QUINNDO Documentation

QUINNDO is a language designed for linear optimization and statistical analysis.

Basic Data Types

Number (num)

`num a = 5`	5
`num a = 5.5`	5.5
`num a = 5.5e6`	5,500,000	These syntaxes are why no symbol can be named "e"
`num a = 1e-3`	0.001	These syntaxes are why no symbol can be named "e"
`num a = 1_000_000`	1,000,000	Numbers can use underscores as a thousands separator

Variable (var)

`var a`
`var a,b`	More than one variable can be declared per line

Alias (alias)

Aliases are linear combinations of variables and numbers used in linear programming models.

`alias a = 2b + 5`
`alias a = b`	Numbers and variables are castable to aliases
`alias a = 5`	Numbers and variables are castable to aliases

Number Vector (nvec)

`nvec v = [2,a]`
`nvec v = [2i for i=1 to 5]`	=> [2,4,6,8,10]
`nvec v = [2i for i=1 until 7 step 2]`	=> [2,6,10]
`nvec v = [2i for i in [6,9] ]`	=> [12,18]

Variable Vector (vvec)

`vvec v = [a,b]`
`vvec v = [x{i} for i=1 to 5]`	=> [x1,x2,x3,x4,x5]

Alias Vector (avec)

avec v = [a,b]

Number Matrix (nmtx)

`nmtx A = [ [1,2] , [3,4] ]`
`nmtx A = ntmx( [1,2,3,4] )`

Variable Matrix (vmtx)

`vmtx A = [ [a,b] , [c,d] ]`
`vmtx A = vtmx( [a,b,c,d] )`

Boolean (bool)

bool b = true

Boolean Vector (bvec)

bvec v = [true,b]

String (str)

str s = "Hello World!"

String Vector (svec)

svec v = ["a",s]

Advanced Data Types

Number Matrix (nmtx)

nmtx( values:nvec , nrow?:num , ncol?:num , byrow?:bool=true )
values	nvec	The values to insert into the number matrix
nrow?	num	The number of rows the matrix should have	If neither option is provided, the most square matrix will be built
nrow?	num	The number of columns of the matrix should have
byrow?	bool	Whether values should be inserted row first

Variable Matrix (vmtx)

vmtx( values:vvec , nrow?:num , ncol?:num , byrow?:bool=true )
values	vvec	The values to insert into the variable matrix
nrow?	num	The number of rows the matrix should have	If neither option is provided, the most square matrix will be built
nrow?	num	The number of columns of the matrix should have
byrow?	bool	Whether values should be inserted row first

Model (model)

A Model is used to represent an optimization problem.

model( obj:alias )
obj	alias	The objective value to optimize

Network (ntwk)

A Network is used with its appended Nodes and Edges.

ntwk( bi?:bool=false )
bi?	bool	Whether to make the network bidirectional

Node (node)

A Node is used to represent a node/vertex in a Network.

node( id:str\|num , source?:bool=false , sink?:bool=false )
id	str\|num	The id of the node
source?	bool	Whether to make the node a source node
sink?	bool	Whether to make the node a sink node

Edge (edge)

A Node is used to represent an edge/arc in a Network.

edge( start:str\|num\|node , end:str\|num\|node , weight?:num=1 )
start	str\|num\|node	The starting node or the id of the starting node	If no matching node is present in the network, a matching node will be created and added
end	str\|num\|node	The ending node or the id of the ending node
weight?	num	The weight assigned to this edge

Date (date)

If no values are provided, date() returns the current data and time in the user's time zone.

date( year?:num , month?:num , day?:num , hour?:num , minute?:num , second?:num )
year?	num	The year in the Gregorian calendar
month?	num	The month in the Gregorian calendar (Jan=1,Feb=2,...,Dec=12)	Note: Throws if present without year
day?	num	The day in the month	Note: Throws if present without month
hour?	num	The hour of the day in 24-hour format [0-23]
minute?	num	The minute of the hour [0-59]	Note: Throws if present without hour
second?	num	The second of the minute [0-59]	Note: Throws if present without minute

Date Vector (dvec)

A Date Vector is an enumerated vector of Date values.

Date Offset (offset)

A Date Offset is used to add or subtract period of time from a date.

offset( year?:num=0 , month?:num=0 , day?:num=0 , hour?:num=0 , minute?:num=0 , second?:num=0 )
year?	num	The number of years to offset
month?	num	The number of months to offset
day?	num	The number of days to offset
hour?	num	The number of hours to offset
minute?	num	The number of minutes to offset
second?	num	The number of seconds to offset

Date Offset Vector (ovec)

A Date Offset Vector is an enumerated vector of Date Offset values.

Measurement (meas)

A Measurement value is a scalar with associated units.

meas( value:num , units:str )
value	num	The scalar of the measurement
units	str	The units of the measurement

Measurement Vector (mvec)

A Measurement Vector is an enumerated vector of Measurement values.

Plot (plot)

A plot is used to render visualization of objects.

plot()
This Inator takes no arguments.

Statistic Test Result (test)

A test object is used to hold the result of a statistical test.

test
This type cannot be created, only returned from another function.

Operators

Assignment (=)

The assignment operator is used to store values and to establish equality constraints in conjunction with a model object.

Addition (+)

Subtraction (-)

Mutliplication (*)

Division (/)

Percent (%)

The percent operator is used to divide a value by 100. For example, 5% is the same as 0.05.

Exponentiation (^)

Modulus (mod)

Factorial (!)

Transpose (')

The transpose operator only works on matrices.

Pointwise Addition (addeach)

Pointwise Subtraction (subeach)

Pointwise Mutliplication (multeach)

Pointwise Division (diveach)

Not (~)

And (&)

Or (|)

Exclusive Or (xor)

Not Or (nor)

Equality (==)

Not Equal (~=)

This symbol is typed as a tilde "~" followed by an equal sign "=".

Strict Equality (===)

When comparing numbers, equality returns true if two numbers are within 10^-8 of each other to avoid floating point errors. However, when comparing numbers, strict equality only returns true if two values are exactly equal. Also applies to inner values within a vector.

Strict Not Equal (~==)

Same difference as Equality versus Strict Equality, but negated. This symbol is typed as a tilde "~" followed by two equal signs "==".

Conditional Ternary (?:)

The conditional ternary operator switches between two values based on the value of a boolean expression. For example, b?1:0 evaluates to 1 if b is true and 0 if b is false.

If-Then (=>)

See description of If-And-Only-If.

If-And-Only-If (<=>)

If-Then and If-And-Only-If are used in constraints when appending to a model object. If-Then and If-And-Only-If are written as "=",">" and "<","=",">", respectively.

Append (<|)

Appends an object to another object. All object that can have values appended to them are the same color. Written as "<" followed by "|".

Piping (|>)

Pipes the previous result into the following function. By default, the piped value will be passed as the first parameter in the following function. This can be changed with the result keyword. Written as "|" followed by ">".

Spread (...)

Spreads the values of a list over the parameters of a function or values of a vector. For example, range(1,10,3) and range(...[1,10,3]) are equivalent. Similarly, [ 0 , 1 , 2 , 3 ] and [ 0 , ...[ 1 , 2 ] , 3 ] are equivalent.

Vector Syntax

Vector Indexes

Vector indexes in QUINNDO are indexed from 1. Negative indexes count from the end. Non-integer indexes are not allowed.


        nvec
        a
        =
        [4,5,6]
        

        assert
        a[1]
        ==
        4
        

        assert
        a[-1]
        ==
        6
        

        assert
        a[0]
        ==
        none
        # Error: No value at index 0
        

        assert
        a[1.5]
        ==
        none
        # Error: Non-integer index

Vector Slicing

Vectors can be sliced with the [start?:end?:step?] syntax. If not provided, the default value of start, end, and step is 1, the end of the vector, and 1, respectively. The sliced vector will include the end index.


        nvec
        a
        =
        [4,5,6,7,8]
        

        assert
        a[1:3]
        ==
        [4,5,6]
        

        assert
        a[:3]
        ==
        [4,5,6]
        

        assert
        a[2::2]
        ==
        [5,7]

Vector Filtering

Vectors can be filtered by using the val keyword in the vector index with a filtering condition.


        nvec
        a
        =
        [5,6,7,8,9]
        

        assert
        a[val>6]
        ==
        [7,8,9]
        

        assert
        a[val>=6]
        ==
        [6,7,8,9]
        

        assert
        a[val
        mod
        2==0]
        ==
        [6,8]
        

        list
        b
        =
        [6,true,none,8,a,10]
        

        assert
        b[val
        is
        num]
        ==
        [6,8,10]

Matrix Indexes

Similar to vector indexes, matrix rows can by retrieved with [index]. Matrix columns can be retrieved with {index}. Matrix rows and columns have the same abilities and restrictions as vector indexes.

Useful Keywords

in

in is used to check if a value is present in a vector.

keyof

keyof is used to check if a given object has a given property.


        test
        a
        =
        ttest(
        [1,2]
        ,
        ~=
        ,
        5
        )
        

        bool
        b
        =
        "rejected"
        keyof
        a
        # true
        

        bool
        c
        =
        "abcdef"
        keyof
        a
        # false

is and can

is and can are used to check the data-type of a value. is returns true if the data type exactly matches, while can returns true if a value can be casted to a given data type.


        list
        a
        =
        [6,7.5,9]
        

        bool
        b
        =
        a
        is
        list
        # true
        

        bool
        c
        =
        a
        is
        nvec
        # false because a is a list
        

        bool
        d
        =
        a
        can
        nvec
        # true because a contains only numbers

fa and fo

fa and fo make up QUINNDO's try...catch syntax. Use these statements to provide a fallback value if code encounters an error.


        num
        a
        =
        1
        /
        0
        # Throws error
        

        num
        b
        =
        fa
        1
        /
        0
        fo
        5
        # b=5
        

        num
        c
        =
        fa
        1
        /
        2
        fo
        5
        # b=1/2

stfu

stfu ("Suppress This Faulty Utterance") is used to disable warnings and recommendations on a line-by-line basis. stfu must the last command on its line.


        num
        a
        =
        4
        mod
        -3
        # Raises warning because one parameter is negative
        

        num
        b
        =
        4
        mod
        -3
        stfu
        # Warning is suppressed
        

        num
        c
        =
        4
        mod
        -3
        stfu
        *
        8
        # Throws error because stfu is not at end of line

assert

assert evaluates a condition and throws an error if the condition is false.


        assert
        5
        ==
        3
        +
        2
        

        assert
        6
        ==
        3
        +
        2
        # Throws error because assertion failed

Macros

Macros are special functions that handle larger operations and do not return a value.

Model Maximizer (maximize)

maximize( lp:model , thres?:num=1 )
lp	model	The model to be maximized
thres?	num	The solver tolerance for problem that contain integer constraints

Model Minimizer (minimize)

minimize( lp:model , thres?:num=1 )
lp	model	The model to be minimized
thres?	num	The solver tolerance for problem that contain integer constraints

Convert to LINDO (lindoize)

Converts a QUINNDO Model object to a LINDO program.

lindoize( lp:model , type:str )
lp	model	The model to be converted to LINDO
type	str	Must be one of "max" or "min"

Shortest Path Finder (min_path)

min_path( net:ntwk , anchor:str\|num\|node , render?:bool=false )
net	ntwk	The network in which to find the shortest path
anchor	str\|num\|node	The point from which to find the shortest path
render?	bool	Whether to print the model to the console on completion

Renderer (render)

render is used to draw plots in the console.

render( obj:plot )
obj	plot	The plot to draw in the console

Print (print)

print is used to print objects to the console.

print( obj:any )
obj	any	The object to print to the console

Math Operations

Sign (sign)

Returns 1 if a number is greater than 0, -1 if a number is less than 0, and 0 if the number is 0.

Natural Logarithm (log)

Base-2 Logarithm (log2)

Base-10 Logarithm (log10)

Exponential (exp)

Absolute Value (abs)

Floor (floor)

Round (round)

Ceiling (ceil)

Square Root (sqrt)

Cube Root (cbrt)

Cosine (cos)

Arc-Cosine (acos)

Sine (sin)

Arc-Sine (asin)

Tangent (tan)

Arc-Tangent (atan)

Statistical Summaries

Sum (sum)

Mean (mean)

Median (median)

Mode (mode)

List Maximum (max)

List Minimum (min)

Sample Standard Deviation (samsd)

Sample Variance (samvar)

Population Standard Deviation (popsd)

Population Variance (popvar)

R-Squared (rsq)

Least Squares Linear Regression (lsr)

lsr( x:nvec\|nmtx , y:nvec , int?:bool=true ): nvec
x	nvec\|nmtx	A vector containing x values for single-variate regression or a matrix with entries in rows and variables in columns for multivariate regression
y	nvec	The expected output values
int?	bool	Whether to include the intercept in the regression - ignored for single-variate regressions

Statistical Tests

One-Sample Z-Test (ztest)

ztest does a one-sample z-test.

ztest( sample:nvec , alt:operator , val:num , sigma:num , alpha?:num=5% ): test
sample	nvec	The sample data
alt	operator	The sign of the alternative hypothesis - must be one of ~=, >, or <
val	num	The threshold value of the alternative hypothesis
sigma	num	The population standard deviation
alpha?	num	The significance level of the test

Two-Sample Z-Test (ztest2)

ztest2 does a two-sample z-test.

ztest2( sample1:nvec , sample2:nvec , sigma1:num , sigma2:num , alt?:operator= ~= , val?:num=0 , alpha?:num=5% ): test
sample1	nvec	The sample data from the first sample
sample2	nvec	The sample data from the second sample
sigma1	num	The population standard deviation for sample1
sigma2	num	The population standard deviation for sample2
alt?	operator	The sign of the alternative hypothesis - must be one of ~=, >, or <
val?	num	The threshold value of the alternative hypothesis
alpha?	num	The significance level of the test

One-Sample T-Test (ttest)

ttest does a one-sample t-test.

ttest( sample:nvec , alt:operator , val:num , alpha?:num=5% ): test
sample	nvec	The sample data
alt	operator	The sign of the alternative hypothesis - must be one of ~=, >, or <
val	num	The threshold value of the alternative hypothesis
alpha?	num	The significance level of the test

Two-Sample T-Test (ttest2)

ttest2 does a two-sample t-test.

ttest2( sample1:nvec , sample2:nvec , alt?:operator= ~= , val?:num=0 , alpha?:num=5% , type?:num=0 ): test
sample1	nvec	The sample data from the first sample
sample2	nvec	The sample data from the second sample
alt?	operator	The sign of the alternative hypothesis - must be one of ~=, >, or <
val?	num	The threshold value of the alternative hypothesis
alpha?	num	The significance level of the test
type?	num	The type of t-test to run (0=Welch's,1=Pooled,2=Student's)

F-Test (ftest)

ftest does an F-test.

ftest( sample1:nvec , sample2:nvec , alt?:operator= ~= , alpha?:num=5% ): test
sample1	nvec	The sample data from the first sample
sample2	nvec	The sample data from the second sample
alt?	operator	The sign of the alternative hypothesis - must be one of ~=, >, or <
alpha?	num	The significance level of the test

ANOVA (anova)

anova does an ANOVA.

anova( samples:nmtx , alpha?:num=5% ): test
samples	nmtx	The data for the ANOVA - each factor must be a row
alpha?	num	The significance level of the test

Goodness of Fit Test (goftest)

goftest does a Χ² goodness of fit test.

goftest( observed:nvec , expected:nvec , alpha?:num=5% ): test
observed	nvec	The observed values
expected	nvec	The expected values to compare against
alpha?	num	The significance level of the test

Χ² Test for Independence (indtest)

indtest does a Χ² test for independence.

indtest( values:nmtx , alpha?:num=5% ): test
values	nmtx	The data for the independence test
alpha?	num	The significance level of the test

Vector & Matrix Functions

Vector Range Builder (range)

range( start?:num=1 , end:num , step?:num=1 ): nvec
start?	num	The start value of the final array
end	num	The end value of the final array, which will be included
step?	num	The step between values

Vector Size (size)

size( x:list\|str ): num
x	list\|str	The value of which to find the size

Matrix Row Count (nrow)

An alias of size for matrices.

nrow( x:nmtx\|vmtx ): num
x	nmtx\|vmtx	The matrix from which to find the number of rows

Matrix Column Count (ncol)

Gets the number of column from a rectangular matrix.

ncol( x:nmtx\|vmtx ): num
x	nmtx\|vmtx	The matrix from which to find the number of columns

Matrix Max Column Count (maxcol)

Gets the number of elements in the longest row of a matrix.

maxcol( x:nmtx\|vmtx ): num
x	nmtx\|vmtx	The matrix from which to find the max row length

Matrix Min Column Count (mincol)

Gets the number of elements in the shortest row of a matrix.

mincol( x:nmtx\|vmtx ): num
x	nmtx\|vmtx	The matrix from which to find the min row length

Unit Vector Normalizer (unit)

Returns a vector normalized to a magnitude of 1.

unit( v:nvec ): nvec
v	nvec	The vector to normalize

Probability Normalizer (prob)

Returns a vector normalized to a valid probability distribution.

prob( v:nvec ): nvec
v	nvec	The vector to convert to a probability distribution

Z-Score Normalizer (norm)

Returns a vector normalized to a mean of 0 and a sample standard deviation of 1.

norm( v:nvec ): nvec
v	nvec	The vector to normalize

Vector Sorter (sort)

sort( v:nvec\|svec , reverse?:bool=false ): nvec
v	nvec\|svec	The vector to sort
reverse?	bool	The direction in which to sort the list - ascending if false, descending if true

Matrix Trace (trace)

trace( m:nmtx ): num
m	nmtx	The matrix of which to find the trace

Matrix Determinant (deter)

deter( m:nmtx ): num
m	nmtx	The matrix of which to find the determinant

Matrix Diagonal Elements (diag)

diag( values:nmtx ): nvec
values	nmtx	The matrix of which to find the diagonal elements

Identity Matrix (identity)

identity( n:num ): nmtx
n	num	The dimension of the identity matrix

Matrix Inversion (inv)

inv( m:nmtx ): nmtx
m	nmtx	The matrix to invert

Unique Elements (unique)

Returns a copy of a list with duplicates removed.

unique( x:list ): list
x	list	The list from which to remove duplicates

Common Elements (union)

Returns a list with values common to two lists.

union( list1:list , list2:list ): list
list1	list	The first list
list2	list	The second list

Miscellaneous Functions

String Vector Joiner (join)

Joins a String Vector into a String with a given string.

join( v:svec , sep?:str=" " ): str
v	svec	The string vector to join
sep?	str	The string with which to join the vector

String Splitter (split)

Splits a String into a String Vector with a given string.

split( s:str , sep?:str=" " ): svec
s	str	The string to split
sep?	str	The string with which to split the string

Examples

Scatter Plot


        nvec
        x
        =
        range(5)
        # [1,2,3,4,5]
        

        nvec
        y
        =
        range(
        5
        ,
        13
        ,
        2
        )
        # [5,7,9,11,13]
        

        plot
        p
        =
        plot.scatter(
        x
        ,
        y
        )
        

        render(p)

Student's 2-Sample T-Test


        nvec
        s1
        =
        [7,2,4]
        

        nvec
        s2
        =
        range(3)
        # [1,2,3]
        

        test
        t
        =
        ttest2(
        s1
        ,
        s2
        ,
        type=ttest2.student
        )

Integer Programming

The Lotus Point Condo Project will contain both homes and apartments. The site can accommodate up to 10,000 dwelling units. The project must contain a recreation project: either a swimming-tennis complex or a sailboat marina, but not both. If a marina is built, then the number of homes in the project must be at least triple the number of apartments in the project. A marina will cost $1.2 million, and a swimming-tennis complex will cost $2.8 million. The developers believe that each apartment will yield revenues with an NPV of $48,000, and each home will yield revenues with an NPV of $46,000. Each home (or apartment) costs $40,000 to build. Formulate an IP to help Lotus Point maximize profits.

Problem From: Winston, W. L., & Goldberg, J. B. (2004). Operations research: Applications and Algorithms. Brooks/Cole.


        var
        a,h,m,t
        # apartments, homes, marina, tennis complex
        

        model
        p
        =
        model(
        8a
        +
        6h
        -
        1200m
        -
        2800t
        )
        

        p
        <|
        a
        +
        h
        <=
        10_000
        # building constraint
        

        p
        <|
        m
        =
        1
        xor
        t
        =
        1
        # either marina or tennis/swimming
        

        p
        <|
        m
        =
        1
        =>
        h
        >=
        3a
        # marina building type constraint
        

        p
        <|
        a,h
        is
        int
        # integer constraint
        

        p
        <|
        m,t
        is
        bin
        # binary constraint
        

        maximize(p)

Shortest Path


        ntwk
        n
        =
        ntwk()
        

        n
        <|
        edge(
        1
        ,
        2
        ,
        1
        )
        # start,end,weight
        

        n
        <|
        edge(
        1
        ,
        3
        ,
        2
        )
        

        n
        <|
        edge(
        2
        ,
        3
        ,
        3
        )
        

        n
        <|
        edge(
        3
        ,
        2
        ,
        1
        )
        

        n
        <|
        edge(
        2
        ,
        4
        ,
        3
        )
        

        n
        <|
        edge(
        3
        ,
        4
        ,
        2
        )
        

        min_path(
        n
        ,
        1
        )
        # Get shortest path to all other nodes from node 1