Introduction
All valid binary operators can be applied as deep operators in order to address the 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 sets (vectors, matrics) is supported. In this case, the scalar
provided as one operand will be calculated with every element in the set specified as the other operand.
If 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 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: |)
- Set: Empty set {}
echo("Deep binary operators on simple 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 matrix( "0", 3, " | ", "a[]=", a[], " b[]=", b[] );
echo matrix( "0", 3, " | ", "a[] + b[] = ", a[] + b[] );
echo matrix( "0", 3, " | ", "a[] +^ b[] = ", a[] +^ b[] );
echo matrix( "0", 3, " | ", "a[] +^^ b[] = ", a[] +^^ b[] );Deep binary operators on simple 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 | | 1 -1 0 |
a[]= | 4 5 6 | b[]= | 2 -2 10 |
| 1 2 3 |
| 4 5 6 |
a[] + b[] = | 1 -1 0 |
| 2 -2 10 |
| 1 2 3 1 -1 0 |
a[] +^ b[] = | 4 5 6 2 -2 10 |
| 2 1 3 |
a[] +^^ b[] = | 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 set until all values in the longer 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 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 matrix( "0", 3, " | ", a[], " + ", b[], " = ", a[] + b[] );
echo matrix( "0", 3, " | ", a[], " +^ ", b[], " = ", a[] +^ b[] );
echo matrix( "0", 3, " | ", a[], " +^^ ", b[], " = ", a[] +^^ b[] );
echo matrix( "0", 3, " | ", a[], " +^^ ", 10, " = ", a[] +^^ 10 ); // Add 10 to all scalars
echo matrix( "0", 3, " | ", a[], " +^^ ", {10}, " = ", a[] +^^ {10} ); // Added to top row
echo matrix( "0", 3, " | ", a[], " +^^:", {10}, " = ", a[] +^^:{10} ); // Repetition rule, add to both rows
echo matrix( "0", 3, " | ", a[], " +^^ ", {10,20}, " = ", a[] +^^{10,20} ); // Top row + 10, bottom row +20
echo matrix( "0", 3, " | ", a[], " +^^:", {10,20}, " = ", a[] +^^:{10,20} ); // Same results
echo matrix( "0", 3, " | ", a[], " +^^ ", {{10}}, " = ", a[] +^^ {{10}} ); // Add to 1st element only
echo matrix( "0", 3, " | ", a[], " +^^:", {{10}}, " = ", a[] +^^:{{10}} ); // Repetition rule, add to all elements
echo matrix( "0", 3, " | ", a[], " +^^ ", {10,20}, " = ", a[] +^^{10,20} ); // Top row + 10, bottom row +20
echo matrix( "0", 3, " | ", a[], " +^^ ", {{10,20}}, " = ", a[] +^^{{10,20}} ); // Addition to upper row
echo matrix( "0", 3, " | ", a[], " +^^:", {{10,20}}, " = ", a[] +^^:{{10,20}} ); // Repetition rule, Done on both rows
echo matrix( "0", 3, " | ", a[], " +^^ ", {{10},{20}}, " = ", a[] +^^{{10},{20}} ); // Addition to left column
echo matrix( "0", 3, " | ", a[], " +^^:", {{10},{20}}, " = ", a[] +^^:{{10},{20}} ); // Addition to both columnsDeep binary operators on simple sets (vectors) and scalars:
{2,3,4,5,6}
{12,8,6,4.8,4}
Matrices combined with vectors and scalars
| 1 2 |
| 1 2 | | 5 6 | | 3 4 |
| 3 4 | + | 7 8 | = | 5 6 |
| 7 8 |
| 1 2 | | 5 6 | | 1 2 5 6 |
| 3 4 | +^ | 7 8 | = | 3 4 7 8 |
| 1 2 | | 5 6 | | 6 8 |
| 3 4 | +^^ | 7 8 | = | 10 12 |
| 1 2 | | 11 12 |
| 3 4 | +^^ 10 = | 13 14 |
| 1 2 | | 11 12 |
| 3 4 | +^^ | 10 | = | 3 4 |
| 1 2 | | 11 12 |
| 3 4 | +^^: | 10 | = | 13 14 |
| 1 2 | | 10 | | 11 12 |
| 3 4 | +^^ | 20 | = | 23 24 |
| 1 2 | | 10 | | 11 12 |
| 3 4 | +^^: | 20 | = | 23 24 |
| 1 2 | | 11 2 |
| 3 4 | +^^ | 10 | = | 3 4 |
| 1 2 | | 11 12 |
| 3 4 | +^^: | 10 | = | 13 14 |
| 1 2 | | 10 | | 11 12 |
| 3 4 | +^^ | 20 | = | 23 24 |
| 1 2 | | 11 22 |
| 3 4 | +^^ | 10 20 | = | 3 4 |
| 1 2 | | 11 22 |
| 3 4 | +^^: | 10 20 | = | 13 24 |
| 1 2 | | 10 | | 11 2 |
| 3 4 | +^^ | 20 | = | 23 4 |
| 1 2 | | 10 | | 11 12 |
| 3 4 | +^^: | 20 | = | 23 24 |
See also
Deep assignment operators
Matrix Operations Summary
echo matrix
print matrix