matrix & jnf(const matrix & m, matrix & jnf_matrix, basis & retbasis)
{
/* jnf:
Beschreibung:
diese Funktion liefert zu einer gegebenen Matrix, die Jordansche Normalform und die zugehoerige Basis
Eingabe:
matrix m, die betrachtete Matrix
vektor eigenwerte, die Eigenwerte der Matrix
Rueckgabe.
jnf_matrix, die Jordan Form der Matrix
basis retbasis, die Jordan Basis der Matrix
*/
int dim=(int)m.size();
//Falls m und jnf_matrix auf die selbe Matrix zeigen
if (&m==&jnf_matrix)
{
matrix source=m;
return jnf(source,jnf_matrix, retbasis);
}
vector< pair<K, int> > eigen;
eigenwerte(m,eigen);
nullmatrix(dim, dim, jnf_matrix);
vector<int> zykel_len;
int pos=0;
for (size_t k=0; k < eigen.size(); k++)
{
// durchlaufe alle Eigenwerte
zykel_len.clear();
primbasis(m, eigen[k], retbasis, zykel_len);
// erstellen die Jordan Form der Matrix
for (size_t i=0; i < zykel_len.size(); i++)
{
jnf_matrix[pos][pos]=eigen[k].first;
pos++;
for (int j=1; j < zykel_len[i]; j++)
{
jnf_matrix[pos][pos]=eigen[k].first;
jnf_matrix[pos][pos-1]=(K)1;
pos++;
}
}
}
return jnf_matrix;
}
TEST(math, jnf) {
ASSERT_FLOAT_EQ(0.0f, jnf(4, 0.0f));
ASSERT_FLOAT_EQ(0.0024766389f, jnf(4, 1.0f));
}
void
domathf (void)
{
#ifndef NO_FLOAT
float f1;
float f2;
int i1;
f1 = acosf(0.0);
fprintf( stdout, "acosf : %f\n", f1);
f1 = acoshf(0.0);
fprintf( stdout, "acoshf : %f\n", f1);
f1 = asinf(1.0);
fprintf( stdout, "asinf : %f\n", f1);
f1 = asinhf(1.0);
fprintf( stdout, "asinhf : %f\n", f1);
f1 = atanf(M_PI_4);
fprintf( stdout, "atanf : %f\n", f1);
f1 = atan2f(2.3, 2.3);
fprintf( stdout, "atan2f : %f\n", f1);
f1 = atanhf(1.0);
fprintf( stdout, "atanhf : %f\n", f1);
f1 = cbrtf(27.0);
fprintf( stdout, "cbrtf : %f\n", f1);
f1 = ceilf(3.5);
fprintf( stdout, "ceilf : %f\n", f1);
f1 = copysignf(3.5, -2.5);
fprintf( stdout, "copysignf : %f\n", f1);
f1 = cosf(M_PI_2);
fprintf( stdout, "cosf : %f\n", f1);
f1 = coshf(M_PI_2);
fprintf( stdout, "coshf : %f\n", f1);
f1 = erff(42.0);
fprintf( stdout, "erff : %f\n", f1);
f1 = erfcf(42.0);
fprintf( stdout, "erfcf : %f\n", f1);
f1 = expf(0.42);
fprintf( stdout, "expf : %f\n", f1);
f1 = exp2f(0.42);
fprintf( stdout, "exp2f : %f\n", f1);
f1 = expm1f(0.00042);
fprintf( stdout, "expm1f : %f\n", f1);
f1 = fabsf(-1.123);
fprintf( stdout, "fabsf : %f\n", f1);
f1 = fdimf(1.123, 2.123);
fprintf( stdout, "fdimf : %f\n", f1);
f1 = floorf(0.5);
fprintf( stdout, "floorf : %f\n", f1);
f1 = floorf(-0.5);
fprintf( stdout, "floorf : %f\n", f1);
f1 = fmaf(2.1, 2.2, 3.01);
fprintf( stdout, "fmaf : %f\n", f1);
f1 = fmaxf(-0.42, 0.42);
fprintf( stdout, "fmaxf : %f\n", f1);
f1 = fminf(-0.42, 0.42);
fprintf( stdout, "fminf : %f\n", f1);
f1 = fmodf(42.0, 3.0);
fprintf( stdout, "fmodf : %f\n", f1);
/* no type-specific variant */
i1 = fpclassify(1.0);
fprintf( stdout, "fpclassify : %d\n", i1);
f1 = frexpf(42.0, &i1);
fprintf( stdout, "frexpf : %f\n", f1);
f1 = hypotf(42.0, 42.0);
fprintf( stdout, "hypotf : %f\n", f1);
i1 = ilogbf(42.0);
fprintf( stdout, "ilogbf : %d\n", i1);
/* no type-specific variant */
i1 = isfinite(3.0);
fprintf( stdout, "isfinite : %d\n", i1);
/* no type-specific variant */
i1 = isgreater(3.0, 3.1);
fprintf( stdout, "isgreater : %d\n", i1);
/* no type-specific variant */
i1 = isgreaterequal(3.0, 3.1);
fprintf( stdout, "isgreaterequal : %d\n", i1);
/* no type-specific variant */
i1 = isinf(3.0);
fprintf( stdout, "isinf : %d\n", i1);
/* no type-specific variant */
i1 = isless(3.0, 3.1);
fprintf( stdout, "isless : %d\n", i1);
/* no type-specific variant */
i1 = islessequal(3.0, 3.1);
fprintf( stdout, "islessequal : %d\n", i1);
/* no type-specific variant */
i1 = islessgreater(3.0, 3.1);
fprintf( stdout, "islessgreater : %d\n", i1);
/* no type-specific variant */
i1 = isnan(0.0);
fprintf( stdout, "isnan : %d\n", i1);
/* no type-specific variant */
i1 = isnormal(3.0);
fprintf( stdout, "isnormal : %d\n", i1);
/* no type-specific variant */
f1 = isunordered(1.0, 2.0);
fprintf( stdout, "isunordered : %d\n", i1);
f1 = j0f(1.2);
fprintf( stdout, "j0f : %f\n", f1);
f1 = j1f(1.2);
fprintf( stdout, "j1f : %f\n", f1);
f1 = jnf(2,1.2);
fprintf( stdout, "jnf : %f\n", f1);
f1 = ldexpf(1.2,3);
fprintf( stdout, "ldexpf : %f\n", f1);
f1 = lgammaf(42.0);
fprintf( stdout, "lgammaf : %f\n", f1);
f1 = llrintf(-0.5);
fprintf( stdout, "llrintf : %f\n", f1);
f1 = llrintf(0.5);
fprintf( stdout, "llrintf : %f\n", f1);
f1 = llroundf(-0.5);
fprintf( stdout, "lroundf : %f\n", f1);
f1 = llroundf(0.5);
fprintf( stdout, "lroundf : %f\n", f1);
f1 = logf(42.0);
fprintf( stdout, "logf : %f\n", f1);
f1 = log10f(42.0);
fprintf( stdout, "log10f : %f\n", f1);
f1 = log1pf(42.0);
fprintf( stdout, "log1pf : %f\n", f1);
f1 = log2f(42.0);
fprintf( stdout, "log2f : %f\n", f1);
f1 = logbf(42.0);
fprintf( stdout, "logbf : %f\n", f1);
f1 = lrintf(-0.5);
fprintf( stdout, "lrintf : %f\n", f1);
f1 = lrintf(0.5);
fprintf( stdout, "lrintf : %f\n", f1);
f1 = lroundf(-0.5);
fprintf( stdout, "lroundf : %f\n", f1);
f1 = lroundf(0.5);
fprintf( stdout, "lroundf : %f\n", f1);
f1 = modff(42.0,&f2);
fprintf( stdout, "lmodff : %f\n", f1);
f1 = nanf("");
fprintf( stdout, "nanf : %f\n", f1);
f1 = nearbyintf(1.5);
fprintf( stdout, "nearbyintf : %f\n", f1);
f1 = nextafterf(1.5,2.0);
fprintf( stdout, "nextafterf : %f\n", f1);
f1 = powf(3.01, 2.0);
fprintf( stdout, "powf : %f\n", f1);
f1 = remainderf(3.01,2.0);
fprintf( stdout, "remainderf : %f\n", f1);
f1 = remquof(29.0,3.0,&i1);
fprintf( stdout, "remquof : %f\n", f1);
f1 = rintf(0.5);
fprintf( stdout, "rintf : %f\n", f1);
f1 = rintf(-0.5);
fprintf( stdout, "rintf : %f\n", f1);
f1 = roundf(0.5);
fprintf( stdout, "roundf : %f\n", f1);
f1 = roundf(-0.5);
fprintf( stdout, "roundf : %f\n", f1);
f1 = scalblnf(1.2,3);
fprintf( stdout, "scalblnf : %f\n", f1);
f1 = scalbnf(1.2,3);
fprintf( stdout, "scalbnf : %f\n", f1);
/* no type-specific variant */
i1 = signbit(1.0);
fprintf( stdout, "signbit : %i\n", i1);
f1 = sinf(M_PI_4);
fprintf( stdout, "sinf : %f\n", f1);
f1 = sinhf(M_PI_4);
fprintf( stdout, "sinhf : %f\n", f1);
f1 = sqrtf(9.0);
fprintf( stdout, "sqrtf : %f\n", f1);
f1 = tanf(M_PI_4);
fprintf( stdout, "tanf : %f\n", f1);
f1 = tanhf(M_PI_4);
fprintf( stdout, "tanhf : %f\n", f1);
f1 = tgammaf(2.1);
fprintf( stdout, "tgammaf : %f\n", f1);
f1 = truncf(3.5);
fprintf( stdout, "truncf : %f\n", f1);
f1 = y0f(1.2);
fprintf( stdout, "y0f : %f\n", f1);
f1 = y1f(1.2);
fprintf( stdout, "y1f : %f\n", f1);
f1 = ynf(3,1.2);
fprintf( stdout, "ynf : %f\n", f1);
#endif
}
__global__ void FloatMathPrecise() {
int iX;
float fX, fY;
acosf(1.0f);
acoshf(1.0f);
asinf(0.0f);
asinhf(0.0f);
atan2f(0.0f, 1.0f);
atanf(0.0f);
atanhf(0.0f);
cbrtf(0.0f);
fX = ceilf(0.0f);
fX = copysignf(1.0f, -2.0f);
cosf(0.0f);
coshf(0.0f);
cospif(0.0f);
cyl_bessel_i0f(0.0f);
cyl_bessel_i1f(0.0f);
erfcf(0.0f);
erfcinvf(2.0f);
erfcxf(0.0f);
erff(0.0f);
erfinvf(1.0f);
exp10f(0.0f);
exp2f(0.0f);
expf(0.0f);
expm1f(0.0f);
fX = fabsf(1.0f);
fdimf(1.0f, 0.0f);
fdividef(0.0f, 1.0f);
fX = floorf(0.0f);
fmaf(1.0f, 2.0f, 3.0f);
fX = fmaxf(0.0f, 0.0f);
fX = fminf(0.0f, 0.0f);
fmodf(0.0f, 1.0f);
frexpf(0.0f, &iX);
hypotf(1.0f, 0.0f);
ilogbf(1.0f);
isfinite(0.0f);
fX = isinf(0.0f);
fX = isnan(0.0f);
j0f(0.0f);
j1f(0.0f);
jnf(-1.0f, 1.0f);
ldexpf(0.0f, 0);
lgammaf(1.0f);
llrintf(0.0f);
llroundf(0.0f);
log10f(1.0f);
log1pf(-1.0f);
log2f(1.0f);
logbf(1.0f);
logf(1.0f);
lrintf(0.0f);
lroundf(0.0f);
modff(0.0f, &fX);
fX = nanf("1");
fX = nearbyintf(0.0f);
nextafterf(0.0f, 0.0f);
norm3df(1.0f, 0.0f, 0.0f);
norm4df(1.0f, 0.0f, 0.0f, 0.0f);
normcdff(0.0f);
normcdfinvf(1.0f);
fX = 1.0f;
normf(1, &fX);
powf(1.0f, 0.0f);
rcbrtf(1.0f);
remainderf(2.0f, 1.0f);
remquof(1.0f, 2.0f, &iX);
rhypotf(0.0f, 1.0f);
fY = rintf(1.0f);
rnorm3df(0.0f, 0.0f, 1.0f);
rnorm4df(0.0f, 0.0f, 0.0f, 1.0f);
fX = 1.0f;
rnormf(1, &fX);
fY = roundf(0.0f);
rsqrtf(1.0f);
scalblnf(0.0f, 1);
scalbnf(0.0f, 1);
signbit(1.0f);
sincosf(0.0f, &fX, &fY);
sincospif(0.0f, &fX, &fY);
sinf(0.0f);
sinhf(0.0f);
sinpif(0.0f);
sqrtf(0.0f);
tanf(0.0f);
tanhf(0.0f);
tgammaf(2.0f);
fY = truncf(0.0f);
y0f(1.0f);
y1f(1.0f);
ynf(1, 1.0f);
}
