Notebooks · lib/stats/lens/nist_digits

NIST's certified linear regressions under the digits lens

Fits one NIST StRD linear least-squares dataset (lib/stats/data/) with the solver slot of lib/stats/linmod.viv and prints the coefficients, for viv digits to perturb:

viv digits --set 'DATASET="Longley"' --set METHOD=0 lib/stats/lens/nist_digits.viv

METHOD 0 is pivoted QR with Bjorck's refinement, 1 the same QR without it, 2 the normal equations by Cholesky. The model is NIST's: Longley's six predictors and an intercept, a polynomial in x of degree DEGREE otherwise (10 for Filip, 5 for Wampler1-5).

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[1]lines 19–72

from stats.linmod import lstsq, LSTSQ_QR, LSTSQ_CHOL

DATASET = "Filip"
DEGREE = 10
METHOD = 0
RANK_TOL = 1e-10
METHOD_QR_PLAIN = 1
METHOD_CHOL = 2

text = read_text("lib/stats/data/" + DATASET + ".dat")
lines = splitlines(text)
start = 0
for i to len(lines) {
    if startswith(strip(lines[i]), "Data:") {
        start = i + 1
    }
}
rows = []
for i from start to len(lines) {
    if len(strip(lines[i])) > 0 {
        rows = append(rows, i)
    }
}
n = len(rows)
first = split(strip(lines[rows[0]]))
ncols = len(first)
y = zeros(n)
cols = DEGREE + 1 if DATASET != "Longley" else ncols
X = zeros(n, cols)
for r to n {
    f = split(strip(lines[rows[r]]))
    y[r] = float(f[0])
    X[r, 0] = 1.0
    if DATASET == "Longley" {
        for j from 1 to ncols {
            X[r, j] = float(f[j])
        }
    }
    else {
        x = float(f[1])
        for j from 1 to cols {
            X[r, j] = X[r, j - 1] * x
        }
    }
}
method = LSTSQ_CHOL if METHOD == METHOD_CHOL else LSTSQ_QR
refine = 0.0 if METHOD == METHOD_QR_PLAIN else 1.0
b, rank, piv, C = lstsq(X, y, method, RANK_TOL, refine)
for j to cols {
    print(fmt(b[j], ".15e"))
}

# SPDX-License-Identifier: MIT OR Apache-2.0
# SPDX-FileCopyrightText: 2026 The Viv authors

from stats.linmod import lstsq, LSTSQ_QR, LSTSQ_CHOL

DATASET = "Filip"
DEGREE = 10
METHOD = 0
RANK_TOL = 1e-10
METHOD_QR_PLAIN = 1
METHOD_CHOL = 2

text = read_text("lib/stats/data/" + DATASET + ".dat")
lines = splitlines(text)
start = 0
for i to len(lines) {
    if startswith(strip(lines[i]), "Data:") {
        start = i + 1
    }
}
rows = []
for i from start to len(lines) {
    if len(strip(lines[i])) > 0 {
        rows = append(rows, i)
    }
}
n = len(rows)
first = split(strip(lines[rows[0]]))
ncols = len(first)
y = zeros(n)
cols = DEGREE + 1 if DATASET != "Longley" else ncols
X = zeros(n, cols)
for r to n {
    f = split(strip(lines[rows[r]]))
    y[r] = float(f[0])
    X[r, 0] = 1.0
    if DATASET == "Longley" {
        for j from 1 to ncols {
            X[r, j] = float(f[j])
        }
    }
    else {
        x = float(f[1])
        for j from 1 to cols {
            X[r, j] = X[r, j - 1] * x
        }
    }
}
method = LSTSQ_CHOL if METHOD == METHOD_CHOL else LSTSQ_QR
refine = 0.0 if METHOD == METHOD_QR_PLAIN else 1.0
b, rank, piv, C = lstsq(X, y, method, RANK_TOL, refine)
for j to cols {
    print(fmt(b[j], ".15e"))
}

# SPDX-License-Identifier: MIT OR Apache-2.0
# SPDX-FileCopyrightText: 2026 The Viv authors