// Norm returns the specified (induced) norm of the matrix a. See
// https://en.wikipedia.org/wiki/Matrix_norm for the definition of an induced norm.
//
// Valid norms are:
// 1 - The maximum absolute column sum
// 2 - Frobenius norm, the square root of the sum of the squares of the elements.
// Inf - The maximum absolute row sum.
// Norm will panic with ErrNormOrder if an illegal norm order is specified and
// with matrix.ErrShape if the matrix has zero size.
func Norm(a Matrix, norm float64) float64 {
r, c := a.Dims()
if r == 0 || c == 0 {
panic(matrix.ErrShape)
}
aU, aTrans := untranspose(a)
var work []float64
switch rma := aU.(type) {
case RawMatrixer:
rm := rma.RawMatrix()
n := normLapack(norm, aTrans)
if n == lapack.MaxColumnSum {
work = make([]float64, rm.Cols)
}
return lapack64.Lange(n, rm, work)
case RawTriangular:
rm := rma.RawTriangular()
n := normLapack(norm, aTrans)
if n == lapack.MaxRowSum || n == lapack.MaxColumnSum {
work = make([]float64, rm.N)
}
return lapack64.Lantr(n, rm, work)
case RawSymmetricer:
rm := rma.RawSymmetric()
n := normLapack(norm, aTrans)
if n == lapack.MaxRowSum || n == lapack.MaxColumnSum {
work = make([]float64, rm.N)
}
return lapack64.Lansy(n, rm, work)
case *Vector:
rv := rma.RawVector()
switch norm {
default:
panic("unreachable")
case 1:
if aTrans {
imax := blas64.Iamax(rma.n, rv)
return math.Abs(rma.At(imax, 0))
}
return blas64.Asum(rma.n, rv)
case 2:
return blas64.Nrm2(rma.n, rv)
case math.Inf(1):
if aTrans {
return blas64.Asum(rma.n, rv)
}
imax := blas64.Iamax(rma.n, rv)
return math.Abs(rma.At(imax, 0))
}
}
switch norm {
default:
panic("unreachable")
case 1:
var max float64
for j := 0; j < c; j++ {
var sum float64
for i := 0; i < r; i++ {
sum += math.Abs(a.At(i, j))
}
if sum > max {
max = sum
}
}
return max
case 2:
var sum float64
for i := 0; i < r; i++ {
for j := 0; j < c; j++ {
v := a.At(i, j)
sum += v * v
}
}
return math.Sqrt(sum)
case math.Inf(1):
var max float64
for i := 0; i < r; i++ {
var sum float64
for j := 0; j < c; j++ {
sum += math.Abs(a.At(i, j))
}
if sum > max {
max = sum
}
}
return max
}
}
func DlangeTest(t *testing.T, impl Dlanger) {
for _, test := range []struct {
m, n, lda int
}{
{4, 3, 0},
{3, 4, 0},
{4, 3, 100},
{3, 4, 100},
} {
m := test.m
n := test.n
lda := test.lda
if lda == 0 {
lda = n
}
a := make([]float64, m*lda)
for i := range a {
a[i] = (rand.Float64() - 0.5)
}
work := make([]float64, n)
for i := range work {
work[i] = rand.Float64()
}
aCopy := make([]float64, len(a))
copy(aCopy, a)
// Test MaxAbs norm.
norm := impl.Dlange(lapack.MaxAbs, m, n, a, lda, work)
var ans float64
for i := 0; i < m; i++ {
idx := blas64.Iamax(n, blas64.Vector{1, aCopy[i*lda:]})
ans = math.Max(ans, math.Abs(a[i*lda+idx]))
}
// Should be strictly equal because there is no floating point summation error.
if ans != norm {
t.Errorf("MaxAbs mismatch. Want %v, got %v.", ans, norm)
}
// Test MaxColumnSum norm.
norm = impl.Dlange(lapack.MaxColumnSum, m, n, a, lda, work)
ans = 0
for i := 0; i < n; i++ {
sum := blas64.Asum(m, blas64.Vector{lda, aCopy[i:]})
ans = math.Max(ans, sum)
}
if math.Abs(norm-ans) > 1e-14 {
t.Errorf("MaxColumnSum mismatch. Want %v, got %v.", ans, norm)
}
// Test MaxRowSum norm.
norm = impl.Dlange(lapack.MaxRowSum, m, n, a, lda, work)
ans = 0
for i := 0; i < m; i++ {
sum := blas64.Asum(n, blas64.Vector{1, aCopy[i*lda:]})
ans = math.Max(ans, sum)
}
if math.Abs(norm-ans) > 1e-14 {
t.Errorf("MaxRowSum mismatch. Want %v, got %v.", ans, norm)
}
// Test Frobenius norm
norm = impl.Dlange(lapack.NormFrob, m, n, a, lda, work)
ans = 0
for i := 0; i < m; i++ {
sum := blas64.Nrm2(n, blas64.Vector{1, aCopy[i*lda:]})
ans += sum * sum
}
ans = math.Sqrt(ans)
if math.Abs(norm-ans) > 1e-14 {
t.Errorf("NormFrob mismatch. Want %v, got %v.", ans, norm)
}
}
}