Create / manipulate diagonal matrices in Chapel - chapel

Question

I have a square matrix A
use LinearAlgebra;
proc main() {
var A = Matrix(
[4.0, 0.8, 1.1, 0.0, 2.0]
,[0.8, 9.0, 1.3, 1.0, 0.0]
,[1.1, 1.3, 1.0, 0.5, 1.7]
,[0.0, 1.0, 0.5, 4.0, 1.5]
,[2.0, 0.0, 1.7, 1.5, 16.0]
);
}
And I want to construct the diagonal matrix D = 1/sqrt(a_ii). It seems like I have have to extract the diagonal, then operate on each element. I expect this matrix is be very large and sparse, if that changes the answer.

Answer 1

Here's a solution using the LinearAlgebra module in 1.16 (pre-release):
use LinearAlgebra;
var A = Matrix(
[4.0, 0.8, 1.1, 0.0, 2.0],
[0.8, 9.0, 1.3, 1.0, 0.0],
[1.1, 1.3, 1.0, 0.5, 1.7],
[0.0, 1.0, 0.5, 4.0, 1.5],
[2.0, 0.0, 1.7, 1.5, 16.0]
);
var S = sqrt(1.0/diag(A));
// Type required because of promotion-flatting
// See Linear Algebra documentation for more details..
var B: A.type = diag(S);
writeln(B);

Answer 2

Did you try this approach?
use Math;
var D: [A.domain];
forall i in D.dim( 1 ) {
D[i,i] = 1 / Math.sqrt( A[i,i] ); // ought get fused-DIV!0 protection
}
( A.T.M. <TiO>-IDE has not so far fully functional the LinearAlgebra package, so cannot show you the results live, yet hope you would enjoy the way forwards )

Answer 3

Here's some code that works with a sparse diagonal array in version 1.15 today without linear algebra library support:
config const n = 10; // problem size; override with --n=1000 on command-line
const D = {1..n, 1..n}, // dense/conceptual matrix size
Diag: sparse subdomain(D) = genDiag(n); // sparse diagonal matrix
// iterator that yields indices describing the diagonal
iter genDiag(n) {
for i in 1..n do
yield (i,i);
}
// sparse diagonal matrix
var DiagMat: [Diag] real;
// assign sparse matrix elements in parallel
forall ((r,c), elem) in zip(Diag, DiagMat) do
elem = r + c/10.0;
// print sparse matrix elements serially
for (ind, elem) in zip(Diag, DiagMat) do
writeln("A[", ind, "] is ", elem);
// dense array
var Dense: [D] real;
// assign from sparse to dense
forall ij in D do
Dense[ij] = DiagMat[ij];
// print dense array
writeln(Dense);