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  11. slogdet

torch.Tensor.Tensor.slogdet

Tensor.slogdet(): { sign: Tensor; logabsdet: Tensor }

Computes the sign and log absolute value of the determinant in a numerically stable way.

Returns both the sign and logarithm of the absolute determinant separately, enabling reconstruction of the full determinant as sign * exp(logabsdet). This provides numerical stability and allows handling negative determinants (e.g., for orientation-reversing transforms).

More informative than logdet() because it preserves sign information, which is important for determinants of transformation matrices (orientation preservation, parity).

Use Cases:

  • Computing oriented volumes in geometric algorithms
  • Checking whether a transformation preserves or reverses orientation
  • Variational inference where sign matters (e.g., flow models)
  • Higher-precision reconstruction: det = exp(log + sign adjustment)
det(A)=sign×elogabsdet\text{det}(A) = \text{sign} \times e^{\text{logabsdet}}det(A)=sign×elogabsdet
  • Sign values: 0 for singular (det=0), ±1 for non-singular matrices
  • Log value: Always non-negative since it's log of absolute value
  • Reconstruction: sign * exp(logabsdet) recovers the actual determinant
  • Orientation: Sign encodes whether transformation preserves orientation
  • Batch support: Works with batched matrices (..., n, n)
  • Singular matrices: Returns sign=0 and logabsdet=-inf
  • Precision loss: exp(logabsdet) may lose precision for very large/small values
  • Orientation: Sign is only meaningful for invertible matrices

Returns

{ sign: Tensor; logabsdet: Tensor }– Object with two properties: - sign: Tensor of shape () with values in -1, 0, 1 indicating sign of det(A) - logabsdet: Tensor of shape () with ln(|det(A)|)

Examples

// Basic sign + log determinant
const A = torch.tensor([[-2, 1], [1, -1]]);
const { sign, logabsdet } = A.slogdet();
sign;     // 1 (positive determinant)
logabsdet;  // log(|1|) = 0
const det = sign * Math.exp(logabsdet.item());  // Recover: 1

// Orientation-reversing transformation (negative determinant)
const reflect = torch.tensor([[1, 0], [0, -1]]);  // y-reflection
const { sign: s, logabsdet: lad } = reflect.slogdet();
s;  // -1 (reverses orientation)
// This shows the reflection is orientation-reversing

// Numerically stable for difficult matrices
const scale_factor = 1e10;
const scaled = torch.eye(3).mul(scale_factor);
const { sign: sig, logabsdet: lad } = scaled.slogdet();
// Reconstruction avoids overflow/underflow
const det_value = sig * Math.exp(lad.item());  // Safe to compute

// Orientation check in 3D
const basis = torch.tensor([[1, 0, 0], [0, 1, 0], [0, 0, 1]]);
const { sign: orientation } = basis.slogdet();
if (orientation > 0) {
  console.log('Right-handed coordinate system');
} else {
  console.log('Left-handed coordinate system');
}

See Also

  • PyTorch torch.slogdet() (or tensor.slogdet())
  • det - Direct determinant (less stable for extreme values)
  • logdet - Log of absolute determinant (loses sign information)
  • inverse - Matrix inversion (non-singular matrices only)
  • lu - LU decomposition (can extract sign from permutation)
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