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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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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 // 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 // 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 []. // 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)) assert(is_matrix(R, square=true))
let(n=len(R)) 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))) 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
transpose? ? reverse(_back_substitute([for(i=[0:n-1]) [for(j=[0:n-1]) R[n-1-j][n-1-i]]],
reverse(back_substitute( reverse(b)))
[for(i=[0:n-1]) [for(j=[0:n-1]) R[n-1-j][n-1-i]]], : _back_substitute(R,b);
reverse(b), x, false
)) : function _back_substitute(R, b, x=[]) =
len(x) == n ? x : let(n=len(R))
let( len(x) == n ? x
ind = n - len(x) - 1 : let(ind = n - len(x) - 1)
) R[ind][ind] == 0 ? []
R[ind][ind] == 0 ? [] : : let(
let( newvalue = len(x)==0
newvalue = ? b[ind]/R[ind][ind]
len(x)==0? b[ind]/R[ind][ind] : : (b[ind]-select(R[ind],ind+1,-1) * x)/R[ind][ind]
(b[ind]-select(R[ind],ind+1,-1) * x)/R[ind][ind] )
) back_substitute(R, b, concat([newvalue],x)); _back_substitute(R, b, concat([newvalue],x));
// Function: det2() // Function: det2()
@@ -865,8 +865,10 @@ function determinant(M) =
// n = optional width of matrix // n = optional width of matrix
// square = set to true to require a square matrix. Default: false // square = set to true to require a square matrix. Default: false
function is_matrix(A,m,n,square=false) = function is_matrix(A,m,n,square=false) =
is_list(A[0]) is_list(A)
    && ( let(v = A*A[0]) is_num(0*(v*v)) ) // a matrix of finite numbers && 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(n) || len(A[0])==n )
    && (is_undef(m) || len(A)==m )     && (is_undef(m) || len(A)==m )
    && ( !square || len(A)==len(A[0]));     && ( !square || len(A)==len(A[0]));