Introduction
All valid binary operators can be applied as deep operators in order to address the parameter set elements directly.
The number of accent circumflex symbols behind the operator determines the depth to use.
A mix of combining simple values (scalars) and parameter sets (vectors, matrics) is supported. In this case, the scalar
provided as one operand will be calculated with every element in the parameter set specified as the other operand.
If parameter sets are specified in both sides of the operator, and the number of elements differ, then the shorter parameter
set will be stuffed with neutral values to match the length of the longer parameter set before doing the calculation.
Example: { 3, 4 } * { 2, 1, 3, 2 } extends to { 3, 4, 1, 1 } * { 2, 1, 3, 2 } where 1 is used as a neutral value for
multiplication.
List of neutral values:
- String: Blank string
- Numeral: 0 for + and -; 1 for * and /
- Dates: 0
- Boolean: true (for AND: &), 0 (for OR: |)
- Parameter set: Empty set {}
echo("Deep binary operators on simple parameter sets (vectors):");
a[] = { 1, 2, 3, 4, 5 };
b[] = { 10,15,20,25,30 };
c[] = { 2,-2,'',-2, 2 };
s[] = { Ha, He, Ho, Hu, Hi };
t[] = { ngar, ring, ney, nger, ll };
echo( a[] + b[]); // Conventional way: Concatenates vectors
echo( a[] *^ b[]); // Multiplies the elements together
echo( s[] +^ t[]); // Combines strings
echo( { rein, 1, date("2020-04-30") } +^ { deer, 2, 1 } );
// Mixed types are OK
echo(new line, "Vectors of different sizes");
echo( a[] *^ { 10, 100, 1000 } ); // First 3 elements are multiplied
echo( b[] -^ { 2,4,5} ); // First 3 elements are negated
echo( { 3,3,3,} -^ a[] ); // First 3 elements are calculated, remaining ones negated
echo( a[] /^ { 2,4,6 } ); // First 3 elemnts are divided
echo( a[] +^ c[] ); // Like with normal arithmetic operators, blank strings
// are interpreted as zero.
echo(new line, "Matrices");
a[] = { { 1, 2, 3 }, { 4, 5, 6 } };
b[] = { { 1, -1, 0 }, { 2, -2, 10 } };
echo( a[] + b[] ); // Simple concatenation
echo( a[] +^ b[] ); // The elements containing 3 numbers are concatenated
echo( a[] +^^ b[] ); // What you want: Addition of the elementsDeep binary operators on simple parameter sets (vectors):
{1,2,3,4,5,10,15,20,25,30}
{10,30,60,100,150}
{'Hangar','Hering','Honey','Hunger','Hill'}
{'reindeer',3,'2020-05-01'}
Vectors of different sizes
{10,200,3000,4,5}
{8,11,15,25,30}
{2,1,0,-4,-5}
{0.5,0.5,0.5,4,5}
{3,0,3,2,7}
Matrices
{{1,2,3},{4,5,6},{1,-1,0},{2,-2,10}}
{{1,2,3,1,-1,0},{4,5,6,2,-2,10}}
{{2,1,3},{6,3,16}}
Repetition Suffix
Particularly useful for operations with matrices of differen length is the repetition suffix which is a colon :. Add the colon after the last accent circumflex symbol to repeat the values in the shorter parameter set until all values in the longer parameter set have been calculated.
Adding the colon as repetition suffix
a[] = { 1, 2, 4, 8, 16 };
b[] = { 2, 3 };
echo( a[] +^ b[] ); // 3, 5, 4, 8, 16
echo( a[] +^:b[] ); // 3, 5, 6, 11, 18Combining vectors and matrices with scalars
echo("Deep binary operators on simple parameter sets (vectors) and scalars:");
a[] = { 1, 2, 3, 4, 5 };
b[] = { 10,15,20,25,30 };
c[] = { 2,-2,'',-2, 2 };
s[] = { Ha, He, Ho, Hu, Hi };
t[] = { ngar, ring, ney, nger, ll };
echo( a[] +^ 1 ); // Add 1 to all elements
echo( 120 /^ b[]); // Divide 120 by all elements
echo(new line, "Matrices combined with vectors and scalars");
a[] = { {1,2},{3,4} };
b[] = { {5,6},{7,8} };
echo( a[] + b[] ); // Catenation: { {1,2},{3,4},{5,6},{7,8} }
echo( a[] +^ b[] ); // Catenating the 1st level elements: { {1,2,5,6},{3,4,7,8} }
echo( a[] +^^ b[] ); // Calculating elements: { {6,8},{10,12} }
echo;
echo( a[] +^^ 10 ); // Adds 10 to all elements
echo( a[] +^^ {10} ); // {10} acts as scalar to {1,2} -> { {11,12},{3,4} }
echo( a[] +^^:{10} ); // Repetition suffix - Repeat the {10}:Like { {1,2},{3,4} } +^^ {10,10} } -> { {11,12},{13,14} }
echo( a[] +^^ {10,10} ); // Like above
echo;
echo( a[] +^^ {{10}} ); // Affects the 1st nested element only: { {11,2},{3,4} }
echo( a[] +^^:{{10}} ); // Repetition suffix - Repeat the {10}: All elements affected: { {11,12},{13,14} }
echo( a[] +^^ {10,20} ); // Calculates { {11,12},{23,24} }
echo( a[] +^^:{10,20} ); // Same result (Repetition suffix)
echo;
echo( a[] +^^ {{10,20}} ); // Calculates { {11,22},{ 3, 4} }
echo( a[] +^^ {{10},{20}} ); // Calculates { {11, 2},{23, 4} }
echo( a[] +^^:{{10},{20}} ); // Calculates { {11,12},{23,24} } (Repetition suffix)Deep binary operators on simple parameter sets (vectors) and scalars:
{2,3,4,5,6}
{12,8,6,4.8,4}
Matrices combined with vectors and scalars
{{1,2},{3,4},{5,6},{7,8}}
{{1,2,5,6},{3,4,7,8}}
{{6,8},{10,12}}
{{11,12},{13,14}}
{{11,12},{3,4}}
{{11,12},{13,14}}
{{11,12},{13,14}}
{{11,2},{3,4}}
{{11,12},{13,14}}
{{11,12},{23,24}}
{{11,12},{23,24}}
{{11,22},{3,4}}
{{11,2},{23,4}}
{{11,12},{23,24}}