From e06519bbfb4026dd51e6518900f688c797149fc9 Mon Sep 17 00:00:00 2001 From: RonaldoCMP Date: Tue, 4 Aug 2020 00:38:36 +0100 Subject: [PATCH] changes to hide recursion args and avoid repetitive arg validations cumsum broken in two to hide recursion args and avoid repetitive arg validations. back_substitute changed to avoid repetitive arg validations in the recursion. minor change in deriv2 and deriv3 to avoid an unecessary call to is_matrix. change in is_matrix for better performance any() and all() broken in two to avoid repetitive arg validation in the recursion and to hide recursion args. change in polymult to call convolve break of poly_div in two to avoid repetitive arg validations in the recursion. --- math.scad | 143 +++++++++++++++++++++++-------------------- tests/test_math.scad | 12 ++-- 2 files changed, 82 insertions(+), 73 deletions(-) diff --git a/math.scad b/math.scad index f112c19..7e16bbe 100644 --- a/math.scad +++ b/math.scad @@ -84,7 +84,7 @@ function hypot(x,y,z=0) = // y = factorial(6); // Returns: 720 // z = factorial(9); // Returns: 362880 function factorial(n,d=0) = - assert(is_int(n) && is_int(d) && n>=0 && d>=0, "Factorial is not defined for negative numbers") + assert(is_int(n) && is_int(d) && n>=0 && d>=0, "Factorial is defined only for non negative integers") assert(d<=n, "d cannot be larger than n") product([1,for (i=[n:-1:d+1]) i]); @@ -164,7 +164,7 @@ function binomial_coefficient(n,k) = function lerp(a,b,u) = assert(same_shape(a,b), "Bad or inconsistent inputs to lerp") is_finite(u)? (1-u)*a + u*b : - assert(is_finite(u) || is_vector(u) || valid_range(u), "Input u to lerp must be a number, vector, or range.") + assert(is_finite(u) || is_vector(u) || valid_range(u), "Input u to lerp must be a number, vector, or valid range.") [for (v = u) (1-v)*a + v*b ]; @@ -387,12 +387,13 @@ function modang(x) = // modrange(90,270,360, step=-45); // Returns: [90,45,0,315,270] // modrange(270,90,360, step=-45); // Returns: [270,225,180,135,90] function modrange(x, y, m, step=1) = - assert( is_finite(x+y+step+m) && !approx(m,0), "Input must be finite numbers. The module value cannot be zero.") + assert( is_finite(x+y+step+m) && !approx(m,0), "Input must be finite numbers and the module value cannot be zero." ) let( a = posmod(x, m), b = posmod(y, m), - c = step>0? (a>b? b+m : b) : (a0? (a>b? b+m : b) + : (a=len(v) ? _total : _sum(v,_total+v[_i], _i+1); // cumsum([2,2,2]); // returns [2,4,6] // 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]] -function cumsum(v,_i=0,_acc=[]) = +function cumsum(v) = + assert(is_consistent(v), "The input is not consistent." ) + _cumsum(v,_i=0,_acc=[]); + +function _cumsum(v,_i=0,_acc=[]) = _i==len(v) ? _acc : - cumsum( + _cumsum( v, _i+1, concat( _acc, @@ -598,7 +603,7 @@ function deltas(v) = // Description: // 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 square matrices, returns a the resulting product matrix. +// If passed a list of square matrices, returns the resulting product matrix. // Arguments: // v = The list to get the product of. // Example: @@ -606,7 +611,7 @@ function deltas(v) = // product([[1,2,3], [3,4,5], [5,6,7]]); // returns [15, 48, 105] function product(v) = assert( is_vector(v) || is_matrix(v) || ( is_matrix(v[0],square=true) && is_consistent(v)), - "Invalid input.") + "Invalid input.") _product(v, 1, v[0]); function _product(v, i=0, _tot) = @@ -691,9 +696,12 @@ function linear_solve(A,b) = zeros = [for(i=[0:mindim-1]) if (approx(R[i][i],0)) i] ) zeros != [] ? [] : - m=len(l) || succ)? succ : - any( l, - i+1, - succ = is_list(l[i]) ? any(l[i]) : !(!l[i]) - ); +function any(l) = + assert(is_list(l), "The input is not a list." ) + _any(l, i=0, succ=false); +function _any(l, i=0, succ=false) = + (i>=len(l) || succ)? succ : + _any( l, + i+1, + succ = is_list(l[i]) ? _any(l[i]) : !(!l[i]) + ); // Function: all() @@ -972,12 +982,15 @@ function any(l, i=0, succ=false) = // all([[0,0], [1,0]]); // Returns false. // all([[1,1], [1,1]]); // Returns true. function all(l, i=0, fail=false) = - (i>=len(l) || fail)? !fail : - all( l, - i+1, - fail = is_list(l[i]) ? !all(l[i]) : !l[i] - ) ; + assert( is_list(l), "The input is not a list." ) + _all(l, i=0, fail=false); +function _all(l, i=0, fail=false) = + (i>=len(l) || fail)? !fail : + _all( l, + i+1, + fail = is_list(l[i]) ? !_all(l[i]) : !l[i] + ) ; // Function: count_true() @@ -1195,12 +1208,12 @@ function C_div(z1,z2) = // where a_n is the z^n coefficient. Polynomial coefficients are real. // The result is a number if `z` is a number and a complex number otherwise. function polynomial(p,z,k,total) = - is_undef(k) - ? assert( is_vector(p) , "Input polynomial coefficients must be a vector." ) - assert( is_finite(z) || is_vector(z,2), "The value of `z` must be a real or a complex number." ) - polynomial( _poly_trim(p), z, 0, is_num(z) ? 0 : [0,0]) - : k==len(p) ? total - : polynomial(p,z,k+1, is_num(z) ? total*z+p[k] : C_times(total,z)+[p[k],0]); +    is_undef(k) +    ?   assert( is_vector(p) , "Input polynomial coefficients must be a vector." ) +        assert( is_finite(z) || is_vector(z,2), "The value of `z` must be a real or a complex number." ) +        polynomial( _poly_trim(p), z, 0, is_num(z) ? 0 : [0,0]) +    : k==len(p) ? total +    : polynomial(p,z,k+1, is_num(z) ? total*z+p[k] : C_times(total,z)+[p[k],0]); // Function: poly_mult() // Usage: @@ -1210,22 +1223,16 @@ function polynomial(p,z,k,total) = // Given a list of polynomials represented as real coefficient lists, with the highest degree coefficient first, // computes the coefficient list of the product polynomial. function poly_mult(p,q) = - is_undef(q) ? - assert( is_list(p) - && []==[for(pi=p) if( !is_vector(pi) && pi!=[]) 0], - "Invalid arguments to poly_mult") - len(p)==2 ? poly_mult(p[0],p[1]) - : poly_mult(p[0], poly_mult(select(p,1,-1))) - : - _poly_trim( - [ - for(n = [len(p)+len(q)-2:-1:0]) - sum( [for(i=[0:1:len(p)-1]) - let(j = len(p)+len(q)- 2 - n - i) - if (j>=0 && j