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inner product version of sum

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Adrian Mariano 2021-03-12 19:17:03 -05:00
parent f90e89c761
commit d8f1581149
1 changed files with 13 additions and 13 deletions
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math.scad
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@ -585,11 +585,11 @@ function lcm(a,b=[]) =
function sum(v, dflt=0) =
v==[]? dflt :
assert(is_consistent(v), "Input to sum is non-numeric or inconsistent")
is_vector(v) ? [for(i=[1:len(v)]) 1]*v :
_sum(v,v[0]*0);
function _sum(v,_total,_i=0) = _i>=len(v) ? _total : _sum(v,_total+v[_i], _i+1);
// Function: cumsum()
// Usage:
// sums = cumsum(v);
@ -1465,35 +1465,35 @@ function deriv3(data, h=1, closed=false) =
// Section: Complex Numbers
// Function: C_times()
// Function: c_mul()
// Usage:
// c = C_times(z1,z2)
// c = c_mul(z1,z2)
// Description:
// Multiplies two complex numbers represented by 2D vectors.
// Returns a complex number as a 2D vector [REAL, IMAGINARY].
// Arguments:
// z1 = First complex number, given as a 2D vector [REAL, IMAGINARY]
// z2 = Second complex number, given as a 2D vector [REAL, IMAGINARY]
function C_times(z1,z2) =
function c_mul(z1,z2) =
assert( is_matrix([z1,z2],2,2), "Complex numbers should be represented by 2D vectors" )
[ z1.x*z2.x - z1.y*z2.y, z1.x*z2.y + z1.y*z2.x ];
// Function: C_div()
// Function: c_div()
// Usage:
// x = C_div(z1,z2)
// x = c_div(z1,z2)
// Description:
// Divides two complex numbers represented by 2D vectors.
// Returns a complex number as a 2D vector [REAL, IMAGINARY].
// Arguments:
// z1 = First complex number, given as a 2D vector [REAL, IMAGINARY]
// z2 = Second complex number, given as a 2D vector [REAL, IMAGINARY]
function C_div(z1,z2) =
function c_div(z1,z2) =
assert( is_vector(z1,2) && is_vector(z2), "Complex numbers should be represented by 2D vectors." )
assert( !approx(z2,0), "The divisor `z2` cannot be zero." )
let(den = z2.x*z2.x + z2.y*z2.y)
[(z1.x*z2.x + z1.y*z2.y)/den, (z1.y*z2.x - z1.x*z2.y)/den];
// For the sake of consistence with Q_mul and vmul, C_times should be called C_mul
// For the sake of consistence with Q_mul and vmul, c_mul should be called C_mul
// Section: Polynomials
@ -1544,7 +1544,7 @@ function polynomial(p,z,k,total) =
        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]);
    : polynomial(p,z,k+1, is_num(z) ? total*z+p[k] : c_mul(total,z)+[p[k],0]);
// Function: poly_mult()
// Usage:
@ -1680,10 +1680,10 @@ function _poly_roots(p, pderiv, s, z, tol, i=0) =
svals = [for(zk=z) tol*polynomial(s,norm(zk))],
p_of_z = [for(zk=z) polynomial(p,zk)],
done = [for(k=[0:n-1]) norm(p_of_z[k])<=svals[k]],
newton = [for(k=[0:n-1]) C_div(p_of_z[k], polynomial(pderiv,z[k]))],
zdiff = [for(k=[0:n-1]) sum([for(j=[0:n-1]) if (j!=k) C_div([1,0], z[k]-z[j])])],
w = [for(k=[0:n-1]) done[k] ? [0,0] : C_div( newton[k],
[1,0] - C_times(newton[k], zdiff[k]))]
newton = [for(k=[0:n-1]) c_div(p_of_z[k], polynomial(pderiv,z[k]))],
zdiff = [for(k=[0:n-1]) sum([for(j=[0:n-1]) if (j!=k) c_div([1,0], z[k]-z[j])])],
w = [for(k=[0:n-1]) done[k] ? [0,0] : c_div( newton[k],
[1,0] - c_mul(newton[k], zdiff[k]))]
)
all(done) ? z : _poly_roots(p,pderiv,s,z-w,tol,i+1);