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Correct under- and overflow protection in l2_norm #184

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Merged
julianlitz merged 2 commits into from
Feb 27, 2026
Merged

Correct under- and overflow protection in l2_norm #184

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476fecc
Remove l2_norm_squared and improve comments
julianlitz Feb 27, 2026
5d93c33
Refactor l2 norm tests and add overflow/underflow cases
julianlitz Feb 27, 2026
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21 changes: 5 additions & 16 deletions include/LinearAlgebra/Vector/vector_operations.h
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Original file line number Diff line number Diff line change
Expand Up @@ -112,18 +112,7 @@ T l1_norm(ConstVector<T> x)
return result;
}

template <typename T>
T l2_norm_squared(ConstVector<T> x)
{
T result = 0.0;
std::size_t n = x.size();
#pragma omp parallel for reduction(+ : result) if (n > 10'000)
for (std::size_t i = 0; i < n; ++i) {
result += x(i) * x(i);
}
return result;
}

// Underflow- and overflow-resistant implementation of the L2 norm
template <typename T>
T l2_norm(ConstVector<T> x)
{
Expand All @@ -137,17 +126,17 @@ T l2_norm(ConstVector<T> x)
scale = abs_val;
}
}
if (equals(scale, T{0})) {
// 2) if the largest absolute value is zero, the norm is zero
if (scale == T{0})
return T{0};
}
// 2) accumulate sum of squares of scaled entries
// 3) accumulate sum of squares of scaled entries
T sum = 0.0;
#pragma omp parallel for reduction(+ : sum) if (n > 10'000)
for (std::size_t i = 0; i < n; ++i) {
T value = x(i) / scale;
sum += value * value;
}
// 3) rescale
// 4) rescale
return scale * std::sqrt(sum);
}

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36 changes: 27 additions & 9 deletions tests/LinearAlgebra/Vector/vector_operations.cpp
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Expand Up @@ -163,28 +163,46 @@ TEST(VectorOperations, l1_vector_norm)
EXPECT_DOUBLE_EQ(l1_norm(ConstVector<double>(v)), 8.0);
}

/* T l2_norm_squared(ConstVector<T>& x); */
/* T l2_norm(ConstVector<T>& x); */

TEST(VectorOperations, l2_vector_norm_squared)
TEST(VectorOperations, l2_vector_norm)
{
Vector<double> v("v", 3);
v(0) = 1;
v(1) = -5;
v(2) = 2;
ConstVector<double> const_v(v);
EXPECT_DOUBLE_EQ(l2_norm_squared(const_v), 30.0);
EXPECT_DOUBLE_EQ(l2_norm(ConstVector<double>(const_v)), std::sqrt(30.0));
}

/* T l2_norm(ConstVector<T>& x); */
TEST(VectorOperations, zero_l2_vector_norm)
{
Vector<double> v("v", 3);
v(0) = 0;
v(1) = 0;
v(2) = 0;
ConstVector<double> const_v(v);
EXPECT_DOUBLE_EQ(l2_norm(ConstVector<double>(const_v)), 0.0);
}

TEST(VectorOperations, l2_vector_norm)
TEST(VectorOperations, underflow_l2_vector_norm)
{
Vector<double> v("v", 3);
v(0) = 1;
v(1) = -5;
v(2) = 2;
v(0) = 1e-300;
v(1) = 1e-300;
v(2) = 1e-300;
ConstVector<double> const_v(v);
EXPECT_DOUBLE_EQ(l2_norm(ConstVector<double>(const_v)), std::sqrt(30.0));
EXPECT_DOUBLE_EQ(l2_norm(ConstVector<double>(const_v)), std::sqrt(3.0) * 1e-300);
}

TEST(VectorOperations, overflow_l2_vector_norm)
{
Vector<double> v("v", 3);
v(0) = 1e+300;
v(1) = 1e+300;
v(2) = 1e+300;
ConstVector<double> const_v(v);
EXPECT_DOUBLE_EQ(l2_norm(ConstVector<double>(const_v)), std::sqrt(3.0) * 1e+300);
}

/* T infinity_norm(ConstVector<T>& x); */
Expand Down