):
x[i] = i + 2.0
#
ax = cppad_py.independent(x)
#
# create dependent variables ay with ay[i] = ax[j] * ax[i]
# where i = mod(j + 1, n)
ay = numpy.empty(n, dtype=cppad_py.a_double)
for j in range(n):
i = j + 1
if i >= n:
i = i - n
#
ay_i = ax[i] * ax[j]
ay[i] = ay_i
#
#
# define af corresponding to f(x)
f = cppad_py.d_fun(ax, ay)
#
# Set select_d (domain) to all true, initial select_r (range) to all false
select_d = numpy.empty(n, dtype=bool)
select_r = numpy.empty(n, dtype=bool)
for i in range(n):
select_d[i] = True
select_r[i] = False
#
#
# only select component 0 of the range function
# f_0 (x) = x_0 * x_{n-1}
select_r[0] = True
#
# loop over forward and reverse mode
for mode in range(2):
pat_out = cppad_py.sparse_rc()
if mode == 0:
f.for_hes_sparsity(select_d, select_r, pat_out)
#
if mode == 1:
f.rev_hes_sparsity(select_d, select_r, pat_out)
#
#
# check that result is sparsity pattern for Hessian of f_0 (x)
ok = ok and pat_out.nnz() == 2
row = pat_out.row()
col = pat_out.col()
for k in range(2):
r = row[k]
c = col[k]
if r <= c:
ok = ok and r == 0
ok = ok and c == n - 1
#
if r >= c:
ok = ok and r == n - 1
ok = ok and c == 0
#
#
#
#
return (ok)