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RonaldoCMP 2020-08-02 01:03:46 +01:00 committed by GitHub
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1 changed files with 15 additions and 13 deletions
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@ -773,11 +773,10 @@ function _qr_factor(A,Q, column, m, n) =
// You can supply a compatible matrix b and it will produce the solution for every column of b. Note that if you want to
// solve Rx=b1 and Rx=b2 you must set b to transpose([b1,b2]) and then take the transpose of the result. If the matrix
// is singular (e.g. has a zero on the diagonal) then it returns [].
function back_substitute(R, b, x=[],transpose = false) =
function back_substitute(R, b, transpose = false) =
assert(is_matrix(R, square=true))
let(n=len(R))
assert(is_vector(b,n) || is_matrix(b,n),str("R and b are not compatible in back_substitute ",n, len(b)))
!is_vector(b) ? transpose([for(i=[0:len(b[0])-1]) back_substitute(R,subindex(b,i),transpose=transpose)]) :
transpose
    ? let( R = [for(i=[0:n-1]) [for(j=[0:n-1]) R[n-1-j][n-1-i]]] )
reverse( back_substitute( R, reverse(b), x ) ) 
@ -792,6 +791,7 @@ function back_substitute(R, b, x=[],transpose = false) =
(b[ind]-select(R[ind],ind+1,-1) * x)/R[ind][ind]
) back_substitute(R, b, concat([newvalue],x));
// Function: det2()
// Description:
// Optimized function that returns the determinant for the given 2x2 square matrix.
@ -1110,19 +1110,21 @@ function _deriv_nonuniform(data, h, closed) =
// closed = boolean to indicate if the data set should be wrapped around from the end to the start.
function deriv2(data, h=1, closed=false) =
assert( is_consistent(data) , "Input list is not consistent or not numerical.")
assert( len(data)>=3, "Input list has less than 3 elements.")
assert( is_finite(h), "The sampling `h` must be a number." )
let( L = len(data) )
closed? [
assert( L>=3, "Input list has less than 3 elements.")
closed
? [
for(i=[0:1:L-1])
(data[(i+1)%L]-2*data[i]+data[(L+i-1)%L])/h/h
] :
]
:
let(
first = L<3? undef :
first =
L==3? data[0] - 2*data[1] + data[2] :
L==4? 2*data[0] - 5*data[1] + 4*data[2] - data[3] :
(35*data[0] - 104*data[1] + 114*data[2] - 56*data[3] + 11*data[4])/12,
last = L<3? undef :
last =
L==3? data[L-1] - 2*data[L-2] + data[L-3] :
L==4? -2*data[L-1] + 5*data[L-2] - 4*data[L-3] + data[L-4] :
(35*data[L-1] - 104*data[L-2] + 114*data[L-3] - 56*data[L-4] + 11*data[L-5])/12
@ -1203,12 +1205,12 @@ 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: