def test_with(m):
i = sage.all.identity_matrix(m.nrows()).column(1).column()
assert i.nrows() == m.nrows()
mZ = flint.fmpz_mat(m)
mQ = flint.fmpq_mat((Integer(1), mZ))
iZ = flint.fmpz_mat(i)
iQ = flint.fmpq_mat((Integer(1), iZ))
try:
sS = m.solve_right(i)
except:
write("-")
singular_test(mZ, mQ, iZ, iQ)
return
Xd, d = mZ.solve_right(iZ)
S_by_d_sage = sage.all.matrix(ZZ, d * sS)
S_by_d = flint.fmpz_mat(S_by_d_sage)
if Xd != S_by_d:
print "integer solve_right() failed, m=\n", m
sys.exit(1)
X = flint.fmpq_mat((d, Xd))
Y = mQ.solve_dixon(iQ)
assert X == Y
write("+")
if watch_canonical:
" check if raw_str() of X and Y are equal "
Xr, Yr = X.raw_str(), Y.raw_str()
if Xr != Yr:
print "m=\n", m
print "Xr=%s" % Xr
print "Yr=%s" % Yr
def test_with( m ): ''' sage method only called once, do not need to clean cache ''' global t_sage, t__inv, t_matz, t_Dixon i=sage.all.identity_matrix( m.nrows() ) mZ=flint.fmpz_mat( m ) mQ=flint.fmpq_mat( (Integer(1), mZ) ) iZ=flint.fmpz_mat( i ) iQ=flint.fmpq_mat( (Integer(1),iZ) ) try: t0=time.time() sS=m.inverse() except: t_sage += time.time()-t0 # ups, this subroutine can be removed, so # the whole file could be a dozen lines shorter singular_test( mZ, mQ, iZ, iQ ) return t1=time.time() t_sage += t1-t0 Xd,d=mZ.solve_right(iZ) t2=time.time() t_matz += t2-t1 Y=mQ.solve_dixon( iQ ) t3=time.time() t_Dixon += t3-t2 W=mQ.inverse() t__inv += time.time()-t3
def test(a,b,loud): assert b>1 assert b<2**64 c=a % b n=flint.nmod_mat(flint.fmpz_mat(a),Integer(b)) d=n.export_nonnegative_fmpz_mat() if d != flint.fmpz_mat(c): print 'mismatch, sage matrice=\n',c print 'd=\n',d assert 0 if loud: print c
def test(a,loud): global t__ntl,t_mine b=abs( a.determinant() ) if b<2 or b>=2**64: print 'bad determinant, internal error' sys.exit(1) t=ntl_HNF_mirror(a) if loud: print 'a=\n',a # benchmark t0=time.time() nmod_r=flint.fmpz_mat_hermite_form( flint.fmpz_mat( a ), b ) t1=time.time() t=t.HNF(b) t2=time.time() # convert result nmod_r=nmod_r.export_sage() if loud: print 'hnf(a)=\n',nmod_r t = ntl_HNF_unmirror( t ) if nmod_r != t: print 'bad result: ntl\n',t sys.exit(1) # update time t__ntl += t2-t1 t_mine += t1-t0
def det_flint(a,way): global t1,tx aF=flint.fmpz_mat( a ) t0=time.time() one=flint.det(aF) t1[way] += time.time()-t0 if loud: print one b=sage.all.copy(a) b[0,0] += 1 bF=flint.fmpz_mat( b ) t0=time.time() not_one=flint.det(bF) tx[way] += time.time()-t0 if loud: print not_one
def random_data(dim):
' returns matrice and absolute value of its determinant '
global coin_fell_on_the_edge
n = m = dim
while 1:
A=sage.all.random_matrix( ZZ, dim, x=-100, y=100 )
B = A.matrix_from_rows(range(m-2)).matrix_from_columns(range(n-1))
c = A.matrix_from_rows([m-2]).matrix_from_columns (range(n-1))
d = A.matrix_from_rows([m-1]).matrix_from_columns (range(n-1))
try:
(d1,d2) = double_det (B,c,d, proof=True)
except:
print 'coin fell on the edge, point 0'
coin_fell_on_the_edge[0] += 1
continue
(g,k,l) = d1._xgcd (d2, minimal=True)
assert g >= 0
if not shut_up:
print "Stein double-det g=%s"%g
CUTOFF = 2**30
# aint not interesting to count HNF of unimodular matrice,
# so disallow g=1
if g==1 or 2*g > CUTOFF:
if not shut_up:
print 'bad det, going back'
continue
W = B.stack (k*c + l*d)
not_g=abs( flint.det(flint.fmpz_mat( W )) )
if not_g != g:
print 'coin fell on the edge, real det=%d != %d' (not_g,g)
coin_fell_on_the_edge[1] += 1
return W,g
def do_with( m ): global t_flint,t_sage i=sage.all.identity_matrix( m.nrows() ) mF,iF=flint.fmpz_mat( m ),flint.fmpz_mat( i ) try: t0=time.time() s=m.solve_right(i) except: pass t1=time.time() t_sage += t1-t0 Xd,d=mF.solve_right(iF) t_flint += time.time()-t1 if dim == m[0,0] // 1000: # this never happens print s,d
def det_flint(a,way): global t1,tx,strange_det aF=flint.fmpz_mat( a ) t0=time.time() one=flint.det(aF) t1[way] += time.time()-t0 if abs(one) != 1: print 'bad determinant, flint' print 'a=\n',a b=sage.all.copy(a) b[0,0] += 1 bF=flint.fmpz_mat( b ) t0=time.time() not_one=flint.det(bF) tx[way] += time.time()-t0 if abs(not_one)==1: strange_det += 1
def test_m(m):
a=flint.fmpz_mat( m )
dG = flint.det(a)
dB = flint.det_20140704( a )
if dG==dB:
#sys.stdout.write('.')
return
print 'test failed, det good/bad=%s/%s' % (dG,dB)
print m
assert 0
def test_m(m,s): a=flint.fmpz_mat( m ) i = is_singular(a) if s and i: return d = flint.det_20140704( a ) if d: assert i==0 else: assert i
def test(a,loud):
b=abs( a.determinant() )
if b<2 or b>=2**63:
print 'bad determinant, internal error'
sys.exit(1)
sage_r=a.hermite_form()
for mult in 1,2:
if loud:
print '\n\n\n'
test_dump(a,sage_r)
print '\n\n'
nmod_r=flint.fmpz_mat_hermite_form( flint.fmpz_mat( a ), b*mult )
if nmod_r != flint.fmpz_mat( sage_r ):
if not loud:
test_dump(a,sage_r)
print 'mult=',mult
nmod_r=nmod_r.export_sage()
print 'nmod result:\n',nmod_r
det_sage=mult_diag(sage_r)
det_nmod=mult_diag(nmod_r)
print 'b=%X det_sage=%X det_nmod=%X' % (b,det_sage,det_nmod)
sys.exit(1)
def test_with( m ):
i=sage.all.identity_matrix( m.nrows() )
mZ=flint.fmpz_mat( m )
mQ=flint.fmpq_mat( (Integer(1), mZ) )
iZ=flint.fmpz_mat( i )
iQ=flint.fmpq_mat( (Integer(1),iZ) )
try:
sS=m.inverse()
except:
write('-')
singular_test( mZ, mQ, iZ, iQ )
return
Xd,d=mZ.solve_right(iZ)
S_by_d_sage=sage.all.matrix( ZZ, d*sS )
S_by_d=flint.fmpz_mat( S_by_d_sage )
if Xd != S_by_d:
print 'integer solve_right() failed, m=\n',m
sys.exit(1)
X=flint.fmpq_mat( (d, Xd) )
Y=mQ.solve_dixon( iQ )
W=mQ.inverse()
assert X == Y
assert Y == W
write('+')
if watch_canonical:
' check if raw_str() of X, Y and W differ '
Xr,Yr,Wr=X.raw_str(),Y.raw_str(),W.raw_str()
m_printed=0
if Xr != Yr:
print 'm=\n',m
print 'Xr=%s' % Xr
print 'Yr=%s' % Yr
m_printed=1
if Yr != Wr:
if not m_printed:
print 'm=\n',m
print 'Yr=%s' % Yr
print 'Wr=%s' % Wr
def test_m(m,p,k,p_deg_k): dG = m.det() % p_deg_k if 0: print 'p=%s k=%s p**k=%s' % (p,k,p_deg_k) print 'm=\n',m dB = flint.det_mod_pk_3arg( flint.fmpz_mat(m), p, k ) if dG==dB: if 0: print 'test passed, det good/bad=%s/%s' % (dG,dB) return print 'p=%s k=%s p**k=%s' % (p,k,p_deg_k) print 'test failed, det good/bad=%s/%s' % (dG,dB) print m assert 0
def test_with(m, precook):
i=sage.all.identity_matrix( m.nrows() )
mF=flint.fmpz_mat( m )
# leave i as-is or convert to fmpz_mat
if precook:
iF=flint.fmpz_mat( i )
else:
iF=i
try:
s=m.solve_right(i) # yep, this line works twice for every matrice
except:
print '\n singular case, dim=%s, calling flint solve_right()' % m.nrows()
try:
Xd,d=mF.solve_right(iF)
except:
print 'singular matrice, exception in flint solve_right()'
return
print '\n singular case, no exception in flint solve_right()'
assert d==0
write('0 ')
return
# matrix non-singular, can do arithmetic
Xd,d=mF.solve_right(iF)
# ups, where is that Matrix_integer_dense?
#Sd=sage.all.Matrix_integer_dense( d*s )
Sd=sage.all.matrix( ZZ, d*s )
Sd=flint.fmpz_mat( Sd )
if Xd != Sd:
print '\n test failed,\n m=\n%s' % m
print 's=%s' % s
print 'd=%d' % d
print 'd=%Xd' % Xd
sys.exit(1)
if 0:
write('+')
else:
write( ' %s' % d )
def test_with( W, g ): global t_sage,t_mine t0=time.time() sage = W._hnf_mod(2*g) t_sage += time.time()-t0 for i in range(3): t1=time.time() r=flint.fmpz_mat_hermite_form( flint.fmpz_mat( W ), g*(i+1) ) t_mine[i] += time.time()-t1 if( r.export_sage() != sage ): print 'result incorrect, g=%s mult=%s\n' % (g,i+1) print W.str() print '\n',sage.str() print '\n',r.export_sage().str() sys.exit(1)
def test_with(m):
global t_sage, t_matz, t_matq
i = sage.all.identity_matrix(m.nrows()).column(1).column()
mZ = flint.fmpz_mat(m)
mQ = flint.fmpq_mat((Integer(1), mZ))
iZ = flint.fmpz_mat(i)
iQ = flint.fmpq_mat((Integer(1), iZ))
singular = 0
t0 = time.time()
try:
sS = m.solve_right(i)
except:
write("-")
singular = 1
t1 = time.time()
Xd, d = mZ.solve_right(iZ)
t2 = time.time()
Y = mQ.solve_dixon(iQ)
t3 = time.time()
t_sage += t1 - t0
t_matz += t2 - t1
t_matq += t3 - t2
if not singular:
write("+")
def test_1( a, a1, p, k):
p_deg_k=p**k
if 0:
print 'p=%s k=%s p**k=%s' % (p,k,p_deg_k)
print 'a=\n',a,'\n'
rez=flint.test_invert_4x4_corner( flint.fmpz_mat(a1), p, k )
if rez==None:
a_det=a.determinant() % p
if a_det==0:
return
print 'a=',a
die('Empty result from test_invert_4x4_corner()')
negate_det,det,i,u=rez
i %= p_deg_k
u %= p_deg_k
try:
iInv=i.change_ring(Zn(p_deg_k)).I
except:
test_1_failed( a, i, u, negate_det, 'i not invertible', p_deg_k )
a_p=a.change_ring(Zn(p_deg_k))
a_det=a.determinant() % p_deg_k
det %= p_deg_k
if negate_det&1:
det=p_deg_k-det
if det != a_det:
print "good/bad determinant: %s / %s" % (a_det,det)
test_1_failed( a, i, u, negate_det, 'bad determinant', p_deg_k )
if u[1,0]==2 and u[2,0]==3 and u[3,0]==4 and u[4,0]==5:
if not iInv==a_p:
print 'p**k=%s' % p_deg_k
print 'a modulo p**k=\n',a % p_deg_k
print "i' modulo p**k=\n",iInv % p_deg_k
test_1_failed( a, i, u, negate_det, 'bad inverse, kind 0', p_deg_k )
else:
a1_p=a1.change_ring(Zn(p_deg_k))
for v in range(4):
for w in range(4):
u[1+v,1+w]=iInv[v,w]
u_p=u.change_ring(Zn(p_deg_k))
try:
a_i=a1_p.I
except:
test_1_failed( a, i, u, negate_det, 'a1 is not invertible', p_deg_k )
v=u_p*a_i
if not is_permutation(v):
print 'u=\n',u
test_1_failed( a, i, u, negate_det, 'a1 is not a row-swapped u', p_deg_k )
def det_flint(a,f,way): global t1 if t1[way]<-0.1: return aF=flint.fmpz_mat( a ) if loud: print 'starts subroutine %s' % f t0=time.time() signal.alarm(time_constraint) try: one=f(aF) t1[way] += time.time()-t0 if loud: print 'spent',t1[way] except: t1[way]=-1 if loud: print 'TiMeOuT'
def test_m(m,i_m_first): global t_FLINT, t_RAZIN a=flint.fmpz_mat( m ) if i_m_first: t0=time.time() dG = flint.det(a) t1=time.time() dB = flint.det_20140704( a ) t2=time.time() t_FLINT += t1-t0 t_RAZIN += t2-t1 else: t0=time.time() dB = flint.det_20140704( a ) t1=time.time() dG = flint.det(a) t2=time.time() t_FLINT += t2-t1 t_RAZIN += t1-t0 if dG==dB: return print 'test failed, det good/bad=%s/%s' % (dG,dB) print m.__repr__() assert 0
def sage_ZZ_to_flint_QQ( d, a ): return F( (Integer(d), flint.fmpz_mat( a ) ) )
import sage.all
import flint_sage as flint
import sys
dim = 2
ZZ = sage.all.ZZ
def straighten(xx):
r = []
for i in xx:
for j in i:
r.append(j)
return r
def random_matrice():
return sage.all.random_matrix(ZZ, dim, dim + 2, x=-100, y=100)
for i in range(10):
a = random_matrice()
# both forms of constructor work
if i & 1:
b = flint.fmpz_mat(a)
else:
b = flint.fmpz_mat((dim, dim + 2, straighten(list(a))))
assert a == b.export_sage()
print "\ntest passed"
