diff --git a/include/pfs/drp/stella/FiberTrace.h b/include/pfs/drp/stella/FiberTrace.h
index 23649696a..707e9a55d 100644
--- a/include/pfs/drp/stella/FiberTrace.h
+++ b/include/pfs/drp/stella/FiberTrace.h
@@ -127,7 +127,7 @@ class FiberTrace {
         ndarray::Array<double, 2, 1> const& profiles,
         ndarray::Array<bool, 2, 1> const& good,
         ndarray::Array<double, 1, 1> const& centers,
-        ndarray::Array<double, 1, 1> const& norm=ndarray::Array<double, 1, 1>()
+        ndarray::Array<Spectrum::ImageT, 1, 1> const& norm=ndarray::Array<Spectrum::ImageT, 1, 1>()
     );
 
   private:
diff --git a/include/pfs/drp/stella/Spectrum.h b/include/pfs/drp/stella/Spectrum.h
index e2083c21c..3e77ea7a4 100644
--- a/include/pfs/drp/stella/Spectrum.h
+++ b/include/pfs/drp/stella/Spectrum.h
@@ -13,8 +13,8 @@ namespace pfs { namespace drp { namespace stella {
  */
 class Spectrum {
   public:
-    using ImageT = double;
-    using VarianceT = double;
+    using ImageT = float;
+    using VarianceT = float;
     using Mask = lsst::afw::image::Mask<lsst::afw::image::MaskPixel>;
     using ImageArray = ndarray::Array<ImageT, 1, 1>;
     using ConstImageArray = ndarray::Array<const ImageT, 1, 1>;
diff --git a/include/pfs/drp/stella/SpectrumSet.h b/include/pfs/drp/stella/SpectrumSet.h
index a3905e64a..b58221f7d 100644
--- a/include/pfs/drp/stella/SpectrumSet.h
+++ b/include/pfs/drp/stella/SpectrumSet.h
@@ -20,8 +20,8 @@ class SpectrumSet {
     using SpectrumPtr = std::shared_ptr<Spectrum>;
     using ConstSpectrumPtr = std::shared_ptr<Spectrum const>;
     using Collection = std::vector<SpectrumPtr>;
-    using ImageArray = ndarray::Array<double, 2, 1>;
-    using CovarianceArray = ndarray::Array<double, 3, 1>;
+    using ImageArray = ndarray::Array<Spectrum::ImageT, 2, 1>;
+    using CovarianceArray = ndarray::Array<Spectrum::ImageT, 3, 1>;
     using MaskArray = ndarray::Array<lsst::afw::image::MaskPixel, 2, 1>;
     using WavelengthArray = ndarray::Array<double, 2, 1>;
     using iterator = Collection::iterator;
diff --git a/python/pfs/drp/stella/fiberProfile.py b/python/pfs/drp/stella/fiberProfile.py
index 9df34d8ef..4bf4f4d0b 100644
--- a/python/pfs/drp/stella/fiberProfile.py
+++ b/python/pfs/drp/stella/fiberProfile.py
@@ -27,7 +27,7 @@ class FiberProfile:
     profiles : array_like of `float`, shape ``(N, M)``
         Profiles for each swath, each of width
         ``M = 2*(radius + 1)*oversample + 1``.
-    norm : array_like of `float`, optional
+    norm : array_like of `np.float32`, optional
         Normalisation for each spectral pixel.
     """
     def __init__(self, radius, oversample, rows, profiles, norm=None):
@@ -220,7 +220,8 @@ def makeFiberTraceFromDetectorMap(self, detectorMap, fiberId):
         """
         return FiberTrace.fromProfile(fiberId, detectorMap.bbox.getDimensions(), self.radius,
                                       self.oversample, self.rows, self.profiles, ~self.profiles.mask,
-                                      detectorMap.getXCenter(fiberId), self.norm)
+                                      detectorMap.getXCenter(fiberId),
+                                      self.norm.astype(np.float32) if self.norm is not None else None)
 
     def makeFiberTrace(self, dimensions, centerFunc, fiberId):
         """Make a FiberTrace object
@@ -244,7 +245,8 @@ def makeFiberTrace(self, dimensions, centerFunc, fiberId):
         """
         rows = np.arange(dimensions.getY(), dtype=float)
         return FiberTrace.fromProfile(fiberId, dimensions, self.radius, self.oversample, self.rows,
-                                      self.profiles, ~self.profiles.mask, centerFunc(rows), self.norm)
+                                      self.profiles, ~self.profiles.mask, centerFunc(rows),
+                                      self.norm.astype(np.float32) if self.norm is not None else None)
 
     def extractSpectrum(self, maskedImage, detectorMap, fiberId):
         """Extract a single spectrum from an image
diff --git a/python/pfs/drp/stella/findLines.py b/python/pfs/drp/stella/findLines.py
index 9fb57cda1..1fa4bb377 100644
--- a/python/pfs/drp/stella/findLines.py
+++ b/python/pfs/drp/stella/findLines.py
@@ -125,7 +125,7 @@ def convolve(self, spectrum, continuum=None):
         size = 2*halfSize + 1
         xx = np.arange(size, dtype=float) - halfSize
         sigma = self.config.width
-        kernel = np.exp(-0.5*xx**2/sigma**2)/sigma/np.sqrt(2.0*np.pi)
+        kernel = (np.exp(-0.5*xx**2/sigma**2)/sigma/np.sqrt(2.0*np.pi)).astype(spectrum.flux.dtype)
 
         flux = np.convolve(spectrum.normFlux if continuum is None else spectrum.normFlux - continuum,
                            kernel, mode="same")
diff --git a/python/pfs/drp/stella/fitContinuum.py b/python/pfs/drp/stella/fitContinuum.py
index d8fa58565..bdf5e4948 100644
--- a/python/pfs/drp/stella/fitContinuum.py
+++ b/python/pfs/drp/stella/fitContinuum.py
@@ -141,13 +141,13 @@ def _fitContinuumImpl(self, values, good):
         fit : `numpy.ndarray`, floating-point
             Fit array.
         """
-        indices = np.arange(len(values), dtype=float)
+        indices = np.arange(len(values), dtype=values.dtype)
         knots, binned = binData(indices, values, good, self.config.numKnots)
         use = np.isfinite(knots) & np.isfinite(binned)
         if not np.any(use):
             raise FitContinuumError("No finite knots when fitting continuum")
         interp = makeInterpolate(knots[use], binned[use], self.fitType)
-        fit = np.array(interp.interpolate(indices))
+        fit = np.array(interp.interpolate(indices)).astype(values.dtype)
 
         if lsstDebug.Info(__name__).plot:
             import matplotlib.pyplot as plt
@@ -285,4 +285,4 @@ def binData(xx, yy, good, numBins):
         select = good[low:high]
         xBinned[ii] = np.median(xx[low:high][select]) if np.any(select) else np.nan
         yBinned[ii] = np.median(yy[low:high][select]) if np.any(select) else np.nan
-    return xBinned, yBinned
+    return xBinned.astype(xx.dtype), yBinned.astype(yy.dtype)
diff --git a/python/pfs/drp/stella/fitLine.cc b/python/pfs/drp/stella/fitLine.cc
index df08a6f13..bfdb36486 100644
--- a/python/pfs/drp/stella/fitLine.cc
+++ b/python/pfs/drp/stella/fitLine.cc
@@ -36,9 +36,10 @@ PYBIND11_PLUGIN(fitLine) {
     lsst::utils::python::addOutputOp(cls, "__repr__");
 
     mod.def("fitLine",
-            py::overload_cast<ndarray::Array<double const, 1, 1> const&,
+            py::overload_cast<ndarray::Array<Spectrum::ImageT const, 1, 1> const&,
                               ndarray::Array<lsst::afw::image::MaskPixel const, 1, 1> const&,
-                              float, float, lsst::afw::image::MaskPixel, std::size_t>(&fitLine<double>),
+                              float, float, lsst::afw::image::MaskPixel,
+                              std::size_t>(&fitLine<Spectrum::ImageT>),
             "flux"_a, "mask"_a, "peakPosition"_a, "rmsSize"_a, "badBitMask"_a,
             "fittingHalfSize"_a=0);
 
diff --git a/python/pfs/drp/stella/mergeArms.py b/python/pfs/drp/stella/mergeArms.py
index 26861dddd..67ab8ea5b 100644
--- a/python/pfs/drp/stella/mergeArms.py
+++ b/python/pfs/drp/stella/mergeArms.py
@@ -328,7 +328,7 @@ def normalizeSpectra(self, spectra):
         assert all(np.all(ss.fiberId == fiberId) for ss in spectra)  # Consistent fibers
 
         # Collect normalisations from each arm, interpolated to common wavelength sampling
-        norm = np.zeros((fiberId.size, wavelength.size))
+        norm = np.zeros((fiberId.size, wavelength.size), dtype=np.float32)
         for ss in spectra:
             badBitmask = ss.flags.get(*self.config.mask)
             for ii in range(len(ss)):
diff --git a/python/pfs/drp/stella/symmetricTridiagonal.cc b/python/pfs/drp/stella/symmetricTridiagonal.cc
index 10a029853..1ceabc781 100644
--- a/python/pfs/drp/stella/symmetricTridiagonal.cc
+++ b/python/pfs/drp/stella/symmetricTridiagonal.cc
@@ -16,8 +16,13 @@ namespace {
 
 template <typename T>
 void declareSymmetricTridiagonal(py::module &mod, std::string const& suffix) {
-    py::class_<SymmetricTridiagonalWorkspace<T>> Workspace(
+    py::class_<SymmetricTridiagonalWorkspace<T>> cls(
         mod, ("SymmetricTridiagonalWorkspace" + suffix).c_str());
+    cls.def(py::init<>());
+    cls.def("reset", &SymmetricTridiagonalWorkspace<T>::reset, "num"_a);
+    cls.def_readonly("longArray1", &SymmetricTridiagonalWorkspace<T>::longArray1);
+    cls.def_readonly("longArray2", &SymmetricTridiagonalWorkspace<T>::longArray2);
+    cls.def_readonly("shortArray", &SymmetricTridiagonalWorkspace<T>::shortArray);
 
     mod.def(("solveSymmetricTridiagonal" + suffix).c_str(), &solveSymmetricTridiagonal<T>,
             "diagonal"_a, "offDiag"_a, "answer"_a, "workspace"_a=SymmetricTridiagonalWorkspace<T>());
diff --git a/python/pfs/drp/stella/symmetricTridiagonal.pyi b/python/pfs/drp/stella/symmetricTridiagonal.pyi
new file mode 100644
index 000000000..887233295
--- /dev/null
+++ b/python/pfs/drp/stella/symmetricTridiagonal.pyi
@@ -0,0 +1,22 @@
+from typing import Optional
+
+import numpy as np
+
+class SymmetricTridiagonalWorkspace:
+    def __init__(self): ...
+    def reset(self, num: int): ...
+    longArray1: np.ndarray
+    longArray2: np.ndarray
+    shortArray: np.ndarray
+
+def solveSymmetricTridiagonal(
+    diagonal: np.ndarray,
+    offDiag: np.ndarray,
+    answer: np.ndarray,
+    workspace: Optional[SymmetricTridiagonalWorkspace] = None,
+) -> np.ndarray: ...
+def invertSymmetricTridiagonal(
+    diagonal: np.ndarray,
+    offDiag: np.ndarray,
+    workspace: Optional[SymmetricTridiagonalWorkspace] = None,
+) -> np.ndarray: ...
diff --git a/src/FiberTrace.cc b/src/FiberTrace.cc
index e1fd62c17..ba2fca83e 100644
--- a/src/FiberTrace.cc
+++ b/src/FiberTrace.cc
@@ -82,7 +82,7 @@ FiberTrace<ImageT, MaskT, VarianceT> FiberTrace<ImageT, MaskT, VarianceT>::fromP
     ndarray::Array<double, 2, 1> const& profiles,
     ndarray::Array<bool, 2, 1> const& good,
     ndarray::Array<double, 1, 1> const& centers,
-    ndarray::Array<double, 1, 1> const& norm
+    ndarray::Array<Spectrum::ImageT, 1, 1> const& norm
 ) {
     int const width = dims.getX();
     std::size_t const height = dims.getY();
diff --git a/src/math/symmetricTridiagonal.cc b/src/math/symmetricTridiagonal.cc
index fd600872b..22603de4b 100644
--- a/src/math/symmetricTridiagonal.cc
+++ b/src/math/symmetricTridiagonal.cc
@@ -1,6 +1,8 @@
+#include "unordered_set"
 #include "ndarray.h"
 #include "lsst/pex/exceptions.h"
 #include "pfs/drp/stella/math/symmetricTridiagonal.h"
+#include "pfs/drp/stella/utils/checkSize.h"
 
 namespace pfs {
 namespace drp {
@@ -36,12 +38,11 @@ ndarray::Array<T, 1, 1> solveSymmetricTridiagonal(
     SymmetricTridiagonalWorkspace<T> & workspace
 ) {
     std::size_t const num = diagonal.getNumElements();  // number of elements
+    utils::checkSize(offDiag.getNumElements(), num - 1, "diagonal vs offDiag");
+    utils::checkSize(answer.getNumElements(), num, "diagonal vs answer");
     std::size_t const last = num - 1;  // index of last element
     std::size_t const penultimate = num - 2;  // index of penultimate element
 
-    assert(offDiag.getNumElements() == num - 1);
-    assert(answer.getNumElements() == num);
-
     workspace.reset(num);
     auto & cPrime = workspace.shortArray;
     auto & dPrime = workspace.longArray1;
@@ -56,19 +57,40 @@ ndarray::Array<T, 1, 1> solveSymmetricTridiagonal(
         return solution;
     }
 
+    std::unordered_set<std::size_t> singular;
     cPrime[0] = offDiag[0]/diagonal[0];
     dPrime[0] = answer[0]/diagonal[0];
     for (std::size_t ii = 1, jj = 0; ii < last; ++ii, ++jj) {  // jj = ii - 1
-        T const denominator = diagonal[ii] - offDiag[jj]*cPrime[jj];
+        double const denominator = diagonal[ii] - offDiag[jj]*cPrime[jj];
+        if (denominator == 0.0) {
+            // Singularity detected. Excise this element so that it won't affect everything else.
+            // Pretend that diagonal[ii] = 1, offDiag[jj] = 0, answer[ii] = 0.
+            cPrime[ii] = 0.0;
+            dPrime[ii] = 0.0;
+            singular.insert(ii);
+            continue;
+        }
         cPrime[ii] = offDiag[ii]/denominator;
         dPrime[ii] = (answer[ii] - offDiag[jj]*dPrime[jj])/denominator;
     }
-    T const denominator = diagonal[last] - offDiag[penultimate]*cPrime[penultimate];
-    dPrime[last] = (answer[last] - offDiag[penultimate]*dPrime[penultimate])/denominator;
+    double const denominator = diagonal[last] - offDiag[penultimate]*cPrime[penultimate];
+    if (denominator == 0.0) {
+        // Singularity detected. Excise this element so that it won't affect everything else.
+        // Pretend that diagonal[last] = 1, offDiag[penultimate] = 0, answer[last] = 0.
+        dPrime[last] = 0.0;
+        singular.insert(last);
+    } else {
+        dPrime[last] = (answer[last] - offDiag[penultimate]*dPrime[penultimate])/denominator;
+    }
 
     solution[last] = dPrime[last];
     for (std::ptrdiff_t ii = penultimate, jj = last; ii >= 0; --ii, --jj) {  // jj = ii + 1
-        solution[ii] = (dPrime[ii] - cPrime[ii]*solution[jj]);
+        solution[ii] = dPrime[ii] - cPrime[ii]*solution[jj];
+    }
+
+    constexpr double nan = std::numeric_limits<T>::quiet_NaN();
+    for (auto const ii: singular) {
+        solution[ii] = nan;
     }
 
     return solution;
diff --git a/tests/test_PfsArm.py b/tests/test_PfsArm.py
index a1bf0b586..3146423aa 100644
--- a/tests/test_PfsArm.py
+++ b/tests/test_PfsArm.py
@@ -30,11 +30,11 @@ def setUp(self):
         self.identity = Identity(self.visit, self.arm, self.spectrograph, self.pfsDesignId)
         self.fiberId = self.synthConfig.fiberId
         self.wavelength = np.vstack([np.linspace(600, 900, self.synthConfig.height)]*num)
-        self.flux = self.rng.uniform(size=shape)
-        self.mask = self.rng.uniform(high=2**31, size=shape).astype(np.int32)
-        self.sky = self.rng.uniform(size=shape)
-        self.norm = self.rng.uniform(size=shape)
-        self.covar = self.rng.uniform(size=(num, 3, self.synthConfig.height))
+        self.flux = self.rng.uniform(size=shape).astype(np.float32)
+        self.mask = self.rng.uniform(high=2**31, size=shape).astype(np.uint32)
+        self.sky = self.rng.uniform(size=shape).astype(np.float32)
+        self.norm = self.rng.uniform(size=shape).astype(np.float32)
+        self.covar = self.rng.uniform(size=(num, 3, self.synthConfig.height)).astype(np.float32)
         self.flags = MaskHelper()
         self.metadata = dict(FOO=12345, BAR=0.9876)  # FITS keywords get capitalised
 
@@ -48,9 +48,9 @@ def makeSpectra(self):
     def assertSpectra(self, spectra):
         """Check that the spectra match what's expected"""
         for name in ("visit", "arm", "spectrograph", "pfsDesignId"):
-            self.assertEqual(getattr(spectra.identity, name), getattr(self, name))
+            self.assertEqual(getattr(spectra.identity, name), getattr(self, name), msg=name)
         for name in ("fiberId", "wavelength", "flux", "mask", "sky", "norm", "covar"):
-            self.assertFloatsEqual(getattr(spectra, name), getattr(self, name))
+            self.assertFloatsEqual(getattr(spectra, name), getattr(self, name), msg=name)
         self.assertDictEqual(spectra.flags.flags, self.flags.flags)
         self.assertDictEqual({**self.metadata, **spectra.metadata}, spectra.metadata)
 
diff --git a/tests/test_Spectrum.py b/tests/test_Spectrum.py
index de7281b63..ed5417d26 100644
--- a/tests/test_Spectrum.py
+++ b/tests/test_Spectrum.py
@@ -23,12 +23,12 @@ def setUp(self):
         # Spectrum
         self.length = 123
         self.fiberId = 456
-        self.image = self.rng.uniform(size=self.length).astype(float)
+        self.image = self.rng.uniform(size=self.length).astype(np.float32)
         self.mask = lsst.afw.image.Mask(self.length, 1)
         self.mask.array[:] = self.rng.randint(0, 2**30, self.length).astype(np.int32)
-        self.background = self.rng.uniform(size=self.length).astype(float)
-        self.norm = self.rng.uniform(size=self.length).astype(float)
-        self.covariance = self.rng.uniform(size=(3, self.length)).astype(float)
+        self.background = self.rng.uniform(size=self.length).astype(np.float32)
+        self.norm = self.rng.uniform(size=self.length).astype(np.float32)
+        self.covariance = self.rng.uniform(size=(3, self.length)).astype(np.float32)
         self.wavelengthArray = np.arange(1, self.length + 1, dtype=float)
 
     def makeSpectrum(self):
@@ -145,7 +145,7 @@ def testBasics(self):
         # Set the variance and ensure it changes the covariance
         spectrum.covariance[:] = self.covariance
         self.assertFloatsEqual(spectrum.covariance, self.covariance)
-        variance = self.rng.uniform(size=self.length)
+        variance = self.rng.uniform(size=self.length).astype(np.float32)
         spectrum.variance = variance
         self.covariance[0] = variance
         self.assertFloatsEqual(spectrum.covariance, self.covariance)
diff --git a/tests/test_SpectrumSet.py b/tests/test_SpectrumSet.py
index 84ecbddbe..0c2154ec5 100644
--- a/tests/test_SpectrumSet.py
+++ b/tests/test_SpectrumSet.py
@@ -21,12 +21,12 @@ def setUp(self):
         # Spectrum
         self.length = 123
         self.fiberId = 456
-        self.image = self.rng.uniform(size=self.length).astype(float)
+        self.image = self.rng.uniform(size=self.length).astype(np.float32)
         self.mask = lsst.afw.image.Mask(self.length, 1)
         self.mask.array[:] = self.rng.randint(0, 2**30, self.length).astype(np.int32)
-        self.background = self.rng.uniform(size=self.length).astype(float)
-        self.norm = self.rng.uniform(size=self.length).astype(float)
-        self.covariance = self.rng.uniform(size=(3, self.length)).astype(float)
+        self.background = self.rng.uniform(size=self.length).astype(np.float32)
+        self.norm = self.rng.uniform(size=self.length).astype(np.float32)
+        self.covariance = self.rng.uniform(size=(3, self.length)).astype(np.float32)
         self.wavelengthArray = np.arange(1, self.length + 1, dtype=float)
 
     def makeSpectrum(self):
diff --git a/tests/test_extractSpectra.py b/tests/test_extractSpectra.py
index aaa10f46e..0ad1c4506 100644
--- a/tests/test_extractSpectra.py
+++ b/tests/test_extractSpectra.py
@@ -37,7 +37,7 @@ def setUp(self):
             lsst.afw.image.makeExposure(self.image), detectorMap=self.detMap
         ).profiles
         for fiberId in self.fiberProfiles:
-            self.fiberProfiles[fiberId].norm = np.full(self.synthConfig.height, self.flux, dtype=float)
+            self.fiberProfiles[fiberId].norm = np.full(self.synthConfig.height, self.flux, dtype=np.float32)
         self.fiberTraces = self.fiberProfiles.makeFiberTracesFromDetectorMap(self.detMap)
         self.assertEqual(len(self.fiberTraces), self.synthConfig.numFibers)
 
@@ -78,7 +78,7 @@ def assertSpectra(self, spectra, flux=None, mask=None):
                 expectMask = 0
 
             bbox = ft.trace.getBBox()
-            expectNorm = np.zeros(self.synthConfig.height, dtype=float)
+            expectNorm = np.zeros(self.synthConfig.height, dtype=np.float32)
             expectNorm[bbox.getMinY():bbox.getMaxY() + 1] = ft.trace.image.array.sum(axis=1)
 
             self.assertEqual(ss.fiberId, ft.fiberId)
@@ -127,7 +127,7 @@ def testUndersizedFiberTrace(self):
         newTrace = type(trace)(trace.trace.Factory(trace.trace, newBox), trace.fiberId)
         self.fiberTraces[index] = newTrace
         spectra = self.fiberTraces.extractSpectra(self.image)
-        expectFlux = np.zeros(self.synthConfig.height, dtype=float)
+        expectFlux = np.zeros(self.synthConfig.height, dtype=np.float32)
         expectFlux[middle:] = self.flux
         expectMask = np.zeros(self.synthConfig.height, dtype=np.int32)
         expectMask[:middle] = trace.trace.mask.getPlaneBitMask("NO_DATA")
@@ -138,7 +138,7 @@ def testUndersizedFiberTrace(self):
         newTrace = type(trace)(trace.trace.Factory(trace.trace, newBox), trace.fiberId)
         self.fiberTraces[index] = newTrace
         spectra = self.fiberTraces.extractSpectra(self.image)
-        expectFlux = np.zeros(self.synthConfig.height, dtype=float)
+        expectFlux = np.zeros(self.synthConfig.height, dtype=np.float32)
         expectFlux[:middle] = self.flux
         expectMask = np.zeros(self.synthConfig.height, dtype=np.int32)
         expectMask[middle:] = trace.trace.mask.getPlaneBitMask("NO_DATA")
@@ -155,7 +155,7 @@ def testSingular(self):
         index = self.synthConfig.numFibers//2
         row = self.synthConfig.height//2
         fiberId = self.synthConfig.fiberId[index]
-        expectFlux = np.full(self.synthConfig.height, self.flux, dtype=float)
+        expectFlux = np.full(self.synthConfig.height, self.flux, dtype=np.float32)
         expectMask = np.zeros(self.synthConfig.height, dtype=np.int32)
         expectFlux[row] = 0.0
         expectMask[row] = self.image.mask.getPlaneBitMask(["BAD_FIBERTRACE", "NO_DATA"])
diff --git a/tests/test_fitLine.py b/tests/test_fitLine.py
index 1c71f5878..8e8499aef 100644
--- a/tests/test_fitLine.py
+++ b/tests/test_fitLine.py
@@ -61,7 +61,7 @@ def makeSpectrum(length, center, amplitude, rmsSize, bgConst=0.0, bgSlope=0.0):
     return spectrum
 
 
-class FindLinesTestCase(lsst.utils.tests.TestCase):
+class FitLinesTestCase(lsst.utils.tests.TestCase):
     def setUp(self):
         self.length = 256
         self.center = 123.45
diff --git a/tests/test_profileNorm.py b/tests/test_profileNorm.py
index a3707c585..3d5ab2cba 100644
--- a/tests/test_profileNorm.py
+++ b/tests/test_profileNorm.py
@@ -59,7 +59,7 @@ def testProfileNorm(self):
         newSpectra = traces.extractSpectra(image)
         for new, old in zip(newSpectra, spectra):
             self.assertFloatsAlmostEqual(new.norm, old.normFlux, rtol=1.0e-7)
-            self.assertFloatsAlmostEqual(new.normFlux, 1.0, atol=1.0e-7)
+            self.assertFloatsAlmostEqual(new.normFlux, 1.0, atol=1.0e-6)
 
 
 class TestMemory(lsst.utils.tests.MemoryTestCase):
diff --git a/tests/test_symmetricTridiagonal.py b/tests/test_symmetricTridiagonal.py
index 73eeff89c..34ac0f7a8 100644
--- a/tests/test_symmetricTridiagonal.py
+++ b/tests/test_symmetricTridiagonal.py
@@ -91,6 +91,62 @@ def testSolve(self):
         for size in (10, 100, 1000):
             self.checkSolve(size, rng)
 
+    def testSingular(self):
+        """Test that we can solve singular matrices
+
+        These values are taken from fiber indices 510 through 519 of
+        visit=76003 at y=1025, where a cosmic ray has wiped out data and left
+        only a single pixel between fiber indices 515 and 516, the full value of
+        which is claimed by both.
+        """
+        diagonal = np.array(
+            [
+                2.04603214245271892e-01,
+                1.77478682035331681e-01,
+                1.86878709397182152e-01,
+                2.30714251670864207e-01,
+                1.93489959968508124e-01,
+                2.72308226631381165e-04,
+                2.74896376556077015e-04,
+                2.33667285475434305e-01,
+                2.31162677238954783e-01,
+                2.31444225252564806e-01,
+            ]
+        )
+        offDiag = np.array(
+            [
+                8.29542189990942528e-04,
+                1.50040111291657426e-03,
+                7.35440581909623209e-04,
+                5.02985261367372362e-04,
+                0.00000000000000000e00,
+                2.73599241240500741e-04,
+                0.00000000000000000e00,
+                3.89897626215648507e-04,
+                3.69925928467314269e-04,
+            ]
+        )
+        answer = np.array(
+            [
+                2.28096719322151216e02,
+                1.88301068255664319e02,
+                1.72575595095778453e02,
+                2.59294852978659037e02,
+                1.90605045408182889e02,
+                2.92346131950238675e-01,
+                2.93732146364626023e-01,
+                2.55098123020953864e02,
+                2.74973877207476960e02,
+                2.50663980370680378e02,
+            ]
+        )
+        self.assertEqual(diagonal[5]*diagonal[6] - offDiag[5]**2, 0.0)  # Singular
+        solution = solveSymmetricTridiagonal(diagonal, offDiag, answer)
+        good = np.ones_like(solution, dtype=bool)
+        good[6] = False
+        self.assertTrue(np.all(np.isfinite(solution[good])))
+        self.assertTrue(np.all(np.isnan(solution[~good])))
+
 
 class TestMemory(lsst.utils.tests.MemoryTestCase):
     pass
@@ -103,6 +159,7 @@ def setup_module(module):
 if __name__ == "__main__":
     setup_module(sys.modules["__main__"])
     from argparse import ArgumentParser
+
     parser = ArgumentParser(__file__)
     parser.add_argument("--display", help="Display backend")
     args, argv = parser.parse_known_args()