The Efficient Array Management subroutines performs operations over all Vector elements via a single long command line, so they don't use slow FOR loops. The Arrays are defined and manipulated in an easy way that don't impose complicated constraints, so the diverse subroutines are simple to understand and use.
- Creation of Arrays
The simplest way to create Vectors and Matrices is directly writting they in SET commands. For example:
Please be aware that the separation of elements in a N-Tuple must be done precisely by one space in order for the manipulation subroutines to work properly. Note that mathematical subroutines does not check that a Vector or Matrix be well formed, so if the operands for these subroutines were not created correctly, the program just will fail.Code: Select all
set "NumericVector=1 1 2 3 5 8" set "NamesVector=John Paul George Ringo" set "Matrix1=10 20 30" set "Matrix2=110 120 130" set "Matrix3=501 502 503" set "Matrix4=700 800 900"
The generation of Vectors with constants or incrementing indices is straigthforward; it is shown here just for reference:
In all management subroutines a vector/matrix parameter is written as the name of a variable or as a vector constant enclosed in quotes; in most subroutines the second vector/matrix can also be a single (scalar) number enclosed in quotes.Code: Select all
set "zeros=" & (for /L %%i in (1,1,%n%) do set "zeros=!zeros! 0") & set "zeros=!zeros:~1!" set "index=" & (for /L %%i in (1,1,%m%) do set "index=!index! %%i") & set "index=!index:~1!" rem Previous vector can also be created in this simpler way: call :indexGen index=%m% for /F "delims==" %%v in ('set identity 2^>nul') do set "%%v=" for /L %%i in (1,1,4) do ( for /L %%j in (1,1,4) do ( set /A "n=^!(%%i-%%j)" set "identity%%i=!identity%%i! !n!" ) set "identity%%i=!identity%%i:~1!" )
The subroutines have not a setlocal command in order to make they faster; all internal subroutine variables are single-letter ones, so if you avoid the use of one letter variable names, your variables and subroutine variables will not conflict.
. - Standard Operations on Vectors
The :vectorOp subroutine performs a series of operations over one or two vectors.
The oper can be any SET /A two-operands operator: * / % + - << >> & ^ |, but you must write the percent (modulo) operator 4 times; enclose poison characters in quotes as usual. Additionally, you can use Max operator for the Greater of the two operands and Min for the Lesser one. You can also use indexOf operator that returns the position of the elements of second operand into the first vector, or 0 if not exists. For example:Code: Select all
call :vectorOp result=vector1 oper [vector2 | "number"]
If the second operand is not given, the one-operand operator is applied to each vector element: ! ~ -:Code: Select all
call :vectorOp resul="2 3 4 5" + "7 8 9 10" echo resul = %resul% resul = 9 11 13 15
Code: Select all
call :vectorOp resul="7 -8 9 -10" - echo resul = %resul% resul = -7 8 -9 10
. - Special Operations
Bracket Indexing.
If the operator is [] (called Bracket Indexing) the elements are selected via the indices vector placed in the second operand:
Note that index elements must be sorted in ascending order.Code: Select all
call :vectorOp result="22 93 5 10 3" [] "1 4 5" echo %result% 22 10 3
Reduction and Scan.
If the second operand is "//" (called Reduction, quotes are mandatory!), then the operator is applied to all elements of the vector. For example, to add up a vector of numbers:
The "\\" (called Scan) is similar except that it works cumulatively on the data, and gives all the intermediate results:Code: Select all
call :vectorOp result="22 93 5 10 3" + "//" echo %result% 133
Compress and Expand.Code: Select all
call :vectorOp result="22 93 5 10 3" + "\\" echo %result% 22 115 120 130 133
These Special Operations can also be placed in the operator's position. In this case the // is called Compress and allows to select some elements from the vector according to the "zero or one" (Boolean) values given in the second operand:
Conversely, \\ (called Expand) will insert fill data into vectors. Elements with zero are inserted at the positions indicated by the 0's:Code: Select all
call :vectorOp result="22 93 5 10 3" // "1 0 1 0 1" echo %result% 22 5 3
Outer and Inner Products (dot operator).Code: Select all
call :vectorOp result="10 20 30" \\ "1 0 1 1 0" echo %result% 10 0 20 30 0
If the operator is the grad-dot-oper combination (called Outer Product, like in °.+ with plus oper as example), then the operator is applied to all combinations of elements in the two vectors. The result is a two-dimensional matrix with the number of rows (first dimension) of the first operand and the number of columns (second dimension) of the second operand. For example:
The Inner Product allows two operators to be applied to the elements, like in +.*. In this case both operands must be two-dimensional arrays and the number of columns in the first matrix must be equal to the number of rows in the second matrix. First each row of the left operand is applied to each column of the right operand using the rightmost operator of the inner product, then the leftmost operator is applied to the intermediate results, like in a Reduction (//) operation.Code: Select all
call :vectorOp result="2 4 6" °.+ "10 20 30 40" set result result1=12 22 32 42 result2=14 24 34 44 result3=16 26 36 46 for /F "tokens=1* delims==" %%a in ('set result') do echo %%b 12 22 32 42 14 24 34 44 16 26 36 46
In this way, the +.* inner product performs the same task of the standard matrix multiplication, but you can use anyone of the SET /A two-operands operators at each side of the dot, including the max and min additional operators. Enclose poison characters in quotes, as usual. For example, min.max inner product first get the Max value of the couples of elements matching left-rows with right-columns. After that, it gets the Min value of all previous intermediate values and place it at the corresponding crossing coordinates of the result matrix.
Note that the Inner Product is an operation over matrices, not vectors, so it can not be used in :vectorOp subroutine, but in the :matrixOp one described next.
Neither the Inner nor Outer Product operations are yet implemented in this first version of this application. The code is here:
Code: Select all
@echo off
setlocal EnableDelayedExpansion
rem Efficient Array Management Operations in Batch files
rem Antonio Perez Ayala - 2021/Sep v.1
rem Efficient Array Management subroutines are placed below the equal-signs line
rem You must extract such a subroutines and include they in your own program
rem
rem The code below are simple examples of the use of those subroutines
rem and a session for the interactive execution of lines of code
for /F "delims==" %%v in ('set a[ 2^>nul') do set "%%v="
cls
echo/
echo Efficient Array Management Operations in Batch files
echo/
:exam
set "letter=A B C D E F G H I J K L M N O P Q R S T U V W X Y Z"
echo letter = %letter%
echo/
echo call :vectorOp vowel=letter [] "1 5 9 15 21"
call :vectorOp vowel=letter [] "1 5 9 15 21"
echo vowel = %vowel%
echo/
echo call :vectorOp resul=letter indexOf vowel
call :vectorOp resul=letter indexOf vowel
echo resul = %resul%
echo/
echo -------------------------------------------
echo/
echo call :vectorOp resul="2 3 4 5" + "7 8 9 10"
call :vectorOp resul="2 3 4 5" + "7 8 9 10"
echo resul = %resul%
echo/
echo call :vectorOp resul="7 8 9 10" + "23"
call :vectorOp resul="7 8 9 10" + "23"
echo resul = %resul%
echo/
echo call :vectorOp resul="20 3 40 5" Max "7 8 9 10"
call :vectorOp resul="20 3 40 5" Max "7 8 9 10"
echo resul = %resul%
echo/
echo call :vectorOp resul="7 -8 9 -10" -
call :vectorOp resul="7 -8 9 -10" -
echo resul = %resul%
echo/
echo Enter command lines for interactive execution of these subroutines
echo Use delayed expansion to show ^^^!variable^^^! values
echo Enter HELP for help, EXAM to re-show examples or just press Enter to end
:nextCommand
echo/
echo Ready...
set "command="
set /P "command="
if not defined command goto :EOF
if /I "!command!" equ "EXAM" goto exam
if /I "!command!" equ "HELP" goto help
%command%
goto nextCommand
:help
echo/
echo Define Vectors as a list of elements separated by *one* space:
echo set "NumericVector=1 1 2 3 5 8"
echo set "NamesVector=John Paul George Ringo"
echo call :indexGen index=4 %%= Same as: set "index=1 2 3 4" =%%
echo/
echo :vectorOp subroutine performs operations over one or two vectors:
echo call :vectorOp result=vector1 oper [vector2 ^| "number"]
echo/
echo ^<oper^> can be anyone of: * / %% + - ^<^< ^>^> ^& ^^ ^| write %% 4 times, or:
echo Max - Get the Greater of two operands
echo Min - Get the Lesser of two operands
echo indexOf - Get the indices of elements of vector2 inside vector1
echo [] - (Bracket Indexing): Get elements selected by indices in vector2
echo // - (Compress): Get elements selected by (0,1) values in vector2
echo \\ - (Expand): Insert fill data in positions indicated by 0 in vector2
echo/
echo If "//" is placed (with quotes) *in place of vector2* (Reduction),
echo then the oper is applied to all elements in the vector:
echo call :vectorOp result="1 2 3 4 5 6" * "//" %%= Factorial of 6 =%%
echo/
echo If "\\" is used instead (Scan), get all intermediate reduction results:
echo call :vectorOp result="1 2 3 4 5 6" * "\\" %%= All factorials of 1..6 =%%
goto nextCommand
=============================================================================
These are the Efficient Array Management subroutines
Copy this section to your own program
Antonio Perez Ayala
2021/Sep - version 1
:indexGen result=n
set "%1=" & (for /L %%i in (1,1,%~2) do set "%1=!%1! %%i") & set "%1=!%1:~1!"
exit /B
:vectorOp result=operand1 operator [operand2]
set "a=%2"
if %a:~0,1%%a:~-1% == "" (set "a=%~2") else set "a=!%~2!"
set "o=%~3" & set "r=" & set "s=" & set "p=%%" & set "b=%4"
if not defined b goto vectorOp1
if %b:~0,1%%b:~-1% == "" (set "b=%~4") else set "b=!%~4!"
if "%o%" == "[]" goto vectorOpBracket
if "%o%" == "//" goto vectorOpCompress
if "%o%" == "\\" goto vectorOpExpand
if /I "%o%" == "indexOf" goto vectorOpIndexOf
if /I "%o%" == "Max" set "o=x-z" & goto vectorOpMaxMin
if /I "%o%" == "Min" set "o=z-x" & goto vectorOpMaxMin
if "%b%" == "//" goto vectorOpReduction
if "%b%" == "\\" goto vectorOpScan
:vectorOpStd
set "x=%a: =" & set "y=!b:* =!" & call set "z=!p!b: !y!=!p!" & set /A "z=x!o!z" & set "r=!r! !z!" & set "b=!y!" & set "x=%" & set /A "z=x!o!y" & set "%1=!r:~1! !z!"
exit /B
:vectorOp1
set "x=%a: =" & set /A "z=!o!x" & set "r=!r! !z!" & set "x=%" & set /A "z=!o!x" & set "%1=!r:~1! !z!"
exit /B
:vectorOpBracket
set "n=0" & set "x=%a: =" & set "y=!b:* =!" & call set "m=!p!b: !y!=!p!" & set /A n+=1 & (if !n! equ !m! set "r=!r! !x!" & set "b=!y!") & set "x=%" & set "%1=!r:~1!"
exit /B
:vectorOpCompress
set "a=%b%" & set "b=%a%"
set "x=%a: =" & set "y=!b:* =!" & call set "z=!p!b: !y!=!p!" & (if "!x!" == "1" set "r=!r! !z!") & set "b=!y!" & set "x=%" & (if "!x!" == "1" set "r=!r! !y!") & set "%1=!r:~1!"
exit /B
:vectorOpExpand
set "a=%b%" & set "b=%a%"
set "x=%a: =" & set "y=!b:* =!" & call set "z=!p!b: !y!=!p!" & (if "!x!" == "1" (set "r=!r! !z!" & set "b=!y!" ) else set "r=!r! 0") & set "x=%" & (if "!x!" == "1" (set "r=!r! !y!") else set "r=!r! 0") & set "%1=!r:~1!"
exit /B
:vectorOpIndexOf
setlocal EnableDelayedExpansion & rem Special case
set "i=0" & set "x=%a: =" & set /A "i+=1,a[!x!]=i" & set "x=%" & set /A "i+=1,a[!x!]=i"
set "x=%b: =" & set /A "y=a[!x!]" & set "r=!r! !y!" & set "x=%" & set /A "y=a[!x!]"
endlocal & set "%1=%r:~1% %y%"
exit /B
:vectorOpMaxMin
set "x=%a: =" & set "y=!b:* =!" & call set "z=!p!b: !y!=!p!" & set /A "s=((!o!)>>31)+1,z=x*s+z*^!s" & set "r=!r! !z!" & set "b=!y!" & set "x=%" & set /A "z=y,s=((!o!)>>31)+1,z=x*s+z*^!s" & set "%1=!r:~1! !z!"
exit /B
:vectorOpScan
set "s=1"
:vectorOpReduction
if "%o%" neq "*" if "%o%" neq "<<" goto notMul
set "z=1" & goto @@
:notMul
if "%o%" neq "+" if "%o%" neq "-" if "%o%" neq "^" if "%o%" neq "|" goto notAdd
set "z=0" & goto @@
:notAdd
if "%o%" equ ">>" set /A "z=0x40000000" & goto @@
if /I "%o%" equ "Max" set /A "z=0x80000000" & goto @@
set /A "z=0x7FFFFFFF"
:@@
set "x=%a: =" & set /A "z!o!=x" & (if defined s set "r=!r! !z!") & set "x=%" & set /A "z!o!=x" & if defined s (set "%1=!r:~1! !z!") else set "%1=!z!"
exit /B
rem Some details missing in Reduction/Scan:
rem The implementation of Max & Min operators is missing
rem The initial values in some cases are not the best ones
rem In some routines a single Scalar number in vector2 don't works as intended
However, I don't have much motivation to do such a thing because some times my work goes unnoticed... However, if an enough number of users reply saying that they are using the package, report bugs and request modificactions, then I could change my mind and continue with the development of this application.
Antonio
PS - If you have interest in this program, you can review additional information at these sites:
- The method used to perform operations on several vector elements in a single line is described with detail at this answer.
- The data and operative scheme to manage arrays was taken from APL programming language.
Less than 1/5 of the original time! 