SSJ User's Guide Package util General basic utilities
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1. Formats the double precision x into a string like 4f in C printf The argument is rounded and converted to decimal notation in the style ddd ddd where the number of digits after the decimal point character is equal to the precision specification If the precision is explicitly 0 no decimal point character appears If a decimal point appears at least one digit appears before it If the one argument form is used a fieldwidth of 0 and a precision of 6 are used If the two arguments form is used a precision of 6 is assumed public static String G double x Same as G 0 6 x public static String G int fieldwidth double x Same as G fieldwidth 6 x public static String G int fieldwidth int precision double x Formats the double precision x into a string like G in C printf The argument is converted in style f or ZE precision specifies the number of significant digits If it is 0 it is treated as 1 Style E is used if the exponent from its conversion is less than 4 or greater than or equal to precision Trailing zeros are removed from the fractional part of the result a decimal point appears only if it is followed by at least one digit If the one argument form is used a fieldwidth of 0 and a precision of 6 are used If the two arguments form is used a precision of 6 is assumed public static String g double x Same as g 0 6 x public static String g int fieldwidth double x Same as g fieldwidth 62. If str is shorter than fieldwidth it is left padded with spaces If fieldwidth is negative the string is right padded with spaces if necessary The String will never be truncated If str is null it calls s fieldwidth null The fieldwidth argument has the same effect for the other methods in this class Integers public static String d long x Same as d 0 1 x May 21 2008 PrintfFormat 10 public static String d int fieldwidth long x Same as d fieldwidth 1 x public static String d int fieldwidth int precision long x Formats the long integer x into a string like d in the C printf function It converts its argument to decimal notation precision gives the minimum number of digits that must appear if the converted value requires fewer digits it is padded on the left with zeros When zero is printed with an explicit precision 0 the output is empty If the one argument form is used a fieldwidth of 0 is assumed and a precision of 1 is used If the two arguments method is used a precision of 1 is assumed public static String format long x Same as d 0 1 x public static String format int fieldwidth long x Converts a long integer to a String with a minimum length of fieldwidth the result is right padded with spaces if necessary but it is not truncated If only one argument is specified a fieldwidth of 0 is assumed public static String formatBase int b long x Same as formatBase 0 b
3. x May 21 2008 PrintfFormat 12 public static String g int fieldwidth int precision double x The same as G except that e is used in the scientific notation public static String format int fieldwidth int accuracy int precision double x Returns a String containing x Uses a total of at least fieldwidth positions including the sign and point when they appear accuracy digits after the decimal point and at least precision significant digits accuracy and precision must be strictly smaller than fieldwidth The number is rounded if necessary If there is not enough space to format the number in decimal notation with at least precision significant digits accuracy or fieldwidth is too small it will be converted to scientific notation with at least precision significant digits In that case fieldwidth is increased if necessary Intervals public static void formatWithError int fieldwidth int fieldwidtherr int accuracy int precision double x double error String res Stores a string containing x into res 0 and a string containing error into res 1 both strings being formatted with the same notation Uses a total of at least fieldwidth positions including the sign and point when they appear for x fieldwidtherr positions for error accuracy digits after the decimal point and at least precision significant digits accuracy and precision must be strictly smaller than fieldwidth The numbers are rounded if nec
4. x public static String formatBase int fieldwidth int b long x Converts the integer x to a String representation in base b Restrictions 2 lt b lt 10 Reals public static String E double x Same as E 0 6 x public static String E int fieldwidth double x Same as E fieldwidth 6 x public static String E int fieldwidth int precision double x Formats a double precision number x like E in C printf The double argument is rounded and converted in the style d dddE dd where there is one digit before the decimal point character and the number of digits after it is equal to the precision if the precision is 0 no decimal point character appears The exponent always contains at least two digits if the value is zero the exponent is 00 If the one argument form is used a fieldwidth of 0 and a precision of 6 are used If the two arguments form is used a precision of 6 is assumed May 21 2008 PrintfFormat 11 public static String e double x Same as e 0 6 x public static String e int fieldwidth double x Same as e fieldwidth 6 x public static String e int fieldwidth int precision double x The same as E except that e is used as the exponent character instead of E public static String f double x Same as f 0 6 x public static String f int fieldwidth double x Same as f fieldwidth 6 x public static String f int fieldwidth int precision double x
5. May 21 2008 15 Chrono Chrono is a small class that acts as an interface to the system clock and calculates the CPU time consumed by parts of a program Part of this class is implemented in the C language and the implementation is unfortunately operating system dependent The C functions for the current class have been compiled on a 32 bit machine running Linux and will not work on 64 bit machines For a platform independent CPU timer valid only with Java 1 5 or later one should use the subclass ChronoSingleThread which is programmed directly in Java see the next class in this guide Every object of class Chrono acts as an independent stopwatch Several Chrono objects can run at any given time The method init resets the stopwatch to zero getSeconds getMinutes and getHours return its current reading and format converts this reading to a String The returned value includes the execution time of the method from Chrono Below is an example of how it may be used A stopwatch named timer is constructed and initialized When 2 1 seconds of CPU have been consumed the stopwatch is read and reset to zero Then after an additional 330 seconds or 5 5 minutes of CPU time the stopwatch is read again and the value is printed to the output in minutes Chrono timer Chrono createForSingleThread suppose 2 1 CPU seconds are used here double t timer getSeconds Here t 2 1 timer init 0 0 t timer getSecon
6. given this method constructs a context using the nullary constructor of InitialContext uses the context to get a DataSource object and uses the data source to obtain a connection This method assumes that JNDI is configured correctly see the class InitialContext for more information about configuring JNDI If no JNDI name is specified the method looks for a JOBC URI If a driver class name is specified along with the URI the corresponding driver is loaded and registered with the JDBC DriverManager The driver manager is then used to obtain the connection using the URI This method throws an SQLException if the connection failed and an IllegalArgumentException if the properties do not contain the required values May 21 2008 JDBCManager 31 public static Connection connectToDatabase InputStream is throws IOException SQLException Returns a connection to the database using the properties read from stream is This method loads the properties from the given stream and calls connectToDatabase to establish the connection public static Connection connectToDatabase File file throws IOException SQLException Equivalent to connectToDatabase new FileInputStream file public static Connection connectToDatabase String fileName throws IOException SQLException Equivalent to connectToDatabase new FileInputStream fileName public static Connection connectToDatabaseFromResource String resource throws IOException SQLException
7. gt gt gt operator in Java otherwise it is equivalent to the lt lt operator public BitVector selfShift int j Shift all the bits of the current BitVector j positions to the right if j is positive and j positions to the left if j is negative The new bits that appears to the left or to the rigth are set to 0 Returns this public boolean scalarProduct BitVector that Returns the scalar product of two BitVector s modulo 2 It returns true if there is an odd number of bits with a value of 1 in the result of the and operator applied on this and that and returns false otherwise May 21 2008 23 BitMatrix This class implements matrices of bits of arbitrary dimensions Basic facilities for bits operations multiplications and exponentiations are provided package umontreal iro lecuyer util public class BitMatrix implements Serializable Cloneable Constructors p blic BitMatrix int r int c Creates a new BitMatrix with r rows and c columns filled with 0 s public BitMatrix BitVector rows Creates a new BitMatrix using the data in rows Each of the BitVector will be one of the rows of the BitMatrix public BitMatrix int data int r int c Creates a new BitMatrix with r rows and c columns using the data in data Note that the orders of the bits for the rows are using the same order than for the BitVector This does mean that the first bit is the lowest order bit of the last int in the row and the last
8. puts the result in the calling object this The return value of the self form is the calling object itself This is done to allow easier manipulation of the results making it possible to chain operations package umontreal iro lecuyer util public class BitVector implements Serializable Cloneable Constructors public BitVector int length Creates a new BitVector of length length with all its bits set to 0 public BitVector int vect int length Creates a new BitVector of length length using the data in vect Component vect 0 makes the 32 lowest order bits with vect 1 being the 32 next lowest order bits and so on The normal bit order is then used to fill the 32 bits the first bit is the lowest order bit and the last bit is largest order bit Note that the sign bit is used as the largest order bit public BitVector int vect Creates a new BitVector using the data in vect The length of the BitVector is always equals to 32 times the length of vect public BitVector BitVector that Creates a copy of the BitVector that Methods public Object clone Creates a copy of the BitVector public boolean equals BitVector that Verifies if two BitVector s have the same length and the same data public int size Returns the length of the BitVector May 21 2008 BitVector 21 public void enlarge int size boolean filling Resizes the BitVector so that its length is equal to size If the BitVector is enla
9. SSJ User s Guide Package util General basic utilities Version May 21 2008 This document describes a set of basic utilities used in the Java software developed in the simulation laboratory of the DIRO at the Universit de Montr al Many of these tools were originally implemented in the Modula 2 language and have been translated in C and then in Java with some adaptations along the road May 21 2008 CONTENTS 1 Contents NM a ae ee ra dra a a a EY 2 A oe ee oe ee ee ee oe ee AN 6 o ese abe ea te ee eh ees hee eee ee Bee Ee a 8 De RR ee a os a ee ee pe Oe A eg a Be 13 Lee tn eee ee E ee ae ee ee ee ee Bee 15 ChronoSingleThread ook AE A A AOR ee AT Gap AA 17 oa eee a yea ae ae oe ee ee A ee eee 18 EMEVECTO e ae oe ad Hal ee Bie he oie Ee a Bare ed we eed 20 ah Te Nei e SEs shoe DS A ae he a ok A A ce HS Ae Be ee ee 23 AA ss AAA AA 26 a ly Sea le o al a e a ee ee 27 E AIR 28 May 21 2008 2 Num This class provides a few constants and some methods to compute numerical quantities such as factorials combinations gamma functions and so on package umontreal iro lecuyer util public class Num Constants public static final double DBL_EPSILON 2 2204460492503131e 16 Difference between 1 0 and the smallest double greater than 1 0 public static final int DBL_MAX_EXP 1024 Largest int x such that 277 is representable approximately as a double public static final int DBL_MIN_EXP 1021 Small
10. Uses connectToDatabase with the stream obtained from the resource resource This method searches the file resource on the class path opens the first resource found and extracts properties from it It then uses connectToDatabase to establish the connection public static double readDoubleData Statement stmt String query throws SQLException Copies the result of the SQL query query into an array of double precision values This method uses the statement stmt to execute the given query and assumes that the first column of the result set contains double precision values Each row of the result set then becomes an element of an array of double precision values which is returned by this method This method throws an SQLException if the query is not valid public static double readDoubleData Connection connection String query throws SQLException Copies the result of the SQL query query into an array of double precision values This method uses the active connection connection to create a statement and passes this state ment with the query to readDoubleData which returns an array of double precision values public static double readDoubleData Statement stmt String table String column throws SQLException Returns the values of the column column of the table table This method is equivalent to readDoubleData stmt SELECT column FROM table public static double readDoubleData Connection connection String table String colu
11. bit is the highest order bit of the first int int the row public BitMatrix BitMatrix that Copy constructor Methods public Object clone Creates a copy of the BitMatrix public boolean equals BitMatrix that Verifies that this and that are strictly identical They must both have the same dimensions and data public String toString Creates a String containing all the data of the BitMatrix The result is displayed in a matrix form with each row being put on a different line Note that the bit at 0 0 is at the upper left of the matrix while the bit at 0 in a BitVector is the least significant bit public String printData Creates a String containing all the data of the BitMatrix The data is displayed in the same format as are the int in Java code This allows the user to print the representation of May 21 2008 BitMatrix 24 a BitMatrix to be put directly in the source code in the constructor BitMatrix int 1 int int The output is not designed to be human readable public int numRows Returns the number of rows of the BitMatrix public int numColumns Returns the number of columns of the BitMatrix public boolean getBool int row int column Returns the value of the bit in the specified row and column If the value is 1 return true If it is 0 return false public void setBool int row int column boolean value Changes the value of the bit in the specified row and column If va
12. derlying DBMS but the creation of the connection adds a DBMS specific portion in the application This class helps the developer in moving the DBMS specific information out of the source code by storing it in a properties file The methods in this class can read such a properties file and establish the JDBC connection The connection can be made by using a DataSource obtained through a JNDI server or by a JDBC URI associated with a driver class Therefore the properties used to connect to the database must be a JNDI name jdbc jndi name or a driver to load jdbc driver with the URI of a database jdbc uri jdbc driver com mysql jdbc Driver jdbc uri jdbc mysql mysql iro umontreal ca database user fookpassword bar The connection is established using the connectToDatabase method Shortcut methods are also available to read the properties from a file or a resource before establishing the connection This class also provides shortcut methods to read data from a database and to copy the data into Java arrays package umontreal iro lecuyer util public class JDBCManager Methods public static Connection connectToDatabase Properties prop throws SQLException Connects to the database using the properties prop and returns the an object representing the connection The properties stored in prop must be a JNDI name jdbc jndi name or the name of a driver jdbc driver to load and the URI of the database jdbc uri When a JNDI name is
13. ds Here t suppose 830 CPU seconds are used here t timer getMinutes Here t System out println timer format Prints o oo Wo package umontreal iro lecuyer util public class Chrono public static Chrono createForSingleThread Creates a Chrono instance adapted for a program using a single thread Under Java 1 5 this method returns an instance of ChronoSingleThread which can measure CPU time for one thread Under Java versions prior to 1 5 this returns an instance of this class This method must not be used to create a timer for a multi threaded program because the obtained CPU times will differ depending on the used Java version 1 From Richard Dans les deux cas le nouveau Chrono d ric fonctionne bien en appelant Chrono timer Chrono createForSingleThread May 21 2008 Chrono 16 Constructor public Chrono Constructs a Chrono object and initializes 1t to zero Timing functions public void init Initializes this Chrono to zero public double getSeconds Returns the CPU time in seconds used by the program since the last call to init for this Chrono public double getMinutes Returns the CPU time in minutes used by the program since the last call to init for this Chrono public double getHours Returns the CPU time in hours used by the program since the last call to init for this Chrono public String format Converts the CPU time used by the program s
14. e May 21 2008 REFERENCES 34 References 1 C W Clenshaw Chebychev series for mathematical functions National Physical Laboratory Mathematical Tables 5 Her Majesty s Stationery Office London 1962 2 D E Knuth The Art of Computer Programming Vol 1 Addison Wesley Reading MA second edition 1973
15. eldwidth characters will be used public PrintfFormat append int fieldwidth int precision double x Uses the f static method to append x to the buffer A minimum of fieldwidth characters will be used with the given precision May 21 2008 PrintfFormat 9 public PrintfFormat append int x Appends x to the buffer public PrintfFormat append int fieldwidth int x Uses the d static method to append x to the buffer A minimum of fieldwidth characters will be used public PrintfFormat append long x Appends x to the buffer public PrintfFormat append int fieldwidth long x Uses the d static method to append x to the buffer A minimum of fieldwidth characters will be used public PrintfFormat append int fieldwidth int accuracy int precision double x Uses the format static method with the same four arguments to append x to the buffer public PrintfFormat append char c Appends a single character to the buffer public void clear Clears the contents of the buffer public StringBuffer getBuffer Returns the StringBuffer associated with that object public String toString Converts the buffer into a String public static String s String str Same as s 0 str If the string str is null it returns the string null public static String s int fieldwidth String str Formats the string str like the s in the C printf function The fieldwidth argument gives the minimum length of the resulting string
16. essary If there is not enough space to format x in decimal notation with at least precision significant digits accuracy or fieldwidth are too small it will be converted to scientific notation with at least precision significant digits In that case fieldwidth is increased if necessary and the error is also formatted in scientific notation public static void formatWithError int fieldwidth int fieldwidtherr int precision double x double error String res Stores a string containing x into res 0 and a string containing error into res 1 both strings being formatted with the same notation This calls formatWithError with the minimal accuracy for which the formatted string for error is non zero If error is 0 the accuracy is 0 If this minimal accuracy causes the strings to be formatted using scientific notation this method increases the accuracy until the decimal notation can be used May 21 2008 13 TableFormat This class provides methods to format arrays and matrices into Strings in different styles This could be useful for printing arrays and subarrays or for putting them in files for further treatment by other softwares such as Mathematica Matlab etc package umontreal iro lecuyer util public class TableFormat Formating styles public static final int PLAIN Plain text matrix printing style public static final int MATHEMATICA Mathematica matrix printing style public static final int MATLAB Matlab matri
17. est int x such that 2 is representable approximately as a normalised double public static final int DBL_MAX_10_EXP 308 Largest int x such that 10 is representable approximately as a double public static final double DBL_MIN 2 2250738585072014e 308 Smallest normalized positive floating point double public static final double LN_DBL_MIN 708 3964185322641 Natural logarithm of DBL_MIN public static final int DBL_DIG 15 Number of decimal digits of precision in a double public static final double EBASE 2 7182818284590452354 The constant e public static final double EULER The Euler Mascheroni constant 0 57721566490153286 public static final double RAC2 1 41421356237309504880 The value of v2 public static final double IRAC2 0 70710678118654752440 The value of 1 V2 May 21 2008 Num 3 public static final double LN2 0 69314718055994530941 The values of In 2 public static final double ILN2 1 44269504088896340737 The values of 1 1n 2 public static final double MAXINTDOUBLE 9007199254740992 0 953 Largest integer ny such that any integer n lt ng is represented exactly as a double public static final double MAXTWOEXP 64 Powers of 2 up to MAXTWOEXP are stored exactly in the array TWOEXP public static final double TWOEXP Contains the precomputed positive powers of 2 One has TWOEXP j 2 for j 0 64 public static final double TEN_NEG_POW C
18. h an approximate relative precision tol Returns x such that f x 0 May 21 2008 28 Misc This class provides miscellaneous functions that are hard to classify Some may be moved to another class in the future package umontreal iro lecuyer util public class Misc Methods public static double quickSelect double t int n int k Returns the kth smallest item of the array t of size n public static int quickSelect int t int n int k Returns the kt smallest item of the array t of size n public static int getTimeInterval double times int start int end double t Returns the index of the time interval corresponding to time t Let tp lt lt tn be simulation times stored in a subset of times This method uses binary search to determine the smallest value for which t lt t lt t 41 and returns i The value of t is stored in times start i whereas n is defined as end start Ift lt to this returns 1 If t gt ty this returns n Otherwise the returned value is greater than or equal to 0 and smaller than or equal to n 1 start and end are only used to set lower and upper limits of the search in the times array the index space of the returned value always starts at 0 Note that if the elements of times with indices start end are not sorted in non decreasing order the behavior of this method is undefined public static void interpol int n double X double Y double C Gi
19. he table table This method is equivalent to readIntData connection SELECT column FROM table public static double readDoubleData2D Statement stmt String query throws SQLException Copies the result of the SQL query query into a rectangular 2D array of double precision values This method uses the statement stmt to execute the given query and assumes that the columns of the result set contain double precision values Each row of the result set then becomes a row of a 2D array of double precision values which is returned by this method This method throws an SQLException if the query is not valid The given statement stmt must not be set up to produce forward only result sets public static double readDoubleData2D Connection connection String query throws SQLException Copies the result of the SQL query query into a rectangular 2D array of double precision values This method uses the active connection connection to create a statement and passes this statement with the query to readDoubleData2D which returns a 2D array of double precision values public static double readDoubleData2DTable Statement stmt String table throws SQLException Returns the values of the columns of the table table This method is equivalent to readDoubleData2D stmt SELECT FROM table public static double readDoubleData2DTable Connection connection String table throws SQLException Returns the values of the columns of the table
20. ince its last call to init for this Chrono to a String in the HH MM SS xx format public static String format double time Converts the time time given in seconds to a String in the HH MM SS xx format May 21 2008 17 ChronoSingleThread The ChronoSingleThread class extends the Chrono class and computes the CPU time for the current thread only It is valid only under Java 1 5 since Java 1 5 provides platform independent facilities to get the CPU time for a single thread through management API The parent class Chrono uses a platform dependent method since it is programmed directly in C to determine the CPU time for all threads Here is an example of how it may be used Chrono timer new ChronoSingleThread double t timer getSeconds timer init t timer getSeconds t timer getMinutes System out println timer format package umontreal iro lecuyer util public class ChronoSingleThread extends Chrono Constructor public ChronoSingleThread Constructs a ChronoSingleThread object and initializes it to zero May 21 2008 18 ArithmeticMod This class provides facilities to compute multiplications of scalars of vectors and of matrices modulo m All algorithms are present in three different versions These allow operations on double int and long The int and long versions work exactly like the double ones package umontreal iro lecuyer util public class ArithmeticMod Method
21. int m int n Computes and returns the Stirling numbers of the second kind mij 44 for 0 lt i lt mand0 lt i lt j lt n 1 public static double volumeSphere double p int t Returns the volume V of a sphere of radius 1 in t dimensions using the norm Lp It is given by the formula _ Pra 1 p aa E where T is the gamma function The case of the sup norm L is obtained by choosing p 0 Restrictions p gt 0 and t gt 1 public static double evalCheby double S int N double x Evaluates a series of Chebyshev polynomials T at x over the basic interval 1 1 using the method of Clenshaw 1 i e computes and returns S N 0 y 2 gt 1 57s J public static double evalChebyStar double S int N double x Evaluates a series of shifted Chebyshev polynomials T at x over the basic interval 0 1 using the method of Clenshaw I i e computes and returns S N 0 Y aT J S T 2 j l public static double besselK025 double x Returns the value of Ky 4 2 where K is the modified Bessel s function of the second kind The relative error on the returned value is less than 0 5 x 1076 for x gt 107300 public static int multMod int a int s int c int m Returns as c mod m Restriction assumes that a c s lt m May 21 2008 Num 5 public static long multMod long a long s long c long m Returns as c mod m Uses the class ArithmeticMod Restriction assumes that a c s lt m public
22. lue is true changes it to 1 If value is false changes it to 0 public BitMatrix transpose Returns the transposed matrix The rows and columns are interchanged public BitMatrix not Returns the BitMatrix resulting from the application of the not operator on the original BitMatrix The effect is to swap all the bits of the BitMatrix turning all 0 into 1 and all 1 into 0 public BitMatrix and BitMatrix that Returns the BitMatrix resulting from the application of the and operator on the original BitMatrix and that Only bits which were at 1 in both BitMatrix are set at 1 in the result All others are set to 0 public BitMatrix or BitMatrix that Returns the BitMatrix resulting from the application of the or operator on the original BitMatrix and that Only bits which were at 0 in both BitMatrix are set at 0 in the result All others are set to 1 public BitMatrix xor BitMatrix that Returns the BitMatrix resulting from the application of the xor operator on the original BitMatrix and that Only bits which were at 1 in only one of the two BitMatrix are set at 1 in the result All others are set to 0 public BitVector multiply BitVector vect Multiplies the column BitVector by a BitMatrix and returns the result The result is A xv where A is the BitMatrix and v is the BitVector public int multiply int vect Multiplies vect seen as a column BitVector by a BitMatrix See BitVector to see the conversion between in
23. mn throws SQLException Returns the values of the column column of the table table This method is equivalent to readDoubleData connection SELECT column FROM table public static int readIntData Statement stmt String query throws SQLException Copies the result of the SQL query query into an array of integers This method uses the statement stmt to execute the given query and assumes that the first column of the result May 21 2008 JDBCManager 32 set contains integer values Each row of the result set then becomes an element of an array of integers which is returned by this method This method throws an SQLException if the query is not valid The given statement stmt must not be set up to produce forward only result sets public static int readIntData Connection connection String query throws SQLException Copies the result of the SQL query query into an array of integers This method uses the active connection connection to create a statement and passes this statement with the query to readIntData which returns an array of integers public static int readIntData Statement stmt String table String column throws SQLException Returns the values of the column column of the table table This method is equivalent to readIntData stmt SELECT column FROM table public static int readIntData Connection connection String table String column throws SQLException Returns the values of the column column of t
24. n This is equivalent to readDoubleData for reading integers public static int readIntData String file throws IOException This is equivalent to readDoubleData for reading integers public static double readDoubleData2D Reader input throws IOException Uses the reader input to obtain a 2 dimensional array of double precision values For each line of text obtained from the given reader this method trims whitespaces and parses the remaining text as an array of double precision values Every character other than the digits the plus and minus signs the period and the letters e and E are ignored and can be used to separate numbers on a line Moreover lines starting with a pound sign are considered as comments and thus skipped The lines containing only a semicolon sign are considered as empty lines The method returns a 2D array containing all the parsed values The returned array is not always rectangular public static double readDoubleData2D File file throws IOException Opens the file referred to by the file object file and calls readDoubleData2D to obtain a matrix of double precision values from the file May 21 2008 TextDataReader 7 public static double readDoubleData2D String file throws IOException Opens the file with name file and calls readDoubleData2D to obtain a matrix of double precision values from the file public static int readIntData2D Reader input throws IOExceptio
25. n This is equivalent to readDoubleData2D for reading integers public static int readIntData2D File file throws IOException This is equivalent to readDoubleData2D for reading integers public static int readIntData2D String file throws IOException This is equivalent to readDoubleData2D for reading integers May 21 2008 8 PrintfFormat This class acts like a StringBuffer which defines new types of append methods It defines certain functionalities of the ANSI C printf function that also can be accessed through static methods The information given here is strongly inspired from the man page of the C printf function package umontreal iro lecuyer util public class PrintfFormat Constructors public PrintfFormat Constructs a new buffer object containing an empty string public PrintfFormat int length Constructs a new buffer object with an initial capacity of length public PrintfFormat String str Constructs a new buffer object containing the initial string str Methods public PrintfFormat append String str Appends str to the buffer public PrintfFormat append int fieldwidth String str Uses the s static method to append str to the buffer A minimum of fieldwidth characters will be used public PrintfFormat append double x Appends x to the buffer public PrintfFormat append int fieldwidth double x Uses the f static method to append x to the buffer A minimum of fi
26. odM int A int BO int m int e Exactly like matTwoPowModM using double but with int instead of double public static void matPowModM int AQ int B 1 int m int c Exactly like matPowModM using double but with int instead of double Methods using long public static long multModM long a long s long c long m Computes a x s c mod m Works also if s or c are negative The result is always positive and thus always between 0 and m 1 public static void matVecModM long A long s long v long m Exactly like matVecModM using double but with long instead of double public static void matMatModM long A long B long C 1 long m Exactly like matMatModM using double but with long instead of double public static void matTwoPowModM long A long B long m int e Exactly like matTwoPowModM using double but with long instead of double public static void matPowModM long A long B long m int c Exactly like matPowModM using double but with long instead of double May 21 2008 20 BitVector This class implements vectors of bits and the operations needed to use them The vectors can be of arbitrary length The operations provided are all the binary operations available to the int and long primitive types in Java All bit operations are present in two forms a normal form and a self form The normal form returns a newly created object containing the result while the self form
27. ontains the precomputed negative powers of 10 One has TEN_NEG_POW j 1077 for 0 16 Methods public static double log2 double x Returns logs x public static double logip double x Deprecated Use Math logip instead Returns a value equivalent to log 1 x accurate also for small x public static double factorial int n Returns the value of n public static double 1nFactorial int n Returns the value of In n the natural logarithm of factorial n Gives 16 decimals of precision relative error lt 0 5 x 10719 public static double lnGamma double x Returns the natural logarithm of the gamma function I x evaluated at x Gives 16 decimals of precision but is implemented only for x gt 0 public static double digamma double x Returns the logarithmic derivative of the Gamma function y x I x T 2 public static double trigamma double x Returns the value of the trigamma function dy x dx the derivative of the digamma func tion evaluated at x May 21 2008 Num 4 public static double tetragamma double x Returns the value of the tetragamma function d 4 x d x the second derivative of the digamma function evaluated at x public static double combination int n int s Returns the value of the number of different combinations of s objects amongst n Uses an algorithm that prevents overflows when computing factorials if possible public static double calcMatStirling
28. r vector are set to 1 The others are set to 0 This is equivalent to the addition in modulo 2 arithmetic a public BitVector selfXor BitVector that Applies the xor operator on this with that Stores the result in this and returns it public BitVector and BitVector that Returns a BitVector which is the result of the and operator with both the this and that BitVector s The and operator is equivalent to the amp operator in Java Only bits which are set to 1 in both this and that are set to 1 in the result all the others are set to 0 public BitVector selfAnd BitVector that Applies the and operator on this with that Stores the result in this and returns it May 21 2008 BitVector 22 public BitVector or BitVector that Returns a BitVector which is the result of the or operator with both the this and that BitVector s The or operator is equivalent to the operator in Java Only bits which are set to 0 in both this and that are set to to 0 in the result all the others are set to 1 public BitVector selfOr BitVector that Applies the or operator on this with that Stores the result in this and returns it public BitVector shift int j Returns a BitVector equal to the original with all the bits shifted j positions to the right if j is positive and shifted j positions to the left if j is negative The new bits that appears to the left or to the right are set to 0 If j is positive this operation is equivalent to the
29. rged then the newly added bits are given the value 1 if filling is set to true and O otherwise public void enlarge int size Resizes the BitVector so that its length is equal to size Any new bit added is set to 0 public boolean getBool int pos Gives the value of the bit in position pos If the value is 1 returns true otherwise returns false public void setBool int pos boolean value Sets the value of the bit in position pos If value is equal to true sets it to 1 otherwise sets it to 0 public int getInt int pos Returns an int containing all the bits in the interval pos x 32 pos x 32 31 public String toString Returns a string containing all the bits of the BitVector starting with the highest order bit and finishing with the lowest order bit The bits are grouped by groups of 8 bits for ease of reading public BitVector not Returns a BitVector which is the result of the not operator on the current BitVector The not operator is equivalent to the operator in Java and thus swap all bits bits previously set to 0 become 1 and bits previously set to 1 become 0 public BitVector selfNot Applies the not operator on the current BitVector and returns it public BitVector xor BitVector that Returns a BitVector which is the result of the xor operator applied on this and that The xor operator is equivalent to the operator in Java All bits which were set to 0 in one of the vector and to 1 in the othe
30. s using double public static double multModM double a double s double c double m Computes a x s c mod m Where m must be smaller than 2 Works also if s or c are negative The result is always positive and thus always between 0 and m 1 public static void matVecModM double A double s double v double m Computes the result of A x s mod m and puts the result in v Where s and v are both column vectors This method works even if s v public static void matMatModM double A double B double COD double m Computes A x B mod m and puts the result in C Works even if A C B CorA B C public static void matTwoPowModM double A double B double m int e Computes A mod m and puts the result in B Works even if A B public static void matPowModM double A double B double m int c Computes A mod m and puts the result in B Works even if A B Methods using int public static int multModM int a int s int c int m Computes a x s c mod m Works also if s or c are negative The result is always positive and thus always between 0 and m 1 public static void matVecModM int AQ int s int v int m Exactly like matVecModM using double but with int instead of double public static void matMatModM int AM int BO 1 int CO int m Exactly like matMatModM using double but with int instead of double May 21 2008 ArithmeticMod 19 public static void matTwoPowM
31. static double multMod double a double s double c double m Returns as c mod m Restriction assumes that a s c are lt m and a s c m are lt 235 May 21 2008 6 TextDataReader Provides static methods to read data from text files package umontreal iro lecuyer util public class TextDataReader public static double readDoubleData Reader input throws IOException Reads an array of double precision values from the reader input For each line of text obtained from the given reader this method trims whitespaces and parses the remaining text as a double precision value This method ignores every character other than the digits the plus and minus signs the period and the letters e and E Moreover lines starting with a pound sign are considered as comments and thus skipped The method returns an array containing all the parsed values public static double readDoubleData File file throws IOException Opens the file referred to by the file object file and calls readDoubleData to obtain an array of double precision values from the file public static double readDoubleData String file throws IOException Opens the file with name file and calls readDoubleData to obtain an array of double precision values from the file public static int readIntData Reader input throws IOException This is equivalent to readDoubleData for reading integers public static int readIntData File file throws IOExceptio
32. t and BitVector The result is A x v where A is the BitMatrix and v is the BitVector May 21 2008 BitMatrix 25 public BitMatrix multiply BitMatrix that Multiplies two BitMatrix s together The result is A x B where A is the this BitMatrix and B is the that BitMatrix public BitMatrix power long p Raises the BitMatrix to the power p public BitMatrix power2e int e Raises the BitMatrix to power 2 Nested Class public class IncompatibleDimensionException extends RuntimeException Runtime exception raised when the dimensions of the BitMatrix are not appropriate for the operation May 21 2008 26 MathFunction This interface should be implemented by classes which represent univariate mathematical functions It is used to pass an arbitrary function of one variable as argument to another function For example it is used in RootFinder to find the zeros of a function package umontreal iro lecuyer util public interface MathFunction public double evaluate double x Returns the value of the function evaluated at x May 21 2008 27 RootFinder This class provides methods to solve non linear equations package umontreal iro lecuyer util public class RootFinder Methods public static double brentDekker double a double b MathFunction f double tol Computes a root x of the function in f using the Brent Dekker method The interval a b must contain the root x The calculations are done wit
33. table This method is equivalent to readDoubleData2D connection SELECT FROM table May 21 2008 JDBCManager 33 public static int readIntData2D Statement stmt String query throws SQLException Copies the result of the SQL query query into a rectangular 2D array of integers This method uses the statement stmt to execute the given query and assumes that the columns of the result set contain integers Each row of the result set then becomes a row of a 2D array of integers which is returned by this method This method throws an SQLException if the query is not valid The given statement stmt must not be set up to produce forward only result sets public static int readIntData2D Connection connection String query throws SQLException Copies the result of the SQL query query into a rectangular 2D array of integers This method uses the active connection connection to create a statement and passes this state ment with the query to readIntData2D which returns a 2D array of integers public static int readIntData2DTable Statement stmt String table throws SQLException Returns the values of the columns of the table table This method is equivalent to readIntData2D stmt SELECT FROM table public static int readIntData2DTable Connection connection String table throws SQLException Returns the values of the columns of the table table This method is equivalent to readIntData2D connection SELECT FROM tabl
34. ven the n 1 distinct points xo yo 11 Y1 Ln Yn with X 0 zx and similarly for Y and C this function computes the n 1 coefficients C i of the Newton interpolating polynomial P x of degree n passing through these points P x co c amp z Lp c2 x xo x x1 enlo zo x 21 Lp 1 public static double evalPoly int n double X double C double z Given n X and C as described in interpol n X Y C this function returns the value of the interpolating polynomial evaluated at z public static double simpsonIntegral MathFunction func double a double b int numIntervals Computes and returns an approximation of the integral of func over a b using the Simp sons 1 3 method with numIntervals intervals This method estimates tow May 21 2008 Misc 29 where f x is the function defined by func and evaluated at x by dividing a b in n numIntervals interval with length h b a n The integral is estimated by h 3 F a f a h 2f a 2h 4f a 3h f d This method assumes that a lt b lt oo and n is even May 21 2008 30 JDBCManager This class provides some facilities to connect to a SQL database and to retrieve data stored in it JDBC provides a standardized interface for accessing a database independently of a specific database management system DBMS The user of JDBC must create a Connection object used to send SQL queries to the un
35. x printing style Functions to convert tables to String public static String format int V int n1 int n2 int k int p Formats a String containing the elements n1 to n2 inclusive of table V k elements per line p positions per element If k 1 the array index will also appear on the left of each element i e each line i will have the form i V i public static String format double V int n1 int n2 int k int pi int p2 int p3 Similar to the previous method but for an array of double s Gives at least p1 positions per element p2 digits after the decimal point and at least p3 significant digits public static String format int Mat int i1 int 12 int j1 int j2 int w int p int style String Name Formats a submatrix of integers public static String format double Mat int i1 int 12 int j1 int j2 int w int p int style String Name Formats the submatrix with lines i1 lt lt i2 and columns j1 lt j lt j2 of the matrix Mat using the formatting style style The elements are formated in w positions each with a precision of p digits The string Name provides an identifier for the submatrix May 21 2008 TableFormat 14 To be treated by Matlab this string containing the matrix must be copied to a file with extension m If the file is named poil m for example it can be accessed by calling poil in Matlab For Mathematica if the file is named poil it will be read using lt lt poil
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