# spectral-norm Chapel #2 program

## source code

```/* The Computer Language Benchmarks Game
https://salsa.debian.org/benchmarksgame-team/benchmarksgame/

derived from the Chapel version by Lydia Duncan et al.
and the Julia version by Adam Beckmeyer and Vincent Yu
*/

config const n = 500;           // the size of A (n x n), u and v (n-vectors)

proc main() {
var tmp, u, v: [0..<n] real;

u = 1.0;

for 1..10 {
multiplyAtAv(u, tmp, v);    // v = A^T*A*u
multiplyAtAv(v, tmp, u);    // u = A^T*A*v
}

writef("%.9dr\n", sqrt(+ reduce (u*v) / + reduce (v*v)));
}

//
// Compute A-transpose * A * v ('AtAv')
//
proc multiplyAtAv(v, tmp, AtAv) {
multiplyAv(v, tmp);
multiplyAtv(tmp, AtAv);
}

//
// Compute A * v ('Av')
//
proc multiplyAv(v: [?Dv], Av: [?DAv]) {
forall i in DAv do
Av[i] = + reduce (for j in Dv by 2 do (A[i,j]*v[j] + A[i,j+1]*v[j+1]));
}

//
// Compute A-tranpose * v ('Atv')
//
proc multiplyAtv(v: [?Dv], Atv: [?DAtv]) {
forall i in DAtv do
Atv[i] = + reduce (for j in Dv by 2 do (A[j,i]*v[j] + A[j+1,i]*v[j+1]));
}

//
// Compute element i,j of the conceptually infinite matrix A
//
inline proc A(i: real, j: real) {
return 1.0 / ((((i+j) * (i+j+1)) / 2) + i + 1);
}
```

## notes, command-line, and program output

```NOTES:
chpl version 1.29.0
built with LLVM version 14.0.0
Hewlett Packard
Enterprise Development LP

Wed, 25 Jan 2023 22:13:43 GMT

MAKE:
mv spectralnorm.chapel-2.chapel spectralnorm.chapel-2.chpl
/opt/src/chapel-1.29.0/bin/chpl --fast spectralnorm.chapel-2.chpl -o spectralnorm.chapel-2.chapel_run
rm spectralnorm.chapel-2.chpl

19.50s to complete and log all make actions

COMMAND LINE:
./spectralnorm.chapel-2.chapel_run --n=5500

PROGRAM OUTPUT:
1.274224153
```