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Minor edits in is_matrix

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RonaldoCMP 2020-08-02 01:15:07 +01:00
parent 84fa648dc5
commit 764420e71d
1 changed files with 21 additions and 19 deletions
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40
math.scad
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@ -773,26 +773,26 @@ 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?
reverse(back_substitute(
[for(i=[0:n-1]) [for(j=[0:n-1]) R[n-1-j][n-1-i]]],
reverse(b), x, false
)) :
len(x) == n ? x :
let(
ind = n - len(x) - 1
)
R[ind][ind] == 0 ? [] :
let(
newvalue =
len(x)==0? b[ind]/R[ind][ind] :
(b[ind]-select(R[ind],ind+1,-1) * x)/R[ind][ind]
) back_substitute(R, b, concat([newvalue],x));
transpose
? reverse(_back_substitute([for(i=[0:n-1]) [for(j=[0:n-1]) R[n-1-j][n-1-i]]],
reverse(b)))
: _back_substitute(R,b);
function _back_substitute(R, b, x=[]) =
let(n=len(R))
len(x) == n ? x
: let(ind = n - len(x) - 1)
R[ind][ind] == 0 ? []
: let(
newvalue = len(x)==0
? b[ind]/R[ind][ind]
: (b[ind]-select(R[ind],ind+1,-1) * x)/R[ind][ind]
)
_back_substitute(R, b, concat([newvalue],x));
// Function: det2()
@ -865,8 +865,10 @@ function determinant(M) =
// n = optional width of matrix
// square = set to true to require a square matrix. Default: false
function is_matrix(A,m,n,square=false) =
is_list(A[0])
    && ( let(v = A*A[0]) is_num(0*(v*v)) ) // a matrix of finite numbers
is_list(A)
&& len(A)>0
&& is_vector(A[0])
    && is_vector(A*A[0]) // a matrix of finite numbers
    && (is_undef(n) || len(A[0])==n )
    && (is_undef(m) || len(A)==m )
    && ( !square || len(A)==len(A[0]));