Mathematical Operations🔗
Trigonometric Functions🔗
| Operation | Meaning | HALCON Operator |
|---|---|---|
sin(a) |
sine of a |
tuple_sin |
cos(a) |
cosine of a |
tuple_cos |
tan(a) |
tangent of a |
tuple_tan |
asin(a) |
arc sine of a in the interval \([-\pi/2,\pi/2], a \in [-1, 1]\) |
tuple_asin |
acos(a) |
arc cosine a in the interval \([-\pi/2,\pi/2], a \in [-1, 1]\) |
tuple_acos |
atan(a) |
arc tangent a in the interval \([-\pi/2,\pi/2], a \in [-\infty, +\infty]\) |
tuple_atan |
atan2(a1,a2) |
arc tangent a1/a2 in the interval \([-\pi,\pi]\) |
tuple_atan2 |
sinh(a) |
hyperbolic sine of a |
tuple_sinh |
cosh(a) |
hyperbolic cosine of a |
tuple_cosh |
tanh(a) |
hyperbolic tangent of a |
tuple_tanh |
asinh(a) |
inverse hyperbolic sine of a |
tuple_asinh |
acosh(a) |
inverse hyperbolic cosine of a |
tuple_acosh |
atanh(a) |
inverse hyperbolic tangent of a |
tuple_atanh |
Exponential Functions🔗
Operation |
Meaning | HALCON operator |
|---|---|---|
exp(a) |
exponential function \(e^a\) | tuple_exp |
exp2(a) |
base 2 exponential function \(2^a\) | tuple_exp2 |
exp10(a) |
base 10 exponential function \(10^a\) | tuple_exp10 |
log(a) |
natural logarithm \(\ln(a)\), \(a>0\) | tuple_log |
log2(a) |
base 2 logarithm, \(\log_2(a)\), \(a>0\) | tuple_log2 |
log10(a) |
base 10 logarithm, \(\log_{10}(a)\), \(a>0\) | tuple_log10 |
pow(a1,a2) |
\(a1^{a2}\) | tuple_pow |
ldexp(a1,a2) |
\(a1\cdot 2^{\operatorname{floor}(a2)}\) | tuple_ldexp |
tgamma(a) |
gamma function \(\Gamma(a)\) | tuple_tgamma |
lgamma(a) |
logarithm of the absolute value of the gamma function \(\log( \| \Gamma(a) \| )\) | tuple_lgamma |
erf(a) |
error function \(erf(a)\) | tuple_erf |
erfc(a) |
complementary error function \(erfc(a)\) | tuple_erfc |
Numerical Functions🔗
| Operation | Meaning | HALCON operator |
|---|---|---|
min(t) |
minimum value of the tuple | tuple_min |
min2(t1,t2) |
elementwise minimum of two tuples | tuple_min2 |
max(t) |
maximum value of the tuple | tuple_max |
max2(t1,t2) |
elementwise maximum of two tuples | tuple_max2 |
sum(t) |
sum of all tuple elements or string concatenation | tuple_sum |
mean(a) |
mean value | tuple_mean |
deviation(a) |
standard deviation | tuple_deviation |
cumul(a) |
cumulative sums of a tuple | tuple_cumul |
median(a) |
median of a tuple | tuple_median |
select_rank(a,i) |
element at rank i of a tuple | tuple_select_rank |
sqrt(a) |
square root \(\sqrt{a}\) | tuple_sqrt |
cbrt(a) |
cube root \(\sqrt[3]{a}\) | tuple_cbrt |
hypot(a,b) |
hypotenuse \(\sqrt{a^2+b^2}\) | tuple_hypot |
deg(a) |
convert radians to degrees | tuple_deg |
rad(a) |
convert degrees to radians | tuple_rad |
real(a) |
convert integer to real |
tuple_real |
int(a) |
truncate real to integer |
tuple_int |
round(a) |
convert real to integer |
tuple_round |
abs(a) |
absolute value of a (integer or real) |
tuple_abs |
fabs(a) |
absolute value of a (always real) |
tuple_fabs |
ceil(a) |
smallest integer value not smaller than a |
tuple_ceil |
floor(a) |
largest integer value not greater than a |
tuple_floor |
fmod(a1,a2) |
fractional part of a1/a2, with the same sign as a1 |
tuple_fmod |
sgn(a) |
elementwise sign of a tuple | tuple_sgn |
Example
The following example (file name: euclid_distance.hdev) shows the use of some numerical functions.
Preview Restrictions
HDevelopEVO does not support vectors yet.
V1 := [18.8,132.4,33,19.3]
V2 := [233.23,32.786,234.4224,63.33]
Diff := V1 - V2
Distance := sqrt(sum(Diff * Diff))
Dotvalue := sum(V1 * V2)
First, the Euclidean distance of the two vectors V1 and V2 is computed by using the formula:
\[d = \sqrt{\sum_i(V1_i - V2_i)^2}\]
The difference and the multiplication (square) are successively applied to each element of both vectors.
Afterward, sum computes the sum of the squares.
Then the square root of the sum is calculated.
After that, the dot product of V1 and V2 is determined by the formula:
\[\left<V1,V2\right> = \sum_i(V1_i \cdot V2_i)\]