/* ------------------------------------------------------------------ */ /* The REXX-idiomatic numeric validation approach is to use the */ /* 'DATATYPE' BIF. For more complex validation needs the 'VERIFY' BIF */ /* may also be used but since it only checks for the presence or the */ /* absence of characters it needs to be augmented with other checks. */ /* */ /* Regex-based validation [once implemented] requires the least work. */ /* The examples make use of a REXXToolkit routine, 'match', which */ /* uses the 'RxRe' external library. See Appendix for details. */ /* ------------------------------------------------------------------ */ /* REXX BIF-based Validation */ /* Accepts: +9 -9 9.0 9.0e+2 9.0E-3 */ if \DATATYPE(string, 'N') then ; say "not a decimal number" /* Accepts: +9 -9 Rejects: 9.0 9.0e+2 9.0E-3 */ if \(DATATYPE(string, 'W') & POS(".", string) == 0) then say "not an integer" /* ----------- */ /* Checks for presence / absence of characters, but does not check position of characters, or presence of patterns. Useful for quick, but not thorough, validation */ if VERIFY(string, "0123456789") \= 0 then ; say "has nondigits" if VERIFY(string, "+-.Ee0123456789") \= 0 then ; say "not a decimal" /* ----------- */ /* Custom function, 'isDecimal', which uses a combination of the PARSE instruction, and DATATYPE BIF to thoroughly validate a decimal value */ tbl = "+934.521e-2 -934.521 934 ", "+934.521e-a +934.521f-2 +934.!e-2 ", "e934.521e-2" entries = WORDS(tbl) do i = 1 for entries entry = WORD(tbl, i) if isDecimal(entry) then ; say entry "is decimal" else ; say entry "is NOT decimal" end exit 0 /* ----------- */ isDecimal : procedure expose (globals) parse upper value ARG(1) with whole "." frac "E" exp if exp \= NULL then ; if \DATATYPE(exp, 'W') then ; return FALSE if frac \= NULL then ; if \DATATYPE(frac, 'W') then ; return FALSE if whole \= NULL then ; if \DATATYPE(whole, 'W') then ; return FALSE return TRUE /* ----------------------------- */ /* Regex-based Validation */ if match(string, "PATTERN") then /* Is a number */ else /* Is not */ /* ----------- */ /* Also rejects: +9 -9 9.0 */ if match(string, "[^[:digit:]]") then ; say "has nondigits" /* Also rejects: +9 -9 9.0 */ if \match(string, "^[[:digit:]]+$") then ; say "not a natural number" /* Rejects: +9 9.0 Accepts: -9 */ if \match(string, "^-?[[:digit:]]+$") then ; say "not an integer" /* Rejects: 9.0 Accepts: +9 -9 */ if \match(string, "^[+-]?[[:digit:]]+$") then ; say "not an integer" /* Accepts: +9 -9 9.0 9.0e+2 9.0E-3 */ decimalRE = "^[+-]?[[:digit:]]+\.?[[:digit:]]+[e|E][+-]?[[:digit:]]+$" if \match(string, decimalRE) then say "not a decimal number" |
/* ------------------------------------------------------------------ */ /* The NUMERIC instruction allows adjustment of: */ /* */ /* * Significant digits used in arithmetic operations [DIGITS] */ /* * Digits to be ignored during arithmetic comparisons [FUZZ] */ /* */ /* Default values are usually adequate. Increasing DIGITS increases */ /* precision, but slows down arithmetic operations. FUZZ is by default*/ /* 0, so all digits are significant in comparison operations. */ /* */ /* The FORMAT BIF may be used like the C-derived, 'sprintf', function */ /* to compare floating point values as strings. */ /* ------------------------------------------------------------------ */ numeric digits 11 a = 1234567.8234 ; b = 1234567.8237 /* Compare 'DIGITS - FUZZ' [11] number of digits */ numeric fuzz 0 if a = b then ; say "a = b" /* FALSE */ /* Compare 'DIGITS - FUZZ' [10] number of digits */ numeric fuzz 1 if a = b then ; say "a = b" /* FALSE */ /* Compare 'DIGITS - FUZZ' [9] number of digits */ numeric fuzz 2 if a = b then ; say "a = b" /* TRUE */ /* ----------------------------- */ /* Returns TRUE if 'num1' and 'num2' are equal to 'accuracy' number of decimal places */ isEqual(num1, num2, accuracy) /* ----------------------------- */ a = 1234567.8234 ; b = 1234567.8237 /* isEqual(a, b, 1) ==> TRUE isEqual(a, b, 2) ==> TRUE isEqual(a, b, 3) ==> TRUE isEqual(a, b, 4) ==> FALSE */ exit 0 /* ----------- */ isEqual : procedure expose (globals) places = ARG(3) ; numeric fuzz 0 return FORMAT(ARG(1),, places) == FORMAT(ARG(2),, places) /* ----------------------------- */ wage = 536 /* $ 5.36 / hr */ week = 40 * wage /* $ 214.40 */ say "One week's wage is: $" FORMAT(week / 100,, 2) |
/* ------------------------------------------------------------------ */ /* The 'FORMAT' BIF is REXX's equivalent to the much-used, C-derived */ /* 'sprintf' function. */ /* ------------------------------------------------------------------ */ /* Truncate to integer value */ truncated = TRUNC(value, length) /* Round value [and possibly justify] */ rounded = FORMAT(value, n_before_decimal, n_after_decimal) /* ----------------------------- */ a = 0.255 ; b = FORMAT(a, 1, 2) say "Unrounded:" a "Rounded:" b say "Unrounded:" a "Rounded:" FORMAT(a, 1, 2) /* Unrounded: 0.255 Rounded: 0.26 Unrounded: 0.255 Rounded: 0.26 */ /* ----------------------------- */ /* Example illustrating external library routine use. Not, however, that the FORMAT BIF can be used to perform the same tasks as 'NInt', 'Floor' and 'Ceil', making library routine use unnecessary */ /* Load [rexxMath] math functions from external library */ call rxFuncAdd 'mathLoadFuncs', 'rexxMath', 'mathLoadFuncs' call mathLoadFuncs tbl = "3.3 3.5 3.7 -3.3" say cstr2rxstr("number\tint\tfloor\tceil") do while tbl <> NULL parse var tbl n tbl line = FORMAT(n, 2, 1) || "\t" ||, FORMAT(NInt(n), 2, 1) || "\t" ||, FORMAT(Floor(n), 2, 1) || "\t" ||, FORMAT(Ceil(n), 2, 1) say cstr2rxstr(line) end /* number int floor ceil 3.3 3.0 3.0 4.0 3.5 4.0 3.0 4.0 3.7 4.0 3.0 4.0 -3.3 -3.0 -4.0 -3.0 */ /* Unload math functions */ call mathDropFuncs exit 0 /* ----------- */ cstr2rxstr : procedure expose (globals) s = ARG(1) ; tbl = "\n 0A \r 0D \t 09" do while tbl \= NULL parse var tbl esc replc tbl s = CHANGESTR(esc, s, X2C(replc)) end return s |
/* ------------------------------------------------------------------ */ /* Binary, hexadecimal, decimal interconversion is well-supported via */ /* the following BIF's: */ /* */ /* * X2D, D2X [hex->dec, dec->hex, respectively] */ /* * X2B, B2X [hex->bin, bin->hex, respectively] */ /* */ /* Easily combined to create functions that interconvert binary and */ /* decimal. */ /* ------------------------------------------------------------------ */ /* Convert binary string to decimal */ decimal = B2D('0110110') /* Convert decimal value to binary string */ binary = D2B(54) exit 0 /* ----------- */ B2D : procedure expose (globals) return X2D(B2X(ARG(1))) D2B : procedure expose (globals) return X2B(D2X(ARG(1))) |
/* ------------------------------------------------------------------ */ /* The 'do' loop is the REXX-idiomatic control structure for */ /* repetitive tasks such as list traversal. Recursive solutions are */ /* possible but less efficient due to argument passing overhead, and */ /* lack of tail-call optimisation. */ /* ------------------------------------------------------------------ */ x = 1 ; y = 5 ; step = 1 /* Number sequence is traversed using 'do' loop */ /* 'i' set from value of 1 through to 5 in 'step' increments */ do i = x to y by step /* do something with 'i' */ end /* ----------- */ /* 'i' set from value of 1 through to 5; default increment of 1 */ do i = x to y /* do something with 'i' */ end /* ----------------------------- */ call CHAROUT , "Infancy is: " do i = 0 to 2 ; call CHAROUT , i || SPACE ; end say NULL call CHAROUT , "Toddling is: " do i = 3 to 4 ; call CHAROUT , i || SPACE ; end say NULL call CHAROUT , "Childhood is: " do i = 5 to 12 ; call CHAROUT , i || SPACE ; end say NULL /* ----------------------------- */ /* REXX does not sport a native 'foreach' control structure, but it is possible to implement similar behaviour provided certain conventions are followed such as generating lists of SPACE or COMMA-separated sequences */ /* ----------------------------- */ sequence = makeIntegerSequence(1, 5, 1) do while sequence <> NULL parse var sequence value sequence call CHAROUT , value || SPACE end /* ----------- */ /* Partial reimplementation of earlier example */ infancy = makeIntegerSequence(0, 2, 1) call CHAROUT , "Infancy is: " do while infancy <> NULL parse var infancy value infancy call CHAROUT , value || SPACE end /* ... */ exit 0 /* ----------- */ /* Iterative ['do' loop-based] */ makeIntegerSequence : procedure expose (globals) x = ARG(1) ; y = ARG(2) ; step = ARG(3) seq = x ; x = x + 1 ; do i = x to y by step ; seq = seq i ; end return seq /* Recursive */ makeIntegerSequenceR : procedure expose (globals) x = ARG(1) ; y = ARG(2) ; step = ARG(3) if x > y then ; return NULL return x makeIntegerSequenceR(x + step, y, step) /* Iterative [Tail Recursive] */ makeIntegerSequenceI : procedure expose (globals) x = ARG(1) ; y = ARG(2) ; step = ARG(3) ; seq = ARG(4) if x > y then ; return STRIP(seq) return makeIntegerSequenceI(x + step, y, step, (seq x)) |
/* ------------------------------------------------------------------ */ /* REXX sports no inbuilt Roman numeral-handling routines. A custom */ /* implementation appears below. */ /* ------------------------------------------------------------------ */ roman = arabic2roman(arabic) arabic = roman2arabic(roaman) /* ----------------------------- */ roman_fifteen = arabic2roman(15) say "Roman for fifteen is" roman_fifteen arabic_fifteen = roman2arabic(roman_fifteen) say "Converted back" roman_fifteen "is" arabic_fifteen exit 0 /* ----------- */ roman2arabic : procedure tbl.I = 1 ; tbl.V = 5 ; tbl.X = 10 ; tbl.L = 50 tbl.C = 100 ; tbl.D = 500 ; tbl.M = 1000 tbl.IV = 4 ; tbl.IX = 9 ; tbl.XL = 40 ; tbl.XC = 90 tbl.CD = 400 ; tbl.CM = 900 roman = " " || TRANSLATE(STRIP(ARG(1))) ; arabic = 0 do i = LENGTH(roman) - 1 to 1 by -1 r = SUBSTR(roman, i, 2) if SYMBOL('tbl.r') == 'VAR' then ; i = i - 1 else ; r = RIGHT(r, 1) arabic = arabic + tbl.r end return arabic /* ----------- */ arabic2roman : procedure arabic = REVERSE(ARG(1)) ; len = LENGTH(arabic) ; roman = "" tbl.1 = "I II III IV V VI VII VIII IX" tbl.2 = "X XX XXX XL L LX LXX LXXX XC" tbl.3 = "C CC CCC CD D DC DCC DCCC CM" if len < 4 then do i = 1 to len j = SUBSTR(arabic, i, 1) ; if j == 0 then ; iterate roman = WORD(tbl.i, j) || roman end else ; do do i = 1 to 3 j = SUBSTR(arabic, i, 1) ; if j == 0 then ; iterate roman = WORD(tbl.i, j) || roman end roman = COPIES("M", REVERSE(SUBSTR(arabic, 4))) || roman end return roman |
/* ------------------------------------------------------------------ */ /* Random number [well, pseudo-random :)] generation is typically */ /* performed using the 'RANDOM' BIF. */ /* ------------------------------------------------------------------ */ random = RANDOM(maxval) /* 0 - maxval [maxval <= 100000] */ random = RANDOM(minval, maxval) /* minval - maxval [as above] */ /* ----------------------------- */ tbl = "abcdefghijklmnop" elt = randomChoice(tbl) /* One of 'a', 'b', ... */ tbl = "12 67 asde cvs +++ &fgt klmnop" elt = randomChoice(tbl) /* One of 12, 67, ... */ /* ----------------------------- */ /* Generate 8 character-length password with randomly chosen chars */ chars = XRANGE("A", "Z") || XRANGE("a", "z") ||, XRANGE("0", "9") || "!$%#@*&" password = NULL do 8 password = password || randomChoice(chars) end exit 0 /* ----------- */ randomChoice : procedure expose (globals) tbl = ARG(1) ; items = WORDS(tbl) if items == 1 then do items = LENGTH(tbl) ; item = SUBSTR(tbl, RANDOM(1, items), 1) end ; else do item = WORD(tbl, RANDOM(1, items)) end return item |
/* ------------------------------------------------------------------ */ /* See comments in previous section */ /* ------------------------------------------------------------------ */ random = RANDOM(,, seed) /* Each such call reseeds the RNG */ |
/* ------------------------------------------------------------------ */ /* Custom functions for this type of task are easily written in REXX. */ /* Examples include: */ /* */ /* * 'lcg', simple linear-congruential RNG */ /* * 'randomSlice' - see example below */ /* ------------------------------------------------------------------ */ random = 47523 ; reps = 10 do reps random = lcg(random) /* do something with 'random' ... */ end /* ----------------------------- */ reps = 10 do reps /* Random length digit sequence; sliced from random position of a default-length 'RANDU'-generated digit sequence */ random = randomSlice() /* 3 digit sequence; as previous */ random = randomSlice(3) /* 4 digit sequence; sliced from random position of a 13 digit length 'RANDU'-generated digit sequence */ random = randomSlice(4, 13) end /* ----------- */ lgc : procedure expose (globals) numeric digits 17 return 16807 * ARG(1) // 2147483647 randomSlice : procedure expose (globals) sizeSlice = ARG(1) ; sizePool = ARG(2) if sizePool == NULL | sizePool > 17 then ; sizePool = 17 if sizeSlice == NULL then ; sizeSlice = RANDOM(1, sizePool - 1) if sizeSlice >= sizePool then ; sizeSlice = sizePool - 1; posSlice = RANDOM(1, sizePool - sizeSlice) numeric digits sizePool parse value RANDU() with "." frac return SUBSTR(frac, posSlice, sizeSlice) |
/* ------------------------------------------------------------------ */ /* Gaussian RNG */ /* ------------------------------------------------------------------ */ /* Need this for access to non-standard, 'RANDU', function */ options 'AREXX_BIFS' /* Using 'rexxMath' Library Routines */ /* Load [rexxMath] math functions from external library */ call rxFuncAdd 'mathLoadFuncs', 'rexxMath', 'mathLoadFuncs' call mathLoadFuncs /* ----------- */ mean = 25.0 ; sdev = 2.0 ; salary = gaussian_rand() * mean + sdev say "You have been hired at:" FORMAT(salary,, 2) /* ----------- */ /* Unload math functions */ call mathDropFuncs exit 0 /* ----------- */ gaussian_rand : procedure w = 2.0 do while w > 1.0 u1 = 2.0 * RANDU() - 1.0 ; u2 = 2.0 * RANDU() - 1.0 w = u1 * u1 + u2 * u2 end w = Sqrt((-2.0 * Log10(w)) / w) ; g2 = u1 * w ; g1 = u2 * w return g1 |
/* ------------------------------------------------------------------ */ /* Aside from supporting the usual arithmetic operations, including */ /* exponentiation [via the '**' operator], and a few BIF's including */ /* 'MIN', 'MAX', 'SIGN' and 'ABS', REXX offers no built-in support for*/ /* mathematical operations. Instead the programmer can implement the */ /* required functionality themselves, or make use of external library */ /* routines. */ /* */ /* REXX-native mathematical functions are easily implementable, but */ /* the string-expressable, arbitrary precision arithmetic model used */ /* ensures they will not be as 'high performance' as hardware-based */ /* implementations, precluding their use for 'serious' number crunch- */ /* ing. On the other hand, external library routines are [like the one*/ /* illustrated here] to be hardware-based, hence offer performance */ /* comparable to that of other languages after both function call and */ /* data conversion overhead is taken into account. */ /* ------------------------------------------------------------------ */ /* Using 'rxMath' Library Routines */ /* Load [rxMath] math functions from external library */ call rxFuncAdd 'mathLoadFuncs', 'rxMath', 'mathLoadFuncs' call mathLoadFuncs /* Accepts argumets in either degree, radian, or gradian form */ say rxCalcSin(30, 'D') say FORMAT(rxCalcSin(60, 'D'),,3) /* Unload math functions */ call mathDropFuncs exit 0 /* ----------- */ /* Using native REXX Routines [need 'Sin' from external library] */ radians = DEG2RAD(degrees) degrees = RAD2DEG(radians) /* ----------------------------- */ /* Load [rexxMath] math functions from external library */ call rxFuncAdd 'mathLoadFuncs', 'rexxMath', 'mathLoadFuncs' call mathLoadFuncs say degree_sin(30) say FORMAT(degree_sin(60),,3) /* Unload math functions */ call mathDropFuncs exit 0 /* ----------- */ degree_sin : procedure expose (globals) /* ARG(1) - Degrees --- 'Sin' [a 'rexxMath' library routine] expects its argument in radians so 'DEG2RAD' used to perform the conversion */ return Sin(DEG2RAD(ARG(1))) DEG2RAD : procedure expose (globals) return ARG(1) / 180 * PI() RAD2DEG : procedure expose (globals) return ARG(1) / PI() * 180 PI : procedure expose (globals) return 3.14159265358979323846264338327 |
/* ------------------------------------------------------------------ */ /* See comments in previous section header */ /* ------------------------------------------------------------------ */ /* Using 'rxMath' Library Routines */ /* Load [rxMath] math functions from external library */ call rxFuncAdd 'mathLoadFuncs', 'rxMath', 'mathLoadFuncs' call mathLoadFuncs /* Accepts argumets in either degree, radian, or gradian form */ theta = 1.7 ; tan = rxCalcSin(theta, 'R') / rxCalcCos(theta, 'R') say "tan of theta" theta "[radians]:" tan say "tan of theta" FORMAT(theta,, 3) "[radians]:" FORMAT(tan,, 3) /* ----------- */ say "tan of theta" theta "[radians]:" rxCalcTan(theta, 'R') say "tan of theta" FORMAT(theta,, 3) "[radians]:", /* ----------- */ theta = 0.37 ; say "acos of" theta "[radians]:" rxCalcArcCos(theta, 'R') /* ----------- */ /* Unload math functions */ call mathDropFuncs exit 0 /* ----------------------------- */ /* Using 'rexxMath' Library Routines */ /* Load [rexxMath] math functions from external library */ call rxFuncAdd 'mathLoadFuncs', 'rexxMath', 'mathLoadFuncs' call mathLoadFuncs theta = 1.7 ; tan = Sin(theta) / Cos(theta) say "tan of theta" theta "[radians]:" tan say "tan of theta" FORMAT(theta,, 3) "[radians]:" FORMAT(tan,, 3) /* ----------- */ say "tan of theta" theta "[radians]:" Tan(theta) say "tan of theta" FORMAT(theta,, 3) "[radians]:" FORMAT(Tan(theta),, 3) /* ----------- */ theta = 0.37 ; say "acos of" theta "[radians]:" ACos(theta) /* ----------- */ /* Unload math functions */ call mathDropFuncs exit 0 |
/* ------------------------------------------------------------------ */ /* See comments in previous section header */ /* ------------------------------------------------------------------ */ /* Using 'rxMath' Library Routines */ /* Load [rxMath] math functions from external library */ call rxFuncAdd 'mathLoadFuncs', 'rxMath', 'mathLoadFuncs' call mathLoadFuncs log_e = rxCalcLog(value) /* ----------- */ log_10 = rxCalcLog10(value) /* ----------- */ answer = rxlog_base(10, 10000) say "log_base(10, 10000) ==>" FORMAT(answer,, 2) say "log10(10000) ==>" FORMAT(rxCalcLog10(10000),, 2) /* ----------- */ /* Unload math functions */ call mathDropFuncs exit 0 /* ----------- */ rxlog_base : procedure expose (globals) base = ARG(1) ; value = ARG(2) return rxCalcLog(value) / rxCalcLog(base) /* ----------------------------- */ /* Using 'rexxMath' Library Routines */ /* Load [rexxMath] math functions from external library */ call rxFuncAdd 'mathLoadFuncs', 'rexxMath', 'mathLoadFuncs' call mathLoadFuncs log_e = Log(value) /* ----------- */ log_10 = Log10(value) /* ----------- */ answer = log_base(10, 10000) say "log_base(10, 10000) ==>" FORMAT(answer,, 2) say "log10(10000) ==>" FORMAT(Log10(10000),, 2) /* ----------- */ /* Unload math functions */ call mathDropFuncs exit 0 /* ----------- */ log_base : procedure expose (globals) base = ARG(1) ; value = ARG(2) return Log(value) / Log(base) |
/* ------------------------------------------------------------------ */ /* REXX offers no matrix-handling BIF's. Below can be found a custom */ /* implementation that, perhaps unusually, represents matrices as str-*/ /* ings. Notes: */ /* */ /* * Since strings are immutable, matrix manipulations result in new */ /* strings being created; high performance, therefore, should not be*/ /* expected */ /* */ /* * Only a smattering of operations are offered, and some of them use*/ /* rather naive algorithms [e.g. multiplication - Winograd's algori-*/ /* thm could instead be used] */ /* */ /* * There is much code redundancy [e.g. 'madd' and 'msub' are identi-*/ /* save for the arithmetic operation performed]. This could have be-*/ /* en avoided via use of both the VALUE BIF and INTERPRET instructi-*/ /* on [an approach much used in Chapter 4], but it was felt that co-*/ /* de would be more readable, and perhaps more easily adapted if ke-*/ /* pt simple, despite the repetition. */ /* */ /* * Decision to model matrices as strings was based on two factors: */ /* */ /* - Avoiding global array use */ /* - Illustrate how ADT's may be modelled using strings, and showca-*/ /* se the REXX PARSE instruction and string manipulation BIF's */ /* */ /* Performance can be significantly improved without resorting to the */ /* use of global arrays by using an external library like T. J. McPhe-*/ /* e's, 'rxHash', that implements arrays as special strings that may */ /* be freely passed around. Chapter 4 makes extensive use of this very*/ /* versatile library. I hope to provide an expanded version of the */ /* present library using this technique as part of the REXXToolkit [to*/ /* be found in the Appendix] sometime in 2007. */ /* ------------------------------------------------------------------ */ /* Global Constants */ FALSE = 0 ; TRUE = 1 ; NULL = "" ; NEWLINE = "0A"X ; SPACE = ' ' NaN = "NaN" /* Matrix-specific global constants */ MTAG = "<M>" ; MHSEP = "|" ; MRAWSEP = "; " ; MRSEP = ";" MTYPE_REGULAR = "R" ; MTYPE_SINGULAR = "S" ; MTYPE_ZERO = "Z" MTYPE_IDENTITY = "I" ; MTYPE_VECTOR = "V" /* -- */ /* Global Roots and 'expose' list */ globals = "sys. env. args. $. FALSE TRUE NULL NEWLINE SPACE NaN" /* Matrix-specific 'expose' list */ matdefs = "MTAG MHSEP MTYPE_REGULAR MTYPE_SINGULAR" , "MTYPE_ZERO MTYPE_IDENTITY MTYPE_VECTOR" , "MRSEP" , "MRAWSEP" /* ----------------------------- */ x = makeMatrix("3 2 3;5 9 8;") ; y = makeMatrix("4 7;9 3;8 1;") z = mmul(x, y) say "z =" ; call mdump z /* ----------------------------- */ say "z determinant:" mdet(z) say "z inverse =" ; call mdump minverse(z), 8 say "trace: " mtrace(z) say "z transpose =" ; call mdump mtranspose(z) exit 0 /* ----------------------------- */ /* * *** IMPORTANT *** Matrix rows and columns numbered from 1, and *not* 0 like so many zero-index-based languages * Variable size, delimited strings represent the matrix type. Each such string has a header section followed by a data section; typically, the string is split, metadata extracted from the header, and the data section returned for subsequent processing * Easy to view matrix contents: just SAY the string. The 'mdump' routine is available for pretty printing * Simple error-handling approach used: a value of, 'NaN', is returned where any error is detected [applies only to routines that do error checking - 'stupid' usage merely sees the script crash] * Matrix Format [EBNF]: <matrix> ::= <header> <data> <header> ::= <type-tag> <rows> <columns> <matrix-type> <EOH> <data> ::= <row>+ <type-tag> ::= '<M>' <rows> ::= <integer> <colums> ::= <integer> <matrix-type> ::= 'S' | 'R' | 'V' | 'Z' | 'I' <EOH> ::= '|' <row> ::= <decimal>+ <EOR> <EOR> ::= ';' <integer> ::= digit+ <decimal> ::= <integer> | digit+ '.' digit+ <digit> ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' * Matrix Format Examples: - 1-row matrices considered vectors 1x1 -> "<M>1 1 V|7;" 1x3 -> "<M>1 3 V|7 8 9;" - Square Matrices; regular, zero, or identity 2x2 Regular -> "<M>2 2 R|1 2;4 5;" 3x3 Regular -> "<M>3 3 R|1 2 3;4 5 6;7 8 9;" 3x3 Zero -> "<M>3 3 Z|0 0 0;0 0 0;0 0 0;" 3x3 Identity -> "<M>3 3 I|1 0 0;0 1 0;0 0 1;" - Singular Matrices 2x3 -> "<M>2 3 S|1 2 3;4 5 6;" 3x2 -> "<M>3 2 S|1 2;3 4;5 6;" * Matrix string contains both metadata and uses a delimiter to mark out rows. Using only one of these items would have allowed determination of the other [i.e. compute metadata by counting delimiters, or tokenise into rows using metadata], but using both allowed for easy type-checking and simplified tokenisation via the PARSE instruction * Routines classed as follows: - Constructors [makeVector, makeMatrix, makeDiagonal] - Type Checkers [isVector, isMatrix, is1x1, is2x2] - Metadata [mrows, mcols] - Comparators [meql] - Selectors [extractMatrix, mrow, mcol, msubset, mminor] - Matrix Arithmetic [madd, msub, mmul, mdiv] - Matrix OPerations [mtranspose, mcofactor, mdet1x1, mdet2x2, mdet, minv1x1, minverse, mtrace] - Elementary Row / Column Operations [mswapc, mswapr, maddc, maddr, mmulc, mmulr]. These are needed for solving linear equations via Echelon method - Pretty Print [mdump] * Routine documentation has the following structure: Parameter List --- Description --- Routine Example(s) Parameter list conventions include: - x | y | z -> One of x or y or z - [optional arguments ...] - Types: + s, s1, s2 -> string(s) + n, n1, n2 -> numeric + v, v1, v2 -> vector(s) + m, m1, m2 -> matrices */ /* ----------- */ makeVector : procedure expose (globals) (matdefs) /* s | n1 [, n2, ...] --- Returns a vector created by parsing, 's', or assembling, 'n1', 'n2' ... --- v = makeVector("1 2 3;") v = makeVector(1, 2, 3) */ argc = ARG() ; if argc == 0 then ; return NaN if argc == 1 then do v = ARG(1) ; argc = WORDS(v) end ; else do v = NULL ; do i = 1 for argc ; v = v ARG(i) ; end ; v = STRIP(v) end return MTAG || 1 argc MTYPE_VECTOR || MHSEP || v || MRSEP makeMatrix : procedure expose (globals) (matdefs) /* s | v1 [, v2, ...] --- Returns a matrix created by parsing, 's', or assembling, 'v1', 'v2' ... --- m = makeMatrix("1 2 3;4 5 6;7 8 9;") m = makeMatrix(makeVector(1, 2, 3)) m = makeMatrix(makeVector(1, 2, 3), makeVector(4, 5, 6),, makeVector(7, 8, 9)) */ argc = ARG() ; if argc == 0 then ; return NaN if argc == 1 then do m = ARG(1) ; if isVector(m) then ; return m rows = COUNTSTR(MRSEP, m) cols = WORDS(SUBSTR(m, 1, POS(MRSEP, m) - 1)) rv = NULL ; do i = 1 for rows parse var m row (MRSEP) m ; rv = rv || row || MRSEP end end ; else do rows = argc ; rv = NULL ; do i = 1 for rows parse value ARG(i) with (MTAG) . cols . (MHSEP) data rv = rv || data end end select when cols == rows then ; type = MTYPE_REGULAR otherwise ; type = MTYPE_SINGULAR end return MTAG || rows cols type || MHSEP || STRIP(rv) makeDiagonal : procedure expose (globals) (matdefs) /* s | v | n1 [, n2, ...] --- Returns a square matrix with a leading diagonal having the values obtained by parsing, 's', assembling, 'v1', 'v2', or from, 'v' --- m = makeDiagonal("1 2 3;") m = makeDiagonal(1, 2, 3) m = makeDiagonal(makeVector(1, 2, 3)) */ argc = ARG() ; if argc == 0 then ; return NaN ONE_ONLY = TRUE ; chksum = 0 if argc == 1 then do v = ARG(1) ; if isVector(v) then do parse var v (MTAG) . cols . (MHSEP) data end ; else do cols = WORDS(SUBSTR(v, 1, POS(MRSEP, v) - 1)) ; data = v end parse var data row (MRSEP) . rows = cols ; rv = NULL ; do i = 1 for rows do j = 1 for cols if i == j then do parse var row item row chksum = chksum + item ; rv = rv item if item > 1 then ; ONE_ONLY = FALSE end ; else ; rv = rv 0 end rv = rv || MRSEP end end ; else do cols = argc ; rows = cols ; rv = NULL do i = 1 for rows do j = 1 for cols if i == j then do value = ARG(i) ; chksum = chksum + value ; rv = rv value if value > 1 then ; ONE_ONLY = FALSE end ; else ; rv = rv 0 end rv = rv || MRSEP end end select when chksum == 0 then ; type = MTYPE_ZERO when chksum == rows & ONE_ONLY then ; type = MTYPE_IDENTITY otherwise ; type = MTYPE_REGULAR end return MTAG || rows cols type || MHSEP ||, STRIP(CHANGESTR(MRAWSEP, rv, MRSEP)) /* -- */ isMatrix : procedure expose (globals) (matdefs) /* m --- TRUE if 'm' determined to be a matrix --- if \isMatrix(m) then ; return NaN */ parse value WORD(ARG(1), 1) with marker +3 rows . return marker == MTAG & rows >= 1 isVector : procedure expose (globals) (matdefs) /* m --- TRUE if 'm' determined to be a vector, a 1-row matrix. Note that a vector is still a matrix, merely a more specialised one --- if \isVector(v) then ; return NaN */ parse value WORD(ARG(1), 1) with marker +3 rows . return marker == MTAG & rows == 1 is2x2 : procedure expose (globals) (matdefs) /* m --- TRUE if 'm' determined to be a 2x2 matrix. Required in recursive matrix operations like determinant, cofactor and inverse --- if is2x2(m) then ; return mdet2x2(m) */ parse value ARG(1) with (MTAG) rows cols . (MHSEP) . return rows == cols & rows == 2 is1x1 : procedure expose (globals) (matdefs) /* m --- TRUE if 'm' determined to be a 1x1 matrix, a single-element, square matrix. Required in recursive matrix operations like determinant, cofactor and inverse --- if is1x1(m) then ; return mdet1x1(m) */ parse value ARG(1) with (MTAG) rows cols . (MHSEP) . return rows == cols & rows == 1 /* ----------- */ mrows : procedure expose (globals) (matdefs) /* m --- Returns number of rows matrix, 'm', possesses --- rows = mrows(m) */ parse value ARG(1) with (MTAG) rows . . (MHSEP) . ; return rows mcols : procedure expose (globals) (matdefs) /* m --- Returns number of columns matrix, 'm', possesses --- columns = mcols(m) */ parse value ARG(1) with (MTAG) . cols . (MHSEP) . ; return cols /* -- */ meql : procedure expose (globals) (matdefs) /* m1, m2 --- TRUE if 'm1' and 'm2' determined to be equal, that is: * Structurally identical i.e. same number of rows and columns * Same type * Same contents --- if meql(m1, m2) then ; return ... */ return ARG(1) == ARG(2) /* -- */ extractMatrix : procedure expose (globals) (matdefs) /* m --- Returns matrix data sans header --- data = extractMatrix(m) */ parse value ARG(1) with (MTAG) . . . (MHSEP) data ; return data mrow : procedure expose (globals) (matdefs) /* m, row --- Extracts specified row number, 'row', from matrix, 'm' --- row = mrow(m, 2) */ parse value ARG(1) with (MTAG) rows . . (MHSEP) data ; r = ARG(2) if r < 1 | r > rows then ; return NaN do i = 1 while data <> NULL parse var data row (MRSEP) data ; if i == r then ; leave end ; return row mcol : procedure expose (globals) (matdefs) /* m, col --- Extracts specified column number, 'col', from matrix, 'm' --- column = mcol(m, 2) */ parse value ARG(1) with (MTAG) . cols . (MHSEP) data ; c = ARG(2) if c < 1 | c > cols then ; return NaN col = NULL ; do while data <> NULL parse var data row (MRSEP) data ; col = col WORD(row, c) end ; return STRIP(col) msubset : procedure expose (globals) (matdefs) /* m, row, col [[, xlen], ylen] --- Returns a matrix extracted from matrix, 'm', data starting from row number, 'row', and column number, 'col'. Entire length of specified items is returned unless an optional length value is specified for each item --- m2 = msubset(m1, 2, 3) m2 = msubset(m1, 2, 3, 5, 5) m2 = msubset(m1, 2, 3, , 5) m2 = msubset(m1, 2, 3, 5) */ argc = ARG() ; rv = NaN if argc <> 3 | argc <> 5 then ; return rv x = ARG(2) ; y = ARG(3) parse value ARG(1) with (MTAG) rows cols . (MHSEP) data if x > rows | y > cols then ; return rv xlen = rows ; if ARG(4, 'E') then ; xlen = ARG(4) ylen = cols ; if ARG(5, 'E') then ; ylen = ARG(5) /* ... to be completed ... */ return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) mminor : procedure expose (globals) (matdefs) /* m, row, col --- Returns a matrix extracted from matrix, 'm', data consisting of all rows and columns except the specified row number, 'row', and column number, 'col'. Such a matrix is known as the 'minor' and is needed for computing a matrix's determinant --- minor = mminor(m, 1, 3) */ argc = ARG() ; rv = NaN if argc <> 3 then ; return rv x = ARG(2) ; y = ARG(3) parse value ARG(1) with (MTAG) rows cols . (MHSEP) data if x > rows | y > cols then ; return rv rv = NULL ; do i = 1 while data <> NULL parse var data row (MRSEP) data if i == x then ; iterate do j = 1 while row <> NULL parse var row item row if j == y then ; iterate rv = rv item end ; rv = rv || MRSEP end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) /* -- */ mdump : procedure expose (globals) (matdefs) /* m [, width] --- Pretty prints matrix, 'm'; default width used unless specified --- call mdump m call mdump m, 8 */ parse value ARG(1) with (MTAG) . . . (MHSEP) data cellwidth = 4 ; if ARG(2, 'E') then ; cellwidth = ARG(2) do while data <> NULL parse var data row (MRSEP) data out = "|" ; do while row <> NULL parse var row item row ; out = out LEFT(item, cellwidth) "|" end say out end ; return /* -- */ madd : procedure expose (globals) (matdefs) /* m1, m2 | n --- Returns matrix where: * 'n' added to each element, or * corresponding elements of matrices added together [each matrix must have the same size i.e. m1:RxC == m2:RxC] --- m3 = madd(m1, m2) m3 = madd(m1, 5) */ m1 = ARG(1) ; m2 = ARG(2) ; rv = NaN if \isMatrix(m1) then ; return rv parse var m1 (MTAG) m1rows m1cols . (MHSEP) m1data if isMatrix(m2) then do parse var m2 (MTAG) m2rows m2cols . (MHSEP) m2data if m1rows <> m2rows | m1cols <> m2cols then ; return rv rv = NULL ; do while m1data <> NULL parse var m1data m1row (MRSEP) m1data parse var m2data m2row (MRSEP) m2data do while m1row <> NULL parse var m1row m1item m1row ; parse var m2row m2item m2row rv = rv (m1item + m2item) end ; rv = rv || MRSEP end end ; else do rv = NULL ; do while m1data <> NULL parse var m1data m1row (MRSEP) m1data do while m1row <> NULL parse var m1row m1item m1row ; rv = rv (m1item + m2) end ; rv = rv || MRSEP end end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) msub : procedure expose (globals) (matdefs) /* m1, m2 | n --- Returns matrix where: * 'n' subtracted from to each element, or * corresponding elements of matrices subtracted [each matrix must have the same size i.e. m1:RxC == m2:RxC] --- m3 = msub(m1, m2) m3 = msub(m1, 5) */ m1 = ARG(1) ; m2 = ARG(2) ; rv = NaN if \isMatrix(m1) then ; return rv parse var m1 (MTAG) m1rows m1cols . (MHSEP) m1data if isMatrix(m2) then do parse var m2 (MTAG) m2rows m2cols . (MHSEP) m2data if m1rows <> m2rows | m1cols <> m2cols then ; return rv rv = NULL ; do while m1data <> NULL parse var m1data m1row (MRSEP) m1data parse var m2data m2row (MRSEP) m2data do while m1row <> NULL parse var m1row m1item m1row ; parse var m2row m2item m2row rv = rv (m1item - m2item) end ; rv = rv || MRSEP end end ; else do rv = NULL ; do while m1data <> NULL parse var m1data m1row (MRSEP) m1data do while m1row <> NULL parse var m1row m1item m1row ; rv = rv (m1item - m2) end ; rv = rv || MRSEP end end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) mmul : procedure expose (globals) (matdefs) /* m1, m2 | n --- Returns matrix where: * 'n' multiplied with each element, or * corresponding elements of matrices multiplied [matrices must meet condition m1:C == m2:R; m3 -> m1:Rxm2:C] --- m3 = mmul(m1, m2) m3 = mmul(m1, 5) */ m1 = ARG(1) ; m2 = ARG(2) ; rv = NaN if \isMatrix(m1) then ; return rv parse var m1 (MTAG) m1rows m1cols . (MHSEP) m1data if isMatrix(m2) then do parse var m2 (MTAG) m2rows m2cols . (MHSEP) m2data if m1cols <> m2rows then ; return rv /* Extract matrix data, load into compound variables, 'a' and 'b' */ r = 1 ; c = 1 ; a.0 = m1rows ; a.0.0 = m1cols do while m1data <> NULL parse var m1data m1row (MRSEP) m1data do while m1row <> NULL parse var m1row item m1row ; a.r.c = item c = c + 1 end r = r + 1 ; c = 1 end r = 1 ; c = 1 ; b.0 = m2rows ; b.0.0 = m2cols do while m2data <> NULL parse var m2data m2row (MRSEP) m2data do while m2row <> NULL parse var m2row item m2row ; b.r.c = item c = c + 1 end r = r + 1 ; c = 1 end /* Perform multiplication using compound variables */ do i = 1 to a.0 /* m1rows */ do j = 1 to b.0.0 /* m2cols */ c.i.j = 0 ; do k = 1 to b.0 /* m2rows */ c.i.j = c.i.j + a.i.k * b.k.j end end end /* Return computed values as new matrix */ rv = NULL ; do i = 1 to m1rows do j = 1 to m2cols ; rv = rv c.i.j ; end rv = rv || MRSEP end end ; else do rv = NULL ; do while m1data <> NULL parse var m1data m1row (MRSEP) m1data do while m1row <> NULL parse var m1row m1item m1row ; rv = rv (m1item * m2) end ; rv = rv || MRSEP end end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) mdiv : procedure expose (globals) (matdefs) /* m1, m2 | n --- Returns matrix where: * 'n' divided into each element, or * corresponding elements of matrices divided [matrices must meet condition m1:C == m2:R, and m2 must be square; m3 -> m1:Rxm2:C] --- m3 = mdiv(m1, m2) m3 = mdiv(m1, 5) */ m1 = ARG(1) ; m2 = ARG(2) ; rv = NaN if \isMatrix(m1) then ; return rv parse var m1 (MTAG) m1rows m1cols . (MHSEP) m1data if isMatrix(m2) then do parse var m2 (MTAG) m2rows m2cols . (MHSEP) m2data if m1cols <> m2rows | m2cols <> m2rows then ; return rv return mmul(m1, minverse(m2)) end ; else do rv = NULL ; do while m1data <> NULL parse var m1data m1row (MRSEP) m1data do while m1row <> NULL parse var m1row m1item m1row ; rv = rv (m1item / m2) end ; rv = rv || MRSEP end end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) /* -- */ maddr : procedure expose (globals) (matdefs) /* m, n | v, row --- Returns matrix with all elements of row number, 'row', of matrix, 'm': * Having, 'n' added, or * corresponding elements from, 'v', added [assumes m:R == v:R] --- m2 = maddr(m1, 4, 3) m2 = maddr(m1, makeVector("1 2 3;"), 3) */ m = ARG(1) ; v = ARG(2) ; row = ARG(3) ; rv = NaN ; isVector = FALSE if \isMatrix(m) then ; return rv parse var m (MTAG) mrows mcols . (MHSEP) mdata if isVector(v) then do parse var v (MTAG) . vcols . (MHSEP) vrow (MRSEP) if row > mrows | mcols <> vcols then ; return rv isVector = TRUE end rv = NULL ; do i = 1 while mdata <> NULL parse var mdata mrow (MRSEP) mdata if i == row then do while mrow <> NULL parse var mrow mitem mrow if isVector then ; parse var vrow vitem vrow ; else ; vitem = v rv = rv (mitem + vitem) end else rv = rv || mrow rv = rv || MRSEP end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) maddc : procedure expose (globals) (matdefs) /* m, n | v, col --- Returns matrix with all elements of column number, 'col', of matrix, 'm': * Having, 'n' added, or * corresponding elements from, 'v', added [assumes m:C == v:C] --- m2 = maddc(m1, 4, 3) m2 = maddc(m1, makeVector("1 2 3;"), 3) */ m = ARG(1) ; v = ARG(2) ; col = ARG(3) ; rv = NaN ; isVector = FALSE if \isMatrix(m) then ; return rv parse var m (MTAG) mrows mcols . (MHSEP) mdata if isVector(v) then do parse var v (MTAG) . vcols . (MHSEP) vrow (MRSEP) if col > mcols | mrows <> vcols then ; return rv isVector = TRUE end rv = NULL ; do while mdata <> NULL parse var mdata mrow (MRSEP) mdata do j = 1 while mrow <> NULL parse var mrow mitem mrow if j == col then do if isVector then ; parse var vrow vitem vrow ; else ; vitem = v rv = rv (mitem + vitem) end ; else do rv = rv mitem end end rv = rv || MRSEP end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) mmulr : procedure expose (globals) (matdefs) /* m, n, row --- Returns matrix with all elements of row number, 'row', of matrix, 'm', multiplied by, 'n' --- m2 = mmulr(m1, 4, 3) */ m = ARG(1) ; n = ARG(2) ; row = ARG(3) ; rv = NaN if \isMatrix(m) then ; return rv parse var m (MTAG) mrows mcols . (MHSEP) mdata if row > mrows then ; return rv rv = NULL ; do i = 1 while mdata <> NULL parse var mdata mrow (MRSEP) mdata if i == row then do while mrow <> NULL parse var mrow mitem mrow ; rv = rv (mitem * n) end else rv = rv mrow rv = rv || MRSEP end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) mmulc : procedure expose (globals) (matdefs) /* m, n, col --- Returns matrix with all elements of column number, 'col', of matrix, 'm', multiplied by, 'n' --- m2 = mmulc(m1, 4, 3) */ m = ARG(1) ; n = ARG(2) ; col = ARG(3) ; rv = NaN if \isMatrix(m) then ; return rv parse var m (MTAG) mrows mcols . (MHSEP) mdata if col > mcols then ; return rv rv = NULL ; do while mdata <> NULL parse var mdata mrow (MRSEP) mdata do j = 1 while mrow <> NULL parse var mrow mitem mrow if j == col then ; rv = rv (mitem * n) else ; rv = rv mitem end rv = rv || MRSEP end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) mswapr : procedure expose (globals) (matdefs) /* m, x, y --- Returns matrix with row numbers, 'x', and 'y', of matrix, 'm', swapped --- m2 = mswapr(m1, 1, 3) */ m = ARG(1) ; x = ARG(2) ; y = ARG(3) ; rv = NaN if \isMatrix(m) then ; return rv parse var m (MTAG) rows . . (MHSEP) data if x > rows | y > rows then ; return rv xr = mrow(m, x) ; yr = mrow(m, y) rv = NULL ; do i = 1 while data <> NULL parse var data row (MRSEP) data if i == x then ; rv = rv yr else ; if i == y then ; rv = rv xr else ; rv = rv row rv = rv || MRSEP end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) mswapc : procedure expose (globals) (matdefs) /* m, x, y --- Returns matrix with column numbers, 'x', and 'y', of matrix, 'm', swapped --- m2 = mswapc(m1, 1, 3) */ m = ARG(1) ; x = ARG(2) ; y = ARG(3) ; rv = NaN if \isMatrix(m) then ; return rv parse var m (MTAG) rows cols . (MHSEP) data if x > cols | y > cols then ; return rv r = 1 ; c = 1 ; a.0 = rows ; a.0.0 = cols do while data <> NULL parse var data row (MRSEP) data do while row <> NULL parse var row item row ; a.r.c = item c = c + 1 end r = r + 1 ; c = 1 end do i = 1 to a.0 tmp = a.i.x ; a.i.x = a.i.y ; a.i.y = tmp end rv = NULL ; do i = 1 to a.0 do j = 1 to a.0.0 ; rv = rv a.i.j ; end rv = rv || MRSEP end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) /* -- */ mtranspose : procedure expose (globals) (matdefs) /* m --- Returns matrix consisting of the transpose of 'm' [i.e. corresponding row / column positions swapped] --- transpose = mtranspose(m) */ m = ARG(1) ; rv = NaN if \isMatrix(m) then ; return rv parse var m (MTAG) rows cols . (MHSEP) data r = 1 ; c = 1 ; a.0 = rows ; a.0.0 = cols do while data <> NULL parse var data row (MRSEP) data do while row <> NULL parse var row item row ; a.r.c = item c = c + 1 end r = r + 1 ; c = 1 end rv = NULL ; do j = 1 to a.0.0 do i = 1 to a.0 ; rv = rv a.i.j ; end rv = rv || MRSEP end return makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP))) mcofactor : procedure expose (globals) (matdefs) /* m, i, j --- Returns the cofactor of the matrix; sign determined via values of row and column numbers, 'i', and 'j', respectively --- cofactor = mcofactor(m, i, j) */ m = ARG(1) ; i = ARG(2) ; j = ARG(3) if ((i + j) // 2) <> 0 then ; sign = -1 ; else ; sign = 1 if is1x1(m) then ; return sign * mdet(m) return sign * mdet(mminor(m, i, j)) mdet1x1 : procedure expose (globals) (matdefs) /* m --- Returns the determinant of a 1x1 square matrix --- determinant = mdet1x1(m) */ parse value ARG(1) with (MTAG) . . . (MHSEP) a (MRSEP) . return a mdet2x2 : procedure expose (globals) (matdefs) /* m --- Returns the determinant of a 2x2 square matrix --- determinant = mdet2x2(m) */ parse value ARG(1) with (MTAG) . . . (MHSEP) a b (MRSEP) c d (MRSEP) . return a * d - b * c mdet : procedure expose (globals) (matdefs) /* m --- Returns the determinant of the square matrix --- determinant = mdet(m) */ m = ARG(1) if is1x1(m) then ; return mdet1x1(m) if is2x2(m) then ; return mdet2x2(m) parse var m (MTAG) . cols . (MHSEP) row (MRSEP) . det = 0 ; do j = 1 to cols det = det + WORD(row, j) * mcofactor(m, 1, j) end ; return det minv1x1 : procedure expose (globals) (matdefs) /* m --- Returns the inverse of the 1x1 matrix --- inverse = minv1x1(m) */ parse value ARG(1) with (MTAG) . . . (MHSEP) a (MRSEP) . return 1 / a minverse : procedure expose (globals) (matdefs) /* m --- Returns the inverse of the square matrix --- inverse = minverse(m) */ m = ARG(1) ; if \isMatrix(m) then ; return NaN parse var m (MTAG) rows cols . (MHSEP) data if rows <> cols then ; return NaN if is1x1(m) then ; return makeVector(minv1x1(m)) rv = NULL ; det = mdet(m) ; do i = 1 for rows do j = 1 for cols ; rv = rv (mcofactor(m, i, j) / det) ; end rv = rv || MRSEP end return mtranspose(makeMatrix(STRIP(CHANGESTR(MRAWSEP, rv, MRSEP)))) mtrace : procedure expose (globals) (matdefs) /* m --- Returns the trace of the square matrix [i.e. sum of the leading diagonal elements] --- trace = mtrace(m) */ m = ARG(1) ; trace = 0 if \isMatrix(m) then ; return NaN parse var m (MTAG) rows cols . (MHSEP) data if rows <> cols then ; return NaN do i = 1 while data <> NULL parse var data row (MRSEP) data do j = 1 while row <> NULL parse var row item row ; if i == j then ; trace = trace + item end end return trace |
/* ------------------------------------------------------------------ */ /* REXX offers no complex number-handling BIF's. However, there are */ /* native-REXX implementations available from: */ /* */ /* http://www.geocities.com/zabrodskyvlada/aat/a_contents.html */ /* */ /* just as there are implementations of many other classic algorithms.*/ /* */ /* The code below, however, is not adapted from the examples at this */ /* site, but is instead inspired by a Scheme implementation in the */ /* very well known publication, 'Structure and Interpretation of Prog-*/ /* rams' by Abelson and Sussman. See: */ /* */ /* http://mitpress.mit.edu/sicp/full-text/sicp/book/node43.html */ /* ------------------------------------------------------------------ */ /* Using 'rexxMath' Library Routines */ /* Load [rexxMath] math functions from external library */ call rxFuncAdd 'mathLoadFuncs', 'rexxMath', 'mathLoadFuncs' call mathLoadFuncs /* ----------- */ a = makeComplex(3, 5) ; b = makeComplex(2, -2) c = cmul(a, b) say "c =" asComplex(c) /* ----------- */ c = cmul(makeComplex(3, 5), makeComplex(2, -2)) say "c =" asComplex(c) /* ----------- */ d = makeComplex(3, 4) say "d =" asComplex(d) say "sqrt(d) =" asComplex(csqrt(d)) /* ----------- */ say "Rectangualar Notation:" asComplex(csqrt(makeComplex(3, 4))) say "Polar Notation:" asPolar(csqrt(makeComplex(3, 4))) /* ----------- */ /* Unload math functions */ call mathDropFuncs exit 0 /* ----------------------------- */ makeComplex : procedure return "<C> " ARG(1) " " ARG(2) makeFromPolar : procedure r = ARG(1) ; a = ARG(2) return makeComplex(r * Cos(a), r * Sin(a)) real : procedure parse value ARG(1) with "<C>" real . ; return real imag : procedure parse value ARG(1) with "<C>" . imag . ; return imag magnitude : procedure parse value ARG(1) with "<C>" real imag . return Sqrt(real * real + imag * imag) angle : procedure parse value ARG(1) with "<C>" real imag . return ATan(imag, real) isNaN : procedure return ARG(1) == "NaN" isComplex : procedure return LEFT(ARG(1), 3) == "<C>" asComplex : procedure z = ARG(1) ; if \isComplex(z) then ; return "NaN" else ; do parse var z "<C>" real imag . dec = 3 ; if ARG(2, E) then ; dec = ARG(2) sign = "+" ; if imag < 0 then ; sign = "-" return FORMAT(real,, dec) sign FORMAT(ABS(imag),, dec) || "i" end asPolar : procedure z = ARG(1) ; if \isComplex(z) then ; return "NaN" else ; do parse var z "<C>" real imag . dec = 3 ; if ARG(2, E) then ; dec = ARG(2) return "(" || FORMAT(magnitude(z),, dec) || ",", FORMAT(angle(z),, dec) || ")" end /* ----------- */ cadd : procedure z1 = ARG(1) ; z2 = ARG(2) if \isComplex(z1) | \isComplex(z1) then ; return "NaN" rz1 = real(z1) ; rz2 = real(z2); iz1 = imag(z1) ; iz2 = imag(z2) return makeComplex((rz1 + rz2), (iz1 + iz2)) csub : procedure z1 = ARG(1) ; z2 = ARG(2) if \isComplex(z1) | \isComplex(z1) then ; return "NaN" rz1 = real(z1) ; rz2 = real(z2); iz1 = imag(z1) ; iz2 = imag(z2) return makeComplex((rz1 - rz2), (iz1 - iz2)) cmul : procedure z1 = ARG(1) ; z2 = ARG(2) if \isComplex(z1) | \isComplex(z1) then ; return "NaN" mz1 = magnitude(z1) ; mz2 = magnitude(z2) ; az1 = angle(z1) az2 = angle(z2) return makeComplex((mz1 * mz2), (az1 + az2)) cdiv : procedure z1 = ARG(1) ; z2 = ARG(2) if \isComplex(z1) | \isComplex(z1) then ; return "NaN" mz1 = magnitude(z1) ; mz2 = magnitude(z2) ; az1 = angle(z1) az2 = angle(z2) return makeComplex((mz1 / mz2), (az1 - az2)) csqrt : procedure z = ARG(1) ; if \isComplex(z) then ; return "NaN" r = magnitude(z) ; a = angle(z) u = makeComplex(Sqrt(r) * Cos(a / 2.0), Sqrt(r) * Sin(a / 2.0)) t = makeComplex(-real(u), -imag(u)) if \(angle(u) < angle(t)) then ; u = t return u |
/* ------------------------------------------------------------------ */ /* Whilst binary, hexadecimal, decimal interconversion is quite well */ /* supported in REXX, octal support is non-existent. This is because */ /* of REXX's mainframe heritage: octal is simply not used on these */ /* platforms. */ /* */ /* It is, however, quite easy to implement suitable custom functions */ /* as has been done here. */ /* ------------------------------------------------------------------ */ hexadecimal = "2A" ; octal = "10" number = X2D(hexadecimal) number = O2D(octal) hexadecimal = D2X(number) octal = D2O(number) /* ----------------------------- */ /* Assumes following input formats: decimal - plain digits octal - leading '0' character hexadecimal - leading '0x' | '0X' character sequence e.g. 14 -> 016 -> 0xE */ call CHAROUT , "Gimme a number in decimal, octal, or hex: " parse value LINEIN() with "0x" hex =1 "0" oct =1 dec select when hex \= NULL then ; number = X2D(hex) when oct \= NULL then ; number = O2D(oct) when dec \= NULL then ; number = dec end say number "d" D2X(number) "h" D2O(number) "o" exit 0 /* ----------- */ D2O : procedure expose (globals) parse arg d, o do until d = 0 ; r = d // 8 ; d = d % 8 ; o = r || o ; end return o O2D : procedure expose (globals) parse value ARG(1) LENGTH(ARG(1)) 0 with ov sp dv do i = 1 for sp parse var ov =(i) oi +1 if oi == "8" | oi == "9" then ; return NULL parse value (dv + ((8 ** (sp - i)) * oi)) with dv end return dv |
/* ------------------------------------------------------------------ */ /* REXX-idiomatic approach to this task is via 'do' loop and string */ /* manipulation BIF since it is cross-platform and guarantees the best*/ /* performance. However, a recursive solution is easily implementable */ /* ------------------------------------------------------------------ */ /* REXX-idiomatic 'do' loop and BIF Example */ commified = commify("12345678") ; say commified exit 0 /* ----------- */ commify : procedure expose (globals) s = ARG(1) ; l = LENGTH(s) - 3 do i = l by -3 while i > 0 ; s = INSERT(",", s, i) ; end return s /* ----------------------------- */ /* Recursive Implementation */ commified = commify("12345678") ; say commified exit 0 /* ----------- */ commify : procedure expose (globals) return STRIP(commify_(REVERSE(ARG(1))), 'T', ",") commify_ : procedure expose (globals) parse value ARG(1) with car +3 cdr if car == NULL then ; return NULL return commify_(cdr) || REVERSE(car) || "," |
/* ------------------------------------------------------------------ */ /* REXX-idiomatic approach to this task is via 'do' loop and the PARSE*/ /* instruction. */ /* ------------------------------------------------------------------ */ duration = 1 say "It took" duration pluralise(duration, "hour") say duration pluralise(duration, "hour"), pluralise(duration, "", "is", "are"), "enough" duration = 5 say "It took" duration pluralise(duration, "hour") say duration pluralise(duration, "hour"), pluralise(duration, "", "is", "are"), "enough" exit 0 /* ----------- */ pluralise : procedure value = ARG(1) ; root = ARG(2) singular = "" ; if ARG(3, 'E') then ; singular = ARG(3) plural = "s" ; if ARG(4, 'E') then ; plural = ARG(4) if value == 1 then ; return root || singular return root || plural /* ----------------------------- */ list = "mess index leaf puppy" do while list <> "" parse var list word list say LEFT(word, 6) "->" plural(word) end exit 0 /* ----------- */ plural : procedure endings = "ss:sses ph:phes sh:shes ch:ches ey:eys ix:ices", "ff:ffs z:zes f:ves y:ies s:ses x:xes" singular = ARG(1) ; plural = singular ; do while endings <> NULL parse var endings key ":" value endings /* === Both approaches below work. First one makes exclusive use of string manipulation BIF's, while the second one uses the PARSE instruction to split a string, and is probably faster /* 1 */ if RIGHT(singular, LENGTH(key)) == key then do plural = LEFT(singular, LENGTH(singular) - LENGTH(key)) || value leave end /* 2 */ pos = LENGTH(singular) - LENGTH(key) parse var singular car +(pos) cdr if cdr == key then do ; plural = car || value ; leave ; end === */ pos = LENGTH(singular) - LENGTH(key) parse var singular car +(pos) cdr if cdr == key then do ; plural = car || value ; leave ; end end return plural |