NLREG Builtin Functions
The following functions are built into NLREG and may be used in expressions. Most of the trig functions have forms
that take angles in units of radians and another form (same name ending with
‘D’) that take angles in units of degrees.
The DEG() and RAD() functions can be used to convert between degrees
and radians.
ABS(x)  Absolute value of x.
ACOS(x)  Arc cosine of x.
The returned value is the angle in radians.
ACOSD(x)  Arc cosine of x.
The returned value is the angle in degrees.
ASIN(x)  Arc sine of x.
The angle must be specified in radians.
ASIND(x)  Arc sine of x.
The angle must be specified in degrees.
ATAN(x)  Arc tangent of x.
The returned angle is in units of radians.
ATAND(x)  Arc tangent of x.
The returned angle is in units of degrees.
BETAI(x,a,b)  Incomplete beta function:
Ix(a,b). The incomplete beta function can be used to compute a variety
of statistical functions. For
example, the probability of Student's t with df degrees of freedom can be computed with BETAI(df/(df+t2),.5*df,.5). The probability of the F statistic with df1 and df2 degrees of freedom can be computed with 2*BETAI(df2/(df2+df1*f),.5*df2,.5*df1).
CEIL(x)  Ceiling of x (an
equivalent name for this function is INT).
Returns the smallest integer that is at least as large as x.
For example, CEIL(1.5)=2; CEIL(4)=4; CEIL(2.6)=2.
COS(x)  Cosine of x.
The angle must be specified in radians.
COSD(x)  Cosine of x.
The angle must be specified in degrees.
COSH(x)  Hyperbolic cosine of x.
COT(x)  Cotangent of x. (COT(x) = 1/TAN(x)). The angle must be
specified in radians.
COTD(x)  Cotangent of x. (COTD(x) = 1/TAND(x)). The angle must be
specified in degrees.
CSC(x)  Cosecant of x. (CSC(x) = 1/SIN(x)). The angle must be
specified in radians.
CSCD(x)  Cosecant of x. (CSCD(x) = 1/SIND(x)). The angle must be
specified in degrees.
CTOP(angle)  Convert an angle in the
compass coordinate system to a polar coordinate angle. The polar coordinate system has the origin
of an angle along the positive X axis and the angle increases in a
counterclockwise direction. The
compass coordinate system has the positive Y axis as the origin (i.e., north)
and the angle increases in a clockwise direction. The PTOC function performs the reverse transformation. The angle is in units of radians.
CTOPD(angle)  Same as ctop() except
the angle is in units of degrees.
DEG(x)  Converts an angle, x, measured in radians to the equivalent number of degrees. Note, the builtin trig functions provided
in NLREG have both radian and degree forms.
The degree versions have the letter “D” appended to the end of their
names such as sin(radians) and sind(degrees).
EI1(alpha,phi)  Elliptic integral of the first kind.
Computes the integral from 0 to phi
(degrees or radians) of the function d.phi/sqrt(1k**2*sin(phi)**2), where k =
sin(alpha). alpha
and phi must be in the range 0 to
90 degrees or p/2
radians. The angle must be specified
in radians.
EI1D(alpha,phi)  Same as ei1() except the angle is specified
in degrees.
EI2(alpha,phi)  Elliptic integral of the
second kind. Computes the integral
from 0 to phi radians of the
function sqrt(1k**2*sin(phi)**2)*d.phi, where k = sin(alpha). alpha and phi must be in the range 0 to p/2
radians.
EI2D(alpha,phi)  Same as ei2() except the
alpha and phi angles must be specified in degrees between 0 and
90.
EIC1(alpha)  Complete elliptic
integral of the first kind. Computes the integral from 0 to p/2
radians of the function d.phi/sqrt(1k**2*sin(phi)**2), where k =
sin(alpha). alpha must be specified in radians and must be in the range 0 to p/2
radians.
EIC1D(alpha)  Same as eic1() except
the angle must be specified in degrees and must be in the range 0 to 90.
EIC2(alpha)  Complete elliptic integral of the second
kind. Computes the integral from 0 to
or p/2
radians of the function sqrt(1k**2*sin(phi)**2)*d.phi, where k = sin(alpha). alpha must be
specified in radians and must be in the range 0 to p/2.
EIC2D(alpha)  Same as eic2() except alpha must be specified in degrees and must be in the range 0 to
90.
ERF(x)  Standard error function
of x.
EXP(x)  e (base of natural
logarithms) raised to the x power.
FAC(x)  x factorial (x!). Note, the FAC function is
computed using the GAMMA function (FAC(x)=GAMMA(x+1)) so noninteger argument values
may be computed.
FLOOR(x)  Floor of x.
Returns the largest integer that is less than or equal to x.
For example, FLOOR(2.5)=2; FLOOR(4)=4; FLOOR(3.6)=4.
GAMMA(x)  Gamma function. Note,
GAMMA(x+1) = x! (i.e., x factorial).
GAMMAI(x)  Reciprocal of GAMMA
function (GAMMAI(x) = 1/GAMMA(x)).
GAMMALN(x)  Log (base e) of the
GAMMA function.
GAMMP(a,x)  Incomplete Gamma function.
HAV(x)  Haversine of x. (HAV(x) = (1COS(x))/2). The angle must be specified in radians.
HAVD(x)  Haversine of x. (HAVD(x) = (1COSD(x))/2). The angle must be specified in degrees.
INT(x)  Ceiling of x (an equivalent name for this
function is CEIL). Returns the smallest integer that is at least as large as x. For example, INT(1.5)=2; INT(4)=4;
INT(2.6)=2.
J0(x)  Bessel function of the
first kind, order zero.
J1(x)  Bessel function of the first
kind, order one.
JN(n,x)  Bessel function of the
first kind, order n.
LOG(x)  Natural logarithm (base
e) of x.
LOG10(x)  Base 10 logarithm of x.
LOG2(x)  Base 2 logarithm of x.
MAX(x1,x2)  Maximum value of x1 or x2.
MIN(x1,x2)  Minimum value of x1 or x2.
NORMAL(x)  Normal probability
distribution of x. X
is in units of standard deviations from the mean. See also the NPD function. NORMAL(x) = NPD(x,0,1);
NPD(x,mean,std)  Normal probability
distribution of x with specified
mean and standard deviation. X is in units of standard deviations
from the mean.
PAREA(x)  Area under the normal
probability distribution curve from infinity to x.
PRINTF("format'',value1,value2,...)  Format and print a
series of values. The NLREG printf function has the same syntax and function
as the printf function in the C language. It causes a string to be written to
your terminal and also the listing file for the analysis. Printf is primarily
useful as a diagnostic tool to give you a way to observe what is happening
during an analysis. Note: since your statements are executed for each data
observation and each iteration, the printf may generate a great deal of
output.
The first
argument to printf (format) is a
quoted string that contains characters to be printed, control codes, and (if
values are to be printed) formatting specifications. If you are familiar with
the C programming language, the NLREG formatting string has the same form and
control codes.
Ordinary
characters and numbers in the format string are printed just as they appear.
Use the control code '\n' to cause a
carriagereturn, linefeed sequence to be printed to terminate a line. For
example, the following statement prints a line of text:
printf("Beginning of analysis\n");
If you wish to insert formatted values in the string, specify one or more
expressions after the format string. Place in the format string at the
location where you want to insert the formatted value the sequence '%lf' (percent sign, lower case L, f) if
you want the number formatted in the style nnnn.nnnnor; use '%lE'
if you want exponential notation (nnn.nnnEnnn). Optionally, you may specify the
width of the formatted value and the number of decimal places between '%' and
'l'. For example, the following sequence produces a formatted value with 8
total characters and 4 decimal places: %8.4lf. Here are several examples:
printf("Processing observation %lf\n",obs);
printf("X
= %lf, Y = %lf\n",x,y);
printf("Predicted = %14.6lE\n",predicted);
PTOC(angle)  Convert an angle in the
polar coordinate system to a compass coordinate angle. The polar coordinate system has the origin
of an angle along the positive X axis and the angle increases in a
counterclockwise direction. The
compass coordinate system has the positive Y axis as the origin (i.e., north)
and the angle increases in a clockwise direction. The CTOP function performs
the reverse transformation. The angle
is in units of radians.
PTOCD(angle)  Same as ptoc() except
the angle is in units of degrees.
PTORX(angle,distance)  Convert a position in
polar coordinates to the corresponding rectangular coordinate. This function
returns the X coordinate of the position; use PTORY to obtain the Y
coordinate. Note: polar coordinates are specified with the positive X axis
being the origin for the angle and with the angle increasing in the counterclockwise
direction. The angle must be
specified in units of radians.
PTORXD(angle,distance)  Same as ptorx() except
the angle must be specified in units of degrees.
PTORY(angle,distance)  Convert a position in
polar coordinates to the corresponding rectangular coordinate. This function
returns the Y coordinate of the position; use PTORX to obtain the X
coordinate. Note: polar coordinates
are specified with the positive X axis being the origin for the angle and
with the angle increasing in the counterclockwise direction. The angle must be specified in units of
radians.
PTORYD(angle,distance)  Same as ptory() except
the angle must be specified in units of degrees.
PULSE(a,x,b)  Pulse function. If the
value of x is less than a or greater than b, the value of the function is 0. If x is greater than or equal to a
and less than or equal to b, the value
of the function is 1. In other words, it is 1 for the domain (a,b) and zero elsewhere. If you need a
function that is zero in the domain (a,b)
and 1 elsewhere, use the expression (1PULSE(a,x,b)).
RAD(x)  Converts an angle
measured in degrees to the equivalent number of radians. Note, the builtin trig functions provided
in NLREG have both radian and degree forms.
The degree versions have the letter “D” appended to the end of their
names such as sin(radians) and sind(degrees).
RANDOM()  Returns a random value
uniformly distributed in the range 0 to 1.
ROUND(x)  Rounds x to the nearest integer. For example, ROUND(1.1)=1; ROUND(1.8)=2;
ROUND(2.8)=3;
RTOPA(x,y)  Convert a rectangular
coordinate (x,y) to the
corresponding polar coordinate (angle,distance). This function returns the angle (in
radians), use RTOPD to get the distance coordinate. Note: polar coordinates are specified with the positive X axis
being the origin for the angle and with the angle increasing in the
counterclockwise direction.
RTPOPAD(x,y)
– Same as RTOPA() except
the angle is in degrees.
RTOPD(x,y)  Convert a rectangular
coordinate to the corresponding polar coordinate. This function returns the distance from the origin, use RTOPA
to get the angle. Note: polar coordinates are specified with the positive X axis
being the origin for the angle and with the angle increasing in the
counterclockwise direction.
SEC(x)  Secant of x. (SEC(x) = 1/COS(x)). The angle must be specified in radians.
SECD(x)  Secant of x. (SECD(x) = 1/COSD(x)). The angle must be specified in degrees.
SEL(a1,a2,v1,v2)  If a1 is less than a2 then
the value of the function is v1. If a1
is greater than or equal to a2,
then the value of the function is v2.
SIN(x)  Sine of x.
The angle must be specified in radians. See TREND.NLR for an example of a function with a sin term.
SIND(x)  Sine of x.
The angle must be specified in degrees.
SINH(x)  Hyperbolic sine of x.
SQRT(x)  Square root of x.
STEP(a,x)  Step function. If x is less than a, the value of the
function is 0. If x is greater than or equal to a, the value of the function is
1. If you need a function which is 1
up to a certain value and then 0 beyond that value, use the expression STEP(x,a).
T(n,x)  Chebyshev polynomial of
order n.
TAN(x)  Tangent of x.
The angle must be in units of radians.
TAND(x)  Tangent of x.
The angle must be in units of degrees.
TANH(x)  Hyperbolic tangent of x.
Y0(x)  Bessel function of the
second kind, order zero.
Y1(x)  Bessel function of the
second kind, order one.
YN(n,x)  Bessel function of the
second kind, order n.
