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# Groovy example source code file (spectralnorm.groovy)

This example Groovy source code file (spectralnorm.groovy) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

## Java - Groovy tags/keywords

a, a, atav, atv, atv, av, av, multiplyatav, multiplyatav, multiplyatv, multiplyav

## The Groovy spectralnorm.groovy source code

```/*
The Computer Language Shootout
http://shootout.alioth.debian.org/

contributed by Jochen Hinrichsen
*/

def approximate(n) {
// create unit vector
def u = [1.0D] * n

// 20 steps of the power method
def v = [0.0D] * n

for (i in 1..10) {
MultiplyAtAv(n,u,v)
MultiplyAtAv(n,v,u)
}

// B=AtA         A multiplied by A transposed
// v.Bv /(v.v)   eigenvalue of v
double vBv = vv = 0.0D
for (i in 0..<n) {
vBv += u[i]*v[i]
vv  += v[i]*v[i]
}

return Math.sqrt(vBv/vv)
}

/* return element i,j of infinite matrix A */
def A(i, j) {
return (1.0D) / ((i+j)*(i+j+(1.0D))/(2.0D) +i+(1.0D))
}

/* multiply vector v by matrix A */
def MultiplyAv(n, v, Av){
for (i in 0..<n) {
Av[i] = 0.0D
for (j in 0..<n) Av[i] += A(i,j)*v[j]
}
}

/* multiply vector v by matrix A transposed */
def MultiplyAtv(n, v, Atv){
for (i in 0..<n) {
Atv[i] = 0.0D
for (j in 0..<n) Atv[i] += A(j,i)*v[j]
}
}

/* multiply vector v by matrix A and then by matrix A transposed */
def MultiplyAtAv(n, v, AtAv){
double[] u = new double[n]
MultiplyAv(n, v, u)
MultiplyAtv(n, u, AtAv)
}

def n = (args.length == 0 ? 100 : args[0].toInteger())
def nf = java.text.NumberFormat.getInstance()
nf.setMaximumFractionDigits(9)
nf.setMinimumFractionDigits(9)
nf.setGroupingUsed(false)
println(nf.format(approximate(n)))

// EOF

```

## Other Groovy examples (source code examples)

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