Introduction
Most mathematical, type conversion, string and date functions, as well as various additional B4P functions, support vectorization in the
first and, in a few cases, second function parameters. This feature enables functions, which accept single values
and return single values, to process sets and also nested sets containing multiple values in any structure and
return sets in the corresponding structure containing the results.
Example: sqrt( {4, 16, { 9, 81 }} ) returns { 2, 4, { 3, 9 }}.
Key benefits:
- Vectors, defined in 1-level sets, can be processed with a single function call
- Matrices, defined in 2-level parameter, can also be processed with a single function call
- Same applies to any form of nested sets
- Complete table columns can be processed with a single assignment without using the table process() function.
- The cumbersome functions deep() and deepr() become unneccessary.
Some functions, including, but not limited to, mod(), pow(), excel coordinates(), round(), support
vectorization on both first two parameters. In these cases, either the two sets must contain the same number
of elements, or a set in one function parameter can be matched with a scalar in the other function parameter
where the scalar will be used repeatedly.
Allowed examples with 2 vectorized parameters:
| Formulation | Functionality |
|---|---|
| pow( {1, 2, 3}, {4, 5, 6 ) | Calculates 1^4, 2^5 and 3^6 |
| pow( 10, {1, 2, 3} ) | Calculates 10^1, 10^2 and 10^3 |
| pow( { 1, 2, 3 }, 2 ) | Calculates 1^2, 2^2 and 3^2 |
| pow( { 1, {2, 3}}, {4, 5} ) | Calculates 1^4, 2^5 and 3^5 |
| pow( { 1, 2, 3}, { 4, 5 } ) | Error: Sizes of sets do not match |
Following functions share the same names for processing strings and sets, so alternative function names
beginning with the prefix letter v have been introduced to support vectorization and avoid confusing between
processing strings and sets.
Deviating function names to support vectorization on processing sets with multiple strings inside:
Note: Vectorization cannot be activated for user-defined procedures and functions.
echo("Simple example with vectorization");
p[] = { 0, 30, 60, 90 };
echo( "With vectorization: ", sin deg( p[] ) );
// And the old way: Same results, but supports 1-level sets only.
echo( "with deep function: ", deep ( sin deg, {p[]} ) );
echo( new line, "Example with nested parameters:");
echo( log( { 1, 10, { 100, 1000 }, { 0.01, 0.001 } } ) );
echo(new line, "Example with matrices:");
m[] = { { 1, 2 }, { 3, 4 } };
m[] *^^= m[]; // Square the four values in the matrix (^^ is 2 level deep operator prefix)
echo("Original value: ", m[], " Square root: ", sqrt(m[]));
echo(new line, "2 vectorized parameters");
echo( "x^y repeated 4x: ", pow( { 1, 2, 3, 4 }, { 4, 3, 2, 1 } ) );
echo( "All squared : ", pow( { 1, 2, 3, 4 }, 2 ) );
echo( "Powers of ten : ", pow( 10, { 1, 2, 3, 4 } ) );
echo(new line, "Do something more sophisticated:");
echo( " Mod(x,7) on all values except the first one: ");
echo( mod( { 10, { 20, 30, { 8, 9 } }}, { 5, 7 } ) );
echo( " Mod(100,x) on all values: ");
echo( mod( 100, { 10, { 20, 30, { 40, 50 } }} ) );Simple example with vectorization
With vectorization: {0,0.5,0.8660254038,1}
with deep function: {0,0.5,0.8660254038,1}
Example with nested parameters:
{0,1,{2,3},{-2,-3}}
Example with matrices:
Original value: {{1,4},{9,16}} Square root: {{1,2},{3,4}}
2 vectorized parameters
x^y repeated 4x: {1,8,9,4}
All squared : {1,4,9,16}
Powers of ten : {10,100,1000,10000}
Do something more sophisticated:
Mod(x,7) on all values except the first one:
{0,{6,2,{1,2}}}
Mod(100,x) on all values:
{0,{0,10,{20,0}}}