def write_cart_poly_code(f):
cps = get_cartesian_powers(7)
cps = [tuple(row) for row in cps[1:]] # chop of the s function
print >>f, " // Shell l=0"
print >>f, " if (lmax <= 0) return -1;"
print >>f
last_shell = 0
begin = -1
end = 0
for px, py, pz in cps:
shell = px+py+pz
if shell > last_shell:
print >>f, " // Shell l=%i" % shell
begin = end
last_shell = shell
if shell > 1:
if shell > 2:
if px != 0:
prev_row = (px-1, py, pz)
symbol = 'output[0]'
elif py != 0:
prev_row = (px, py-1, pz)
symbol = 'output[1]'
else:
prev_row = (px, py, pz-1)
symbol = 'output[2]'
formula = '%s*output[%i]' % (symbol, cps.index(prev_row))
else:
symbols = ["output[0]"]*px + ["output[1]"]*py + ["output[2]"]*pz
formula = "*".join(symbols)
print >>f, " output[%i] = %s;" % (end, formula)
end += 1
if end >= begin+get_ncart(shell):
print >>f, " if (lmax <= %i) return %i;" % (shell, begin)
print >>f
print >> f, ' throw std::domain_error("Encountered lmax > 7.");'
def write_cart_poly_code(f):
cps = get_cartesian_powers(7)
cps = [tuple(row) for row in cps[1:]] # chop of the s function
print >>f, " // Shell l=0"
print >>f, " if (lmax <= 0) return -1;"
print >>f
last_shell = 0
begin = -1
end = 0
for px, py, pz in cps:
shell = px+py+pz
if shell > last_shell:
print >>f, " // Shell l=%i" % shell
begin = end
last_shell = shell
if shell > 1:
if shell > 2:
if px != 0:
prev_row = (px-1, py, pz)
symbol = 'output[0]'
elif py != 0:
prev_row = (px, py-1, pz)
symbol = 'output[1]'
else:
prev_row = (px, py, pz-1)
symbol = 'output[2]'
formula = '%s*output[%i]' % (symbol, cps.index(prev_row))
else:
symbols = ["output[0]"]*px + ["output[1]"]*py + ["output[2]"]*pz
formula = "*".join(symbols)
print >>f, " output[%i] = %s;" % (end, formula)
end += 1
if end >= begin+get_ncart(shell):
print >>f, " if (lmax <= %i) return %i;" % (shell, begin)
print >>f
print >> f, ' throw std::domain_error("Encountered lmax > 7.");'
def write_cart_rotation_code(f):
import numpy as np
from sympy import Symbol, Wild, Add, Mul, Integer
R = [Symbol('R_%d' % i) for i in xrange(9)]
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
lmax = 4
cartesian_powers = [tuple(row) for row in get_cartesian_powers(lmax)]
print cartesian_powers
ncart = len(cartesian_powers)
transforms = []
def get_power(term, base):
p = Wild("p")
c = Wild("c")
d = term.match(c*base**p)
if d is None:
return 0
else:
return int(d[p])
icart = 0
for ishell in xrange(lmax+1):
shell_rules = []
transforms.append(shell_rules)
for ifn in xrange(((ishell+1)*(ishell+2))/2):
px0, py0, pz0 = cartesian_powers[icart]
rules = []
shell_rules.append(rules)
poly = (
(R[0]*x + R[1]*y + R[2]*z)**px0
*(R[3]*x + R[4]*y + R[5]*z)**py0
*(R[6]*x + R[7]*y + R[8]*z)**pz0
).expand()
print poly
if isinstance(poly, Add):
terms = poly.args
else:
terms = [poly]
for term in terms:
px1 = get_power(term, x)
py1 = get_power(term, y)
pz1 = get_power(term, z)
prs = [get_power(term, R[i]) for i in xrange(9)]
col = cartesian_powers.index((px1, py1, pz1)) - cartesian_powers.index((px1+py1+pz1, 0, 0))
assert col >= 0
coeff = 1
if isinstance(term, Mul):
for factor in term.args:
if isinstance(factor, Integer):
coeff *= int(factor)
rule = (col, coeff, prs)
rules.append(rule)
icart += 1
def format_rule(rule):
l = [rule[0], rule[1]]
prs = rule[2]
for j in xrange(9):
for p in xrange(prs[j]):
l.append(j)
#if prs[j] > 0:
# l.append(j)
# l.append(prs[j])
return '[%s]' % (', '.join('%2i' % i for i in l))
print >> f, 'cartesian_transforms = ['
for shell_rules in transforms:
print >> f, ' ['
for rules in shell_rules:
if len(rules) == 1:
print >> f, ' [%s],' % format_rule(rules[0])
else:
rules = sorted(rules)
print >> f, ' [%s,' % format_rule(rules[0])
for rule in rules[1:-1]:
print >> f, ' %s,' % format_rule(rule)
print >> f, ' %s],' % format_rule(rules[-1])
print >> f, ' ],'
print >> f, ']'
def write_cart_rotation_code(f):
import numpy as np
from sympy import Symbol, Wild, Add, Mul, Integer
R = [Symbol('R_%d' % i) for i in xrange(9)]
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
lmax = 4
cartesian_powers = [tuple(row) for row in get_cartesian_powers(lmax)]
ncart = len(cartesian_powers)
transforms = []
def get_power(term, base):
p = Wild("p")
c = Wild("c")
d = term.match(c*base**p)
if d is None:
return 0
else:
return int(d[p])
for px0, py0, pz0 in cartesian_powers:
rules = []
transforms.append(rules)
poly = (
(R[0]*x + R[1]*y + R[2]*z)**px0
*(R[3]*x + R[4]*y + R[5]*z)**py0
*(R[6]*x + R[7]*y + R[8]*z)**pz0
).expand()
print poly
if isinstance(poly, Add):
terms = poly.args
else:
terms = [poly]
for term in terms:
px1 = get_power(term, x)
py1 = get_power(term, y)
pz1 = get_power(term, z)
prs = [get_power(term, R[i]) for i in xrange(9)]
col = cartesian_powers.index((px1, py1, pz1))
coeff = 1
if isinstance(term, Mul):
for factor in term.args:
if isinstance(factor, Integer):
coeff *= int(factor)
rule = (col, coeff, prs)
rules.append(rule)
def format_rule(rule):
l = [rule[0], rule[1]]
prs = rule[2]
for j in xrange(9):
for p in xrange(prs[j]):
l.append(j)
#if prs[j] > 0:
# l.append(j)
# l.append(prs[j])
return '[%s]' % (', '.join('%2i' % i for i in l))
print >> f, 'cartesian_transforms = ['
for rules in transforms:
if len(rules) == 1:
print >> f, ' [%s],' % format_rule(rules[0])
else:
rules = sorted(rules)
print >> f, ' [%s,' % format_rule(rules[0])
for rule in rules[1:-1]:
print >> f, ' %s,' % format_rule(rule)
print >> f, ' %s],' % format_rule(rules[-1])
print >> f, ']'
