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sum/product optimizations

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Adrian Mariano 2024-06-25 19:24:48 -04:00
parent c6e58b926b
commit 054052144e
2 changed files with 68 additions and 52 deletions
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108
math.scad
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@ -721,16 +721,17 @@ function deltas(v, wrap=false) =
// cumsum([1,2,3]); // returns [1,3,6] // cumsum([1,2,3]); // returns [1,3,6]
// cumsum([[1,2,3], [3,4,5], [5,6,7]]); // returns [[1,2,3], [4,6,8], [9,12,15]] // cumsum([[1,2,3], [3,4,5], [5,6,7]]); // returns [[1,2,3], [4,6,8], [9,12,15]]
function cumsum(v) = function cumsum(v) =
v==[] ? [] :
assert(is_consistent(v), "The input is not consistent." ) assert(is_consistent(v), "The input is not consistent." )
len(v)<=1 ? v : [for (a = v[0],
_cumsum(v,_i=1,_acc=[v[0]]); i = 1
;
function _cumsum(v,_i=0,_acc=[]) = i <= len(v)
_i>=len(v) ? _acc : ;
_cumsum( v, _i+1, [ each _acc, _acc[len(_acc)-1] + v[_i] ] ); a = i<len(v) ? a+v[i] : a,
i = i+1)
a];
// Function: product() // Function: product()
// Synopsis: Returns the multiplicative product of a list of values. // Synopsis: Returns the multiplicative product of a list of values.
// Topics: Math, Statistics // Topics: Math, Statistics
@ -739,24 +740,35 @@ function _cumsum(v,_i=0,_acc=[]) =
// x = product(v); // x = product(v);
// Description: // Description:
// Returns the product of all entries in the given list. // Returns the product of all entries in the given list.
// If passed a list of vectors of same dimension, returns a vector of products of each part. // If passed a list of vectors of same length, returns a vector of the component-wise products of the input.
// If passed a list of square matrices, returns the resulting product matrix. // If passed a list of square matrices, returns the resulting product matrix. Matrices are multiplied in the order they appear in the list.
// Arguments: // Arguments:
// v = The list to get the product of. // v = The list to get the product of.
// Example: // Example:
// product([2,3,4]); // returns 24. // product([2,3,4]); // returns 24.
// product([[1,2,3], [3,4,5], [5,6,7]]); // returns [15, 48, 105] // product([[1,2,3], [3,4,5], [5,6,7]]); // returns [15, 48, 105]
function product(v) = function product(list,right=true) =
assert( is_vector(v) || is_matrix(v) || ( is_matrix(v[0],square=true) && is_consistent(v)), list==[] ? [] :
"Invalid input.") is_matrix(list) ?
_product(v, 1, v[0]); [for (a = list[0],
i = 1
function _product(v, i=0, _tot) = ;
i>=len(v) ? _tot : i <= len(list)
_product( v, ;
i+1, a = i<len(list) ? v_mul(a,list[i]) : 0,
( is_vector(v[i])? v_mul(_tot,v[i]) : _tot*v[i] ) ); i = i+1)
if (i==len(list)) a][0]
:
assert(is_vector(list) || (is_matrix(list[0],square=true) && is_consistent(list)),
"Input must be a vector, a list of vectors, or a list of matrices.")
[for (a = list[0],
i = 1
;
i <= len(list)
;
a = i<len(list) ? a*list[i] : 0,
i = i+1)
if (i==len(list)) a][0];
// Function: cumprod() // Function: cumprod()
@ -777,37 +789,29 @@ function _product(v, i=0, _tot) =
// cumprod([1,3,5]); // returns [1,3,15] // cumprod([1,3,5]); // returns [1,3,15]
// cumprod([2,2,2]); // returns [2,4,8] // cumprod([2,2,2]); // returns [2,4,8]
// cumprod([[1,2,3], [3,4,5], [5,6,7]])); // returns [[1, 2, 3], [3, 8, 15], [15, 48, 105]] // cumprod([[1,2,3], [3,4,5], [5,6,7]])); // returns [[1, 2, 3], [3, 8, 15], [15, 48, 105]]
function cumprod(list,right=false) = function cumprod(list,right=false) =
is_vector(list) ? _cumprod(list) : list==[] ? [] :
assert(is_consistent(list), "Input must be a consistent list of scalars, vectors or square matrices") is_matrix(list) ?
assert(is_bool(right)) [for (a = list[0],
is_matrix(list[0]) ? assert(len(list[0])==len(list[0][0]), "Matrices must be square") _cumprod(list,right) i = 1
: _cumprod_vec(list); ;
i <= len(list)
function _cumprod(v,right,_i=0,_acc=[]) = ;
_i==len(v) ? _acc : a = i<len(list) ? v_mul(a,list[i]) : 0,
_cumprod( i = i+1)
v, right, _i+1, a]
concat( :
_acc, assert(is_vector(list) || (is_matrix(list[0],square=true) && is_consistent(list)),
[ "Input must be a listector, a list of listectors, or a list of matrices.")
_i==0 ? v[_i] [for (a = list[0],
: right? _acc[len(_acc)-1]*v[_i] i = 1
: v[_i]*_acc[len(_acc)-1] ;
] i <= len(list)
) ;
); a = i<len(list) ? (right ? a*list[i] : list[i]*a) : 0,
i = i+1)
function _cumprod_vec(v,_i=0,_acc=[]) = a];
_i==len(v) ? _acc :
_cumprod_vec(
v, _i+1,
concat(
_acc,
[_i==0 ? v[_i] : v_mul(_acc[len(_acc)-1],v[_i])]
)
);
// Function: convolve() // Function: convolve()

12
tests/test_math.scad
View file

@ -371,6 +371,7 @@ test_deltas();
module test_product() { module test_product() {
assert_equal(product([]),[]);
assert_equal(product([2,3,4]), 24); assert_equal(product([2,3,4]), 24);
assert_equal(product([[1,2,3], [3,4,5], [5,6,7]]), [15, 48, 105]); assert_equal(product([[1,2,3], [3,4,5], [5,6,7]]), [15, 48, 105]);
m1 = [[2,3,4],[4,5,6],[6,7,8]]; m1 = [[2,3,4],[4,5,6],[6,7,8]];
@ -613,6 +614,7 @@ module test_cumprod(){
assert_equal(cumprod([]),[]); assert_equal(cumprod([]),[]);
assert_equal(cumprod([[2,3],[4,5],[6,7]]), [[2,3],[8,15],[48,105]]); assert_equal(cumprod([[2,3],[4,5],[6,7]]), [[2,3],[8,15],[48,105]]);
assert_equal(cumprod([[5,6,7]]),[[5,6,7]]); assert_equal(cumprod([[5,6,7]]),[[5,6,7]]);
assert_equal(cumprod([up(5),down(5)]), [up(5),IDENT]);
assert_equal(cumprod([ assert_equal(cumprod([
[[1,2],[3,4]], [[1,2],[3,4]],
[[-4,5],[6,4]], [[-4,5],[6,4]],
@ -623,6 +625,16 @@ module test_cumprod(){
[[11,12],[18,28]], [[11,12],[18,28]],
[[45,24],[98,132]] [[45,24],[98,132]]
]); ]);
assert_equal(cumprod([
[[1,2],[3,4]],
[[-4,5],[6,4]],
[[9,-3],[4,3]]
],right=true),
[
[[1,2],[3,4]],
[[8, 13],[12,31]],
[[124, 15],[232,57]]
]);
assert_equal(cumprod([[[1,2],[3,4]]]), [[[1,2],[3,4]]]); assert_equal(cumprod([[[1,2],[3,4]]]), [[[1,2],[3,4]]]);
} }
test_cumprod(); test_cumprod();