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RonaldoCMP 2020-08-16 23:38:17 +01:00
parent b4e26c035c
commit 143ba06467
1 changed files with 10 additions and 4 deletions
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math.scad
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@ -675,7 +675,7 @@ function convolve(p,q) =
// Usage: linear_solve(A,b)
// Description:
// Solves the linear system Ax=b. If A is square and non-singular the unique solution is returned. If A is overdetermined
// the least squares solution is returned. If A is underdetermined, the minimal norm solution is returned.
// the least squares solution is returned. If A is underdetermined, the minimal norm solution is returned.
// If A is rank deficient or singular then linear_solve returns []. If b is a matrix that is compatible with A
// then the problem is solved for the matrix valued right hand side and a matrix is returned. Note that if you
// want to solve Ax=b1 and Ax=b2 that you need to form the matrix transpose([b1,b2]) for the right hand side and then
@ -686,7 +686,7 @@ function linear_solve(A,b) =
m = len(A),
n = len(A[0])
)
assert(is_vector(b,m) || is_matrix(b,m),"Incompatible matrix and right hand side")
assert(is_vector(b,m) || is_matrix(b,m),"Invalid right hand side or incompatible with the matrix")
let (
qr = m<n? qr_factor(transpose(A)) : qr_factor(A),
maxdim = max(n,m),
@ -727,7 +727,7 @@ function qr_factor(A) =
n = len(A[0])
)
let(
qr =_qr_factor(A, Q=ident(m), column=0, m = m, n=n),
qr = _qr_factor(A, Q=ident(m), column=0, m = m, n=n),
Rzero =
let( R = qr[1] )
[ for(i=[0:m-1]) [
@ -745,7 +745,13 @@ function _qr_factor(A,Q, column, m, n) =
u = x - concat([alpha],repeat(0,m-1)),
v = alpha==0 ? u : u / norm(u),
Qc = ident(len(x)) - 2*outer_product(v,v),
Qf = [for(i=[0:m-1]) [for(j=[0:m-1]) i<column || j<column ? (i==j ? 1 : 0) : Qc[i-column][j-column]]]
Qf = [for(i=[0:m-1])
[for(j=[0:m-1])
i<column || j<column
? (i==j ? 1 : 0)
: Qc[i-column][j-column]
]
]
)
_qr_factor(Qf*A, Q*Qf, column+1, m, n);