# Changeset 706f466 in sasmodels

Ignore:
Timestamp:
Sep 28, 2017 4:40:23 PM (7 years ago)
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
6ab64c9
Parents:
62d7601
Message:

fix doc strings for python-based sas special functions

Files:
2 edited

### Legend:

Unmodified
 r4f611f1 """ r""" Special Functions ................. M_PI, M_PI_2, M_PI_4, M_SQRT1_2, M_E: $\pi$, $\pi/2$, $\pi/4$, $1/\sqrt{2}$ and Euler's constant $e$ exp, log, pow(x,y), expm1, sqrt: Power functions $e^x$, $\ln x$, $x^y$, $e^x - 1$, $\sqrt{x}$. The function expm1(x) is accurate across all $x$, including $x$ very close to zero. sin, cos, tan, asin, acos, atan: Trigonometry functions and inverses, operating on radians. sinh, cosh, tanh, asinh, acosh, atanh: Hyperbolic trigonometry functions. atan2(y,x): Angle from the $x$\ -axis to the point $(x,y)$, which is equal to atan(y/x) would return a value in quadrant I. Similarly for quadrants II and IV when $x$ and $y$ have opposite sign. fmin(x,y), fmax(x,y), trunc, rint: Floating point functions.  rint(x) returns the nearest integer. NAN: NaN, Not a Number, $0/0$.  Use isnan(x) to test for NaN.  Note that you cannot use :code:x == NAN to test for NaN values since that will always return false.  NAN does not equal NAN! INFINITY: $\infty, 1/0$.  Use isinf(x) to test for infinity, or isfinite(x) to test for finite and not NaN. erf, erfc, tgamma, lgamma:  **do not use** Special functions that should be part of the standard, but are missing M_PI_180, M_4PI_3: $\frac{\pi}{180}$, $\frac{4\pi}{3}$ SINCOS(x, s, c): Macro which sets s=sin(x) and c=cos(x). The variables *c* and *s* must be declared first. square(x): $x^2$ cube(x): $x^3$ sas_sinx_x(x): $\sin(x)/x$, with limit $\sin(0)/0 = 1$. powr(x, y): $x^y$ for $x \ge 0$; this is faster than general $x^y$ on some GPUs. pown(x, n): $x^n$ for $n$ integer; this is faster than general $x^n$ on some GPUs. FLOAT_SIZE: The number of bytes in a floating point value.  Even though all ... code for single precision ... #endif SAS_DOUBLE: A replacement for :code:double so that the declared variable will sorted from highest to lowest. :code:source = ["lib/polevl.c", ...] (link to code _) p1evl(x, c, n): Evaluation of normalized polynomial $p(x) = x^n + \sum_{i=0}^{n-1} c_i x^i$ sorted from highest to lowest. :code:source = ["lib/polevl.c", ...] (link to code _) sas_gamma(x): Gamma function $\text{sas_gamma}(x) = \Gamma(x)$. The standard math function, tgamma(x) is unstable for $x < 1$ on some platforms. :code:source = ["lib/sasgamma.c", ...] (link to code _) sas_erf(x), sas_erfc(x): on some platforms. :code:source = ["lib/polevl.c", "lib/sas_erf.c", ...] (link to error functions' code _) sas_J0(x): Bessel function of the first kind $\text{sas_J0}(x)=J_0(x)$ where The standard math function j0(x) is not available on all platforms. :code:source = ["lib/polevl.c", "lib/sas_J0.c", ...] (link to Bessel function's code _) sas_J1(x): Bessel function of the first kind  $\text{sas_J1}(x)=J_1(x)$ where The standard math function j1(x) is not available on all platforms. :code:source = ["lib/polevl.c", "lib/sas_J1.c", ...] (link to Bessel function's code _) sas_JN(n, x): The standard math function jn(n, x) is not available on all platforms. :code:source = ["lib/polevl.c", "lib/sas_J0.c", "lib/sas_J1.c", "lib/sas_JN.c", ...] (link to Bessel function's code _) sas_Si(x): Sine integral $\text{Si}(x) = \int_0^x \tfrac{\sin t}{t}\,dt$. - \frac{x^3}{3\times 3!} + \frac{x^5}{5 \times 5!} - \frac{x^7}{7 \times 7!} + \frac{x^9}{9\times 9!} - \frac{x^{11}}{11\times 11!} :code:source = ["lib/Si.c", ...] (link to code _) sas_3j1x_x(x): This function uses a Taylor series for small $x$ for numerical accuracy. :code:source = ["lib/sas_3j1x_x.c", ...] (link to code _) sas_2J1x_x(x): and first order. :code:source = ["lib/polevl.c", "lib/sas_J1.c", ...] (link to Bessel form's code _) Gauss76Z[i], Gauss76Wt[i]: Similar arrays are available in :code:gauss20.c for 20-point quadrature and in :code:gauss150.c for 150-point quadrature. :code:source = ["lib/gauss76.c", ...] (link to code _) """ retvalue = (sin(x) - x*cos(x))/x**2 retvalue[x == 0.] = 0. def sas_3j1x_x(x): if np.isscalar(x): Gauss20Wt = np.array([ .0176140071391521, .0406014298003869, .0626720483341091, .0832767415767047, .10193011981724, .118194531961518, .131688638449177, .142096109318382, .149172986472604, .152753387130726, .152753387130726, .149172986472604, .142096109318382, .131688638449177, .118194531961518, .10193011981724, .0832767415767047, .0626720483341091, .0406014298003869, .0176140071391521 .0176140071391521, .0406014298003869, .0626720483341091, .0832767415767047, .10193011981724, .118194531961518, .131688638449177, .142096109318382, .149172986472604, .152753387130726, .152753387130726, .149172986472604, .142096109318382, .131688638449177, .118194531961518, .10193011981724, .0832767415767047, .0626720483341091, .0406014298003869, .0176140071391521 ]) Gauss20Z = np.array([ -.993128599185095, -.963971927277914, -.912234428251326, -.839116971822219, -.746331906460151, -.636053680726515, -.510867001950827, -.37370608871542, -.227785851141645, -.076526521133497, .0765265211334973, .227785851141645, .37370608871542, .510867001950827, .636053680726515, .746331906460151, .839116971822219, .912234428251326, .963971927277914, .993128599185095 -.993128599185095, -.963971927277914, -.912234428251326, -.839116971822219, -.746331906460151, -.636053680726515, -.510867001950827, -.37370608871542, -.227785851141645, -.076526521133497, .0765265211334973, .227785851141645, .37370608871542, .510867001950827, .636053680726515, .746331906460151, .839116971822219, .912234428251326, .963971927277914, .993128599185095 ]) Gauss76Wt = np.array([ .00126779163408536,             #0 .00294910295364247, .00462793522803742, .00629918049732845, .00795984747723973, .00960710541471375, .0112381685696677, .0128502838475101, .0144407317482767, .0160068299122486, .0175459372914742,              #10 .0190554584671906, .020532847967908, .0219756145344162, .0233813253070112, .0247476099206597, .026072164497986, .0273527555318275, .028587223650054, .029773487255905, .0309095460374916,              #20 .0319934843404216, .0330234743977917, .0339977794120564, .0349147564835508, .0357728593807139, .0365706411473296, .0373067565423816, .0379799643084053, .0385891292645067, .0391332242205184,              #30 .0396113317090621, .0400226455325968, .040366472122844, .0406422317102947, .0408494593018285, .040987805464794, .0410570369162294, .0410570369162294, .040987805464794, .0408494593018285,              #40 .0406422317102947, .040366472122844, .0400226455325968, .0396113317090621, .0391332242205184, .0385891292645067, .0379799643084053, .0373067565423816, .0365706411473296, .0357728593807139,              #50 .0349147564835508, .0339977794120564, .0330234743977917, .0319934843404216, .0309095460374916, .029773487255905, .028587223650054, .0273527555318275, .026072164497986, .0247476099206597,              #60 .0233813253070112, .0219756145344162, .020532847967908, .0190554584671906, .0175459372914742, .0160068299122486, .0144407317482767, .0128502838475101, .0112381685696677, .00960710541471375,             #70 .00795984747723973, .00629918049732845, .00462793522803742, .00294910295364247, .00126779163408536              #75 (indexed from 0) .00126779163408536,         #0 .00294910295364247, .00462793522803742, .00629918049732845, .00795984747723973, .00960710541471375, .0112381685696677, .0128502838475101, .0144407317482767, .0160068299122486, .0175459372914742,          #10 .0190554584671906, .020532847967908, .0219756145344162, .0233813253070112, .0247476099206597, .026072164497986, .0273527555318275, .028587223650054, .029773487255905, .0309095460374916,          #20 .0319934843404216, .0330234743977917, .0339977794120564, .0349147564835508, .0357728593807139, .0365706411473296, .0373067565423816, .0379799643084053, .0385891292645067, .0391332242205184,          #30 .0396113317090621, .0400226455325968, .040366472122844, .0406422317102947, .0408494593018285, .040987805464794, .0410570369162294, .0410570369162294, .040987805464794, .0408494593018285,          #40 .0406422317102947, .040366472122844, .0400226455325968, .0396113317090621, .0391332242205184, .0385891292645067, .0379799643084053, .0373067565423816, .0365706411473296, .0357728593807139,          #50 .0349147564835508, .0339977794120564, .0330234743977917, .0319934843404216, .0309095460374916, .029773487255905, .028587223650054, .0273527555318275, .026072164497986, .0247476099206597,          #60 .0233813253070112, .0219756145344162, .020532847967908, .0190554584671906, .0175459372914742, .0160068299122486, .0144407317482767, .0128502838475101, .0112381685696677, .00960710541471375,         #70 .00795984747723973, .00629918049732845, .00462793522803742, .00294910295364247, .00126779163408536          #75 (indexed from 0) ]) Gauss76Z = np.array([ -.999505948362153,              #0 -.997397786355355, -.993608772723527, -.988144453359837, -.981013938975656, -.972229228520377, -.961805126758768, -.949759207710896, -.936111781934811, -.92088586125215, -.904107119545567,              #10 -.885803849292083, -.866006913771982, -.844749694983342, -.822068037328975, -.7980001871612, -.77258672828181, -.74587051350361, -.717896592387704, -.688712135277641, -.658366353758143,              #20 -.626910417672267, -.594397368836793, -.560882031601237, -.526420920401243, -.491072144462194, -.454895309813726, -.417951418780327, -.380302767117504, -.342012838966962, -.303146199807908,              #30 -.263768387584994, -.223945802196474, -.183745593528914, -.143235548227268, -.102483975391227, -.0615595913906112, -.0205314039939986, .0205314039939986, .0615595913906112, .102483975391227,                       #40 .143235548227268, .183745593528914, .223945802196474, .263768387584994, .303146199807908, .342012838966962, .380302767117504, .417951418780327, .454895309813726, .491072144462194,               #50 .526420920401243, .560882031601237, .594397368836793, .626910417672267, .658366353758143, .688712135277641, .717896592387704, .74587051350361, .77258672828181, .7980001871612, #60 .822068037328975, .844749694983342, .866006913771982, .885803849292083, .904107119545567, .92088586125215, .936111781934811, .949759207710896, .961805126758768, .972229228520377,               #70 .981013938975656, .988144453359837, .993608772723527, .997397786355355, .999505948362153                #75 -.999505948362153,          #0 -.997397786355355, -.993608772723527, -.988144453359837, -.981013938975656, -.972229228520377, -.961805126758768, -.949759207710896, -.936111781934811, -.92088586125215, -.904107119545567,          #10 -.885803849292083, -.866006913771982, -.844749694983342, -.822068037328975, -.7980001871612, -.77258672828181, -.74587051350361, -.717896592387704, -.688712135277641, -.658366353758143,          #20 -.626910417672267, -.594397368836793, -.560882031601237, -.526420920401243, -.491072144462194, -.454895309813726, -.417951418780327, -.380302767117504, -.342012838966962, -.303146199807908,          #30 -.263768387584994, -.223945802196474, -.183745593528914, -.143235548227268, -.102483975391227, -.0615595913906112, -.0205314039939986, .0205314039939986, .0615595913906112, .102483975391227,                   #40 .143235548227268, .183745593528914, .223945802196474, .263768387584994, .303146199807908, .342012838966962, .380302767117504, .417951418780327, .454895309813726, .491072144462194,           #50 .526420920401243, .560882031601237, .594397368836793, .626910417672267, .658366353758143, .688712135277641, .717896592387704, .74587051350361, .77258672828181, .7980001871612,     #60 .822068037328975, .844749694983342, .866006913771982, .885803849292083, .904107119545567, .92088586125215, .936111781934811, .949759207710896, .961805126758768, .972229228520377,           #70 .981013938975656, .988144453359837, .993608772723527, .997397786355355, .999505948362153            #75 ]) Gauss150Z = np.array([ -0.9998723404457334, -0.9993274305065947, -0.9983473449340834, -0.9969322929775997, -0.9950828645255290, -0.9927998590434373, -0.9900842691660192, -0.9869372772712794, -0.9833602541697529, -0.9793547582425894, -0.9749225346595943, -0.9700655145738374, -0.9647858142586956, -0.9590857341746905, -0.9529677579610971, -0.9464345513503147, 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