Vector · matrix · tensor
Run the example to see its linear genome vector, pairwise genome matrix, and remaining 3D tensor—with the original tensor beside it.
The same three outputs for every tensor.
Each demo contains a saved raw tensor. Clicking Run recomputes its normalization. The original simulator trajectory or chromosome experiment is not repeated.
Use the same workflow on your counts. Everything is processed locally in this browser tab.
NPY · NPZ · JSON · coordinate CSV/TSV
raw, plus optional scalar snapshots.{"shape":[n,n,n],"raw":[...],"snapshots":S}.i,j,k,value, zero-based, every voxel exactly once.The linear component, the pairwise component, and the tensor that remains, shown as synchronized slices.
Compare the original 3D tensor with the remaining 3D tensor. Drag either to rotate both.
Near-1 values fade back so deviations are easier to see.
All axis orientations are retained in the exports. Inspect the other pair matrices below.
For a symmetric tensor, the three vectors and three pair matrices agree up to numerical precision. All orientations are kept so no data are discarded.
c is an overall geometric scale. The original arithmetic mean is shown separately. Each vector has mean log 0; each pair matrix has row and column mean logs 0. W is the selected normalized tensor.
The factorization reconstructs the smoothed input. Subtract 0.5 afterward to recover raw counts. A numerical log remainder is retained in exports.
Inspect individual i, j, or k planes and their exact values.
Original values are preserved; the display scale is optional.
Same slice coordinates. Click a cell to inspect exact values.
Scroll to inspect every row and column. All coordinates are zero-based.
Raw counts, all normalized outputs, exact components, and the full text report.
Exact in-memory double-precision values. The table is paged; exports contain the complete arrays.
The stopping history and pooled deviations check this run; the scatter compares all three methods.
Each solver starts independently from the same raw input.
Actual changes and balance after each iteration.
The same slice, updated after each real solver iteration.
The counters and convergence graph update from real solver iterations. Results opens automatically when the run finishes.
One voxel, three normalized values.
Errors across the entire tensor, after each accepted update. The dashed line is the requested tolerance.
The stopping rule checks change and balance together.
All fibers, pooled across i, j and k.
Deviation = (largest sum − smallest sum) / smallest sum. Zero is perfect balance.
Compare a recorded iteration with this run’s last output at the same voxel coordinates. Both axes use the same fixed range.
The last updates must satisfy the change, fiber, and plane limits together. A tiny update alone is insufficient.
These numbers include points outside the displayed range and all points omitted by display sampling.
Agreement is checked independently of the stopping rule; it does not substitute for fiber balance.
Measured numerical checks for the selected normalizer.
The reconstruction check uses the full tensor. Exports also retain the numerical log remainder, so the complete product recovers the input to floating-point accuracy. These checks provide evidence for this calculation; they do not identify the physical source of a remaining signal.
Open a saved example or import a finite, nonnegative n × n × n tensor. Every coordinate must be present, including repeated indices. Missing-cell masks and structural-zero constraints are not implemented. An observed zero is treated as a measured zero and receives the same 0.5 pseudocount as every other voxel.
Press Run all three normalizers. The three calculations begin separately with A = raw + 0.5. Their final weights are scaled to full-cube arithmetic mean 1. A value of 2 means twice this common reference level; it is not a contact probability.
Compute all fiber and plane sums from the current W. With total T, pair sums P, Q, R, and plane sums U, V, Z, form D = T·P·Q·R/(U·V·Z). Update W ← mean_one(W/√D). The square root applies to the entire divisor.
Project log(A) onto its three-way interaction by subtracting all lower-order log terms. Exponentiate. Then balance fibers sequentially along i, j, and k until the arithmetic fiber sums agree across all orientations.
Requires symmetry under coordinate permutations and the actual snapshot/exposure count S, with 0 ≤ raw ≤ S. Fit a symmetric pair logistic background using Newton-CG. Remove fitted odds with an outer objective-decrease line search. A globally reduced numerical probability scale keeps trial probabilities feasible. It never clips individual voxels or substitutes another normalizer.
For chromosome 21 examples, S is the supplied number of canonical read triples, not a count of simulation snapshots. The normalized output remains a relative-weight tensor. The original-scale probability feasibility check appears in the result metadata.
At the chosen tolerance, the maximum relative voxel update, the pooled fiber ratio minus 1, and the pooled plane ratio minus 1 must all pass for three consecutive updates. An initially balanced binomial input can return immediately. An iteration cap, failed line search, or tiny step with unresolved imbalance is displayed as a failure or an unfinished run.
Let B = log(A) − log(W). Decompose B into a constant cₗ, three centered single-axis vectors, and three doubly centered pair matrices using ordinary log-ANOVA means. Exponentiating gives the multiplicative factors in the Components view. This centering convention removes the arbitrary transfer of constants between factors.
The overall factor c = exp(cₗ) is not generally the arithmetic mean of A. Both are retained. For symmetric data there is effectively one shared vector and one shared pair matrix, but all three copies are exported to preserve the actual calculation.
The small three-way remainder of B measures numerical reconstruction error and is exported explicitly. Including exp(remainder) in the product makes the factorization recover A to floating-point accuracy. Subtracting 0.5 recovers raw.
W has balanced arithmetic fiber sums. H(log A) is a signed three-way log interaction, and is separately available as a slice table and in the exports. These are different representations. Neither a remaining peak nor agreement of methods identifies the physical source of a three-body signal.
raw and optional scalar snapshots. Extra reference arrays are ignored. Masks are rejected.{"shape":[n,n,n],"raw":[…],"snapshots":S}, a nested cube, or a complete exported session. Flat arrays use C order: k changes fastest.i,j,k,value, zero-based coordinates, every voxel exactly once. Missing coordinates and duplicates are rejected.Browser limits: side length ≤128; input files ≤150 MiB. Dense arrays scale as n³. Cancel stops the worker. For larger cubes or scripted processing, use the included Python runner with NumPy and SciPy.
The four demos contain saved raw tensors from the latest Tensor_Normalization_Explorer_Complete.zip: chromosome 21 at 1 Mb, moving loops, patchwork chain, and sticky hubs. Clicking Run recomputes normalization. The physical trajectories are not resimulated. Source and validation records are included in the software package.
NPY, NPZ, JSON, or full-cube coordinate CSV/TSV. No upload: files stay in this browser tab.
Each method starts independently from raw + 0.5. All output weights use arithmetic mean 1. Repeated-index cells are included.
Results ZIP includes numerical outputs, factors and checks. Download the offline app to run the software without a server.