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LIBRY4A.DOC
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1989-11-10
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.pa
QUICK LIST OF MATHEMATICAL FUNCTIONS
AERF..... arc-error function
APOLY.... area of a polygon
BETA..... complete beta function
BETAR.... incomplete beta function
BINML.... binomial coefficient
BINMLD... double precision form of BINML
CHEBY.... Chebyshev polynomial of N-th degree
DERF..... double precision error function
DERFC.... double precision complementary error function
DEXPI.... double precision exponential integral
DWSN..... Dawson's integral
ERF...... error function
ERFC..... complementary error function
EXPI..... exponential integral
FACT..... factorial
FGQ0I.... numerical integration from zero to infinity
FGQ0ID... double precision form of FGI0I
FGQ1..... numerical integration over definite interval
FGQ1D.... double precision form of FGQ1
FGQ2..... numerical integration over definite interval in 2 dimensions
FGQ2D.... double precision form of FGQ2
FGQ3..... numerical integration over definite interval in 3 dimensions
FGQ3D.... double precision form of FGQ3
FPG...... normal probability distribution in percent
FRF...... cubic error function
FTC95.... Student's T-distribution for 95% confidence
GAMAL.... natural log of the Gamma function for large values
GAMMA.... Gamma function
GXNYM.... numerical integration of X**N*Y**M*dXdY over polygonal region
IRAND.... random number generator (integer)
PLG0..... Legendre polynomial of N-th degree
PLG1..... Legendre polynomial of N-th degree (first derivative)
PLG2..... Legendre polynomial of N-th degree (second derivative)
PLG3..... Legendre polynomial of N-th degree (third derivative)
PPLG0.... Legendre polynomial of N-th degree in 2 dimensions
RPQ...... rational polynomial evaluation
RPQD..... double precision form of RPQ
SEVAL.... cubic spline evaluation
XRAND.... random number generator (real, normally distributed)
.pa
MATHEMATICAL FUNCTIONS
NAME: AERF
PURPOSE: arc-error function
TYPE: REAL*4 function (far external)
SYNTAX: X=AERF(E)
INPUT: E (REAL*4) the erf of something
OUTPUT: X (REAL*4) the arc-erf
NAME: APOLY
PURPOSE: area of a polygon
TYPE: REAL*4 function (far external)
SYNTAX: A=APOLY(X,Y,N)
INPUT: X,Y (REAL*4) an array of points (X,Y)
OUTPUT: A (REAL*4) the area enclosed
NOTE: points must be in the order you draw a "connect-the-dots"
picture, the connection between the last point and the first
point is assumed (e.g. for a triangular region N=3)
NAME: BETA
PURPOSE: complete beta function
TYPE: REAL*4 function (far external)
SYNTAX: B=BETA(X,Y)
INPUT: X,Y (REAL*4)
OUTPUT: B (REAL*4)
NAME: BETAR
PURPOSE: incomplete beta function
TYPE: REAL*4 function (far external)
SYNTAX: B=BETAR(X,Y,R)
INPUT: X,Y,R (REAL*4)
OUTPUT: B (REAL*4)
NAME: BINML
PURPOSE: binomial coefficient
TYPE: REAL*4 function (far external)
SYNTAX: B=BINML(N,I)
INPUT: N,I (INTEGER*2)
OUTPUT: B (REAL*4)
NAME: CHEBY
PURPOSE: Chebyshev polynomial of N-th degree
TYPE: REAL*4 function (far external)
SYNTAX: C=CHEBY(N,X)
INPUT: X (REAL*4), N (INTEGER*2)
OUTPUT: C (REAL*4)
NAME: DWSN
PURPOSE: Dawson's integral
TYPE: REAL*4 function (far external)
SYNTAX: D=DWSN(X)
INPUT: X (REAL*4)
OUTPUT: D (REAL*4)
NAME: ERF
PURPOSE: error function
TYPE: REAL*4 function (far external)
SYNTAX: E=ERF(X)
INPUT: X (REAL*4)
OUTPUT: E (REAL*4)
NOTE: for double precision use DERF
NAME: ERFC
PURPOSE: complementary error function
TYPE: REAL*4 function (far external)
SYNTAX: E=ERFC(X)
INPUT: X (REAL*4)
OUTPUT: E (REAL*4)
NOTE: for double precision use DERFC
NAME: EXPI
PURPOSE: exponential integral (Abramowitz & Stegun use the notation E1(X) in
their NBS publication "Handbook of Mathematical Functions"; it is
also called the "Theis Well Function" by groundwater folks; it is
the integral from X to infinity of EXP(-X)/X dX.)
TYPE: REAL*4 function (far external)
SYNTAX: E=EXPI(X)
INPUT: X (REAL*4)
OUTPUT: E (REAL*4)
NOTE: for double precision use DEXPI
NAME: FACT
PURPOSE: factorial
TYPE: REAL*4 function (far external)
SYNTAX: F=FACT(N)
INPUT: N (INTEGER*2)
OUTPUT: F (REAL*4)
NAME: FGQ0I (note the "0" (zero))
PURPOSE: numerical integration from zero to infinity
TYPE: REAL*4 function (far external)
SYNTAX: FI=FGQ0I(F)
INPUT: F (REAL*4 function) that YOU MUST SUPPLY and must be
called by the sequence FX=F(X)
OUTPUT: the integral
NOTE: for double precision use FGQ0ID
20-point Gauss quadrature is used (96-point for double
precision)
NAME: FGQ1
PURPOSE: numerical integration over definite interval
TYPE: REAL*4 function (far external)
SYNTAX: FI=FGQ1(F,A,B)
INPUT: A,B (REAL*4) interval over which to integrate
F (REAL*4 function) that YOU MUST SUPPLY and must be
called by the sequence FX=F(X)
OUTPUT: the integral
NOTE: your function will be integrated from A to B
for double precision use FGQ1D
20-point Gauss quadrature is used (96-point for double
precision)
NAME: FGQ2
PURPOSE: numerical integration over definite interval in 2-D
TYPE: REAL*4 function (far external)
SYNTAX: FI=FGQ2(F,FY1,FY2,A,B)
INPUT: A,B (REAL*4) interval over which to integrate F
F (REAL*4 function) that YOU MUST SUPPLY and must be
called by the sequence FXY=F(X,Y)
FY1 (REAL*4 function) that YOU MUST SUPPLY and must be
called by the sequence Y1=FY1(X)
FY2 (REAL*4 function) that YOU MUST SUPPLY and must be
called by the sequence Y2=FY2(X)
OUTPUT: the integral
NOTE: your function will be integrated in X from A to B and Y
from FY1(X) to FY2(X), 20*20=400 point Gauss quadrature
is used (96*96=9216 points for double precision)
for double precision use FGQ2D
NAME: FGQ3
PURPOSE: numerical integration over definite interval in 3-D
TYPE: REAL*4 function (far external)
SYNTAX: FI=FGQ3(F,FZ1,FZ2,FY1,FY2,A,B)
INPUT: A,B (REAL*4) interval over which to integrate F
F (REAL*4 function) that YOU MUST SUPPLY and must be
called by the sequence FXYZ=F(X,Y,Z)
FY1 (REAL*4 function) that YOU MUST SUPPLY and must be
called by the sequence Y1=FY1(X)
FY2 (REAL*4 function) that YOU MUST SUPPLY and must be
called by the sequence Y2=FY2(X)
FZ1 (REAL*4 function) that YOU MUST SUPPLY and must be
called by the sequence Z1=FZ1(X,Y)
FZ2 (REAL*4 function) that YOU MUST SUPPLY and must be
called by the sequence Z2=FZ2(X,Y)
OUTPUT: the integral
NOTE: your function will be integrated in X from A to B and Y
from FY1(X) to FY2(X) and Z from FZ1(X,Y) to FZ2(X,Y)
20*20*20=8000 point Gauss quadrature is used (96*96*96=884736
for double precision)
for double precision use FGQ3D
NAME: FPG
PURPOSE: normal probability distribution in percent
TYPE: REAL*4 function (far external)
SYNTAX: F=FPG(XBAR,SIGMA,X,DX)
INPUT: XBAR (REAL*4) mean
SIGMA (REAL*4) standard deviation
X (REAL*4) independent variable
DX (REAL*4) increment in X (if you want to know the
probability of 0,5,10,15,20,25,...,95,100%, then X=0,5,10,...
and DX=5)
OUTPUT: F (REAL*4) probability in %
NAME: FRF
PURPOSE: cubic error function
TYPE: REAL*4 function (far external)
SYNTAX: F=FRF(X)
INPUT: X (REAL*4)
OUTPUT: F (REAL*4)
NOTE: FRF is similar to ERF and also varies from -1 to 1 as X varies
from -infinity to +infinity, it pops up in some problems like
the error function (e.g. statistical thermodynamics)
NAME: FTC95
PURPOSE: Student's T-distribution for 95% confidence
TYPE: REAL*4 function (far external)
SYNTAX: F=FTC95(