# Lingo11.0破解与高级教程

LINGO11.0发布了，其中主要加入了计算段编程，能够实现目标规划等等，教程我有空写写，破解文件在附件里面，解压后直接运行就可以了！

Mathematical Functions

LINGO offers a number of standard, mathematical functions. These functions return a single result based on one or more scalar arguments. These functions are listed below:
@ABS( X)
Returns the absolute value ofX.
@ACOS( X)
Returns the inverse cosine, or arccosine, ofX,whereXis an angle in radians.
@ACOSH( X)
Returns the inverse hyperbolic cosine ofX, whereXis an angle in radians.
@ASIN( X)
Returns the inverse sine, or arcsine, ofX,whereXis an angle in radians.
@ASINH( X)
Returns the inverse hyperbolic sine ofX, whereXis an angle in radians.
@ATAN( X)
Returns the inverse tangent, or arctangent, ofX,whereXis an angle in radians.
@ATAN2( Y, X)
Returns the inverse tangent ofY/X.
@ATANH( X)
Returns the inverse hyperbolic tangent ofX, whereXis an angle in radians.
@COS( X)
Returns the cosine ofX, whereXis an angle in radians.
@COSH( X)
Returns the hyperbolic cosine ofX, whereXis an angle in radians.
@EXP( X)
Returnse(2.718281...) raised to the powerX.
@FLOOR( X)
This returns the integer part ofX. To be specific, ifX
≥≥0,@FLOORreturns the largest integer,I, such thatI
≤≤
X. IfXis negative,@FLOORreturns the most negative integer,I, such thatI
≥≥
X.
@LGM( X)
Returns the natural (basee) logarithm of the gamma function ofX(i.e., log of (X- 1)!). It is extended to non-integer values ofXby linear interpolation.
@LOG( X)
Returns the natural logarithm ofX.
@LOG10( X)
Returns the base-10 logarithm ofX.
@MOD( X, Y)
Returns the value of
XmoduloY, or, in other words, the remainder of an integer divide ofXbyY.
@POW( X, Y)
Returns the value ofXraised to theYpower.
@SIGN( X)
Returns -1 ifX< 0. Otherwise, it returns +1.
@SIN( X)
Returns the
sine ofX, whereXis the angle in radians.
@SINH( X)
Returns the hyperbolic sine ofX, whereXis an angle in radians.
@SMAX( X1, X2,..., XN)
Returns the maximum value ofX1,X2, ..., andXN.
@SMIN( X1, X2,..., XN)
Returns the minimum value ofX1,X2, ..., andXN.
@SQR(X)
Returns the value of X squared.
@SQRT( X)
Returns the square root
ofX.
@TAN( X)
Returns the tangent ofX, whereXis the angle in radians.
@TANH( X)
Returns the hyperbolic tangent ofX, whereXis an angle in radians.

Probability Functions
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LINGO has a number of probability related functions. There are examples that make use of most of these functions inDeveloping More Advanced Modelsand inAdditional Examples of LINGO Modeling.
@NORMSINV( P)
This is the inverse of the standard normal cumulative distribution.  Given a probability,P, this function returns the valueZsuch that the probability of a normally distributed random variable with standard deviation of 1 being less-than-or-equal toZisP.
@PBN( P, N, X)
This is the cumulative binomial probability. It returns the probability that a sample ofNitems, from a universe with a fraction ofPof those items defective, hasXor less defective items. It is extended to non-integer values ofXandNby linear interpolation.
@PCX( N, X)
This is the cumulative distribution function for the Chi-squared distribution withN
degrees of freedom. It returns the probability that an observation from this distribution is less-than-or-equal-toX.
@PEB( A, X)
This is Erlang’s busy probability for a service system withXservers and an arriving load ofA,with infinite queue allowed. The result of@PEBcan be interpreted as either the fraction of time all servers are busy or the fraction of customers that must wait in the queue. It is extended to noninteger values ofXby linear interpolation. The arriving load,
A, is the expected number of customers arriving per unit of time multiplied by the expected time to process one customer.
@PEL( A, X)
This is Erlang’s loss probability for a service system withXservers and an arriving load ofA,no
queue allowed. The result of@PELcan be interpreted as either the fraction of time all servers are busy or the fraction of customers lost due to all servers being busy when they arrive. It is extended to noninteger values ofXby linear interpolation. The arriving load,A, is the expected number of customers arriving per unit of time multiplied by the expected time to process one customer.
@PFD( N, D, X)
This is the cumulative distribution function for the F distribution withNdegrees of freedom in the numerator andDdegrees of freedom in the denominator. It returns the probability that an observation from this distribution is less-than-or-equal-toX.
@PFS( A, X, C)
This returns the expected number of customers waiting for or under repair in a finite source Poisson service system withXservers in parallel,Ccustomers, and a limiting loadA. It is extended to noninteger values ofXandCby linear interpolation.A, the limiting load, is the number of customers multiplied by the mean service time divided by the mean repair time.
@PHG( POP, G, N, X)
This is the cumulative hypergeometric probability. It returns the probability thatXor fewer items in the sample are good, given a sample without replacement ofNitems from a population of sizePOPwhereG
items in the population are good. It is extended to noninteger values ofPOP,G,N, andX
by linear interpolation.
@PPL( A, X)
This is the linear loss function for the Poisson distribution. It returns the expected value ofMAX( 0, Z-X), whereZis a Poisson random variable with mean value
A.
@PPS( A, X)
This is the cumulative Poisson probability distribution. It returns the probability that a Poisson random variable, with mean valueA, is less-than-or-equal-toX. It is extended to noninteger values ofXby linear interpolation.
@PSL( X)
This is the unit normal linear loss function.
It returns the expected value ofMAX( 0, Z-X), whereZis a standard normal random variable. In inventory modeling,@PSL( X)is the expected amount that demand exceeds a levelX, if demand has a standard normal distribution.
@PSN( X)
This is the cumulative standard normal probability distribution. A standard normal random variable has mean 0.0 and standard deviation 1.0 (the bell curve, centered on the origin). The value returned by@PSNis the area under the curve to the left of the point on the ordinate indicated byX.
@PTD( N, X)
This is the cumulative distribution function for the t distribution withN
degrees of freedom. It returns the probability that an observation from this distribution is less-than-or-equal-toX.
@QRAND( SEED)
The@QRANDproduces a sequence of "quasi-random" uniform numbers in the interval (0,1).@QRANDis only permitted in a data section. It will fill an entire attribute with quasi-random numbers. Generally, you will be filling two-dimensional tables with, say,mrows andnvariables.mrepresents the number of scenarios, or experiments, you want to run.nrepresents the number of random variables you need for each scenario or experiment. Within a row, the numbers are independently distributed. Among rows, the numbers are "super uniformly" distributed. That is, the numbers are more uniformly distributed than you would expect by chance. These numbers are generated by a form of "stratified sampling".