Python gamfcn Examples

Example #1

def students_t(x, amplitude=1.0, center=0.0, sigma=1.0):
    """Student's t distribution:
        gamma((sigma+1)/2)   (1 + (x-center)**2/sigma)^(-(sigma+1)/2)
     =  -------------------------
        sqrt(sigma*pi)gamma(sigma/2)

    """
    s1  = (sigma+1)/2.0
    denom = (sqrt(sigma*pi)*gamfcn(sigma/2))
    return amplitude*(1 + (x-center)**2/sigma)**(-s1) * gamfcn(s1) / denom

Example #2

File: lineshapes.py Project: danielballan/lmfit-py

def students_t(x, amplitude=1.0, center=0.0, sigma=1.0):
    """Student's t distribution:
        gamma((sigma+1)/2)   (1 + (x-center)**2/sigma)^(-(sigma+1)/2)
     =  -------------------------
        sqrt(sigma*pi)gamma(sigma/2)

    """
    s1  = (sigma+1)/2.0
    denom = (sqrt(sigma*pi)*gamfcn(sigma/2))
    return amplitude*(1 + (x-center)**2/sigma)**(-s1) * gamfcn(s1) / denom

Example #3

def pearson7(x, area, center, sigma, expon):
    """Return a Pearson7 lineshape.
    Using the wikipedia definition:
    pearson7(x, center, sigma, expon) =
        amplitude*(1+arg**2)**(-expon)/(sigma*beta(expon-0.5, 0.5))
    where arg = (x-center)/sigma
    and beta() is the beta function.
    """
    arg = (x - center) / sigma
    scale = area * gamfcn(expon) / (gamfcn(0.5) * gamfcn(expon - 0.5))
    return scale * (1 + arg**2)**(-expon) / sigma

Example #4

File: lineshapes.py Project: danielballan/lmfit-py

def pearson7(x, amplitude=1.0, center=0.0, sigma=1.0, expon=1.0):
    """pearson7 lineshape, using the wikipedia definition:

    pearson7(x, center, sigma, expon) =
      amplitude*(1+arg**2)**(-expon)/(sigma*beta(expon-0.5, 0.5))

    where arg = (x-center)/sigma
    and beta() is the beta function.
    """
    arg = (x-center)/sigma
    scale = amplitude * gamfcn(expon)/(gamfcn(0.5)*gamfcn(expon-0.5))
    return  scale*(1+arg**2)**(-expon)/sigma

Example #5

def students_t(x, amplitude=1.0, center=0.0, sigma=1.0):
    """Return Student's t-distribution.

    students_t(x, amplitude, center, sigma) =

             gamma((sigma+1)/2)
        ---------------------------- * (1 + (x-center)**2/sigma)^(-(sigma+1)/2)
        sqrt(sigma*pi)gamma(sigma/2)

    """
    s1 = (sigma+1)/2.0
    denom = max(tiny, (sqrt(sigma*pi)*gamfcn(max(tiny, sigma/2))))
    return amplitude*(1 + (x-center)**2/max(tiny, sigma))**(-s1) * gamfcn(s1) / denom

Example #6

File: lineshapes.py Project: lmfit/lmfit-py

def students_t(x, amplitude=1.0, center=0.0, sigma=1.0):
    """Return Student's t distribution.

    students_t(x, amplitude, center, sigma) =

        gamma((sigma+1)/2)   (1 + (x-center)**2/sigma)^(-(sigma+1)/2)
        -------------------------
        sqrt(sigma*pi)gamma(sigma/2)

    """
    s1 = (sigma+1)/2.0
    denom = max(tiny, (sqrt(sigma*pi)*gamfcn(max(tiny, sigma/2))))
    return amplitude*(1 + (x-center)**2/max(tiny, sigma))**(-s1) * gamfcn(s1) / denom

Example #7

def pearson7(x, amplitude=1.0, center=0.0, sigma=1.0, expon=1.0):
    """Return a Pearson7 lineshape.

    Using the Wikipedia definition:

    pearson7(x, center, sigma, expon) =
        amplitude*(1+arg**2)**(-expon)/(sigma*beta(expon-0.5, 0.5))

    where ``arg = (x-center)/sigma`` and `beta` is the beta function.

    """
    expon = max(tiny, expon)
    arg = (x - center) / max(tiny, sigma)
    scale = amplitude * gamfcn(expon) / (gamfcn(0.5) * gamfcn(expon - 0.5))
    return scale * (1 + arg**2)**(-expon) / max(tiny, sigma)

Example #8

File: lineshapes.py Project: ChiLi90/LifetimeFit

def _gamma(x):
    """Return the gamma function."""
    return gamfcn(x)

Example #9

File: lineshapes.py Project: shineusn/lmfit-py

def _gamma(x):
    """gamma function"""
    return gamfcn(x)

Example #10

File: lineshapes.py Project: danielballan/lmfit-py

def _gamma(x):
    """gamma function"""
    return gamfcn(x)

Example #11

File: lineshapes.py Project: lmfit/lmfit-py

def _gamma(x):
    """Return the gamma function."""
    return gamfcn(x)