erfcx_real_vectorreturns an array of values of the scaled complementary error function .
For full information please refer to the NAG Library document for s15au
- xfloat, array-like, shape
The argument of the function, for .
- ffloat, ndarray, shape
, the function values.
- ivalidint, ndarray, shape
contains the error code for , for .
is too large and positive. The threshold value is the same as for = 1 in
was in the interval . The threshold values are the same as for = 2 in
is too small and positive. The threshold value is the same as for = 3 in
- (errno )
On entry, .
- (errno )
On entry, at least one value of produced a result with reduced accuracy.
Check for more information.
erfcx_real_vectorcalculates approximate values for the scaled complementary error function
for an array of arguments , for .
Let be the root of the equation (then ). For the value of is based on the following rational Chebyshev expansion for :
where denotes a rational function of degree in the numerator and in the denominator.
For the value of is based on a rational Chebyshev expansion for : for the value is based on the expansion
and for it is based on the expansion
For each expansion, the specific values of and are selected to be minimal such that the maximum relative error in the expansion is of the order , where is the maximum number of decimal digits that can be accurately represented for the particular implementation (see
Asymptotically, . There is a danger of setting underflow in whenever , where is the largest positive model number (see
machine.real_largest) and is the smallest positive model number (see
machine.real_smallest). In this case
erfcx_real_vectorexits with = 1 and returns with . For in the range , where is the machine precision, the asymptotic value is returned for , , and
erfcx_real_vectorexits with = 1.
There is a danger of setting overflow in whenever . In this case
erfcx_real_vectorexits with = 1 and returns with .
NIST Digital Library of Mathematical Functions
Cody, W J, 1969, Rational Chebyshev approximations for the error function, Math.Comp. (23), 631–637