--- a/liboctave/numeric/oct-norm.cc	Thu Dec 01 14:23:45 2022 -0800
+++ b/liboctave/numeric/oct-norm.cc	Thu Dec 01 18:02:15 2022 -0800
@@ -65,261 +65,261 @@
 
 OCTAVE_BEGIN_NAMESPACE(octave)
 
-  // Theory: norm accumulator is an object that has an accum method able
-  // to handle both real and complex element, and a cast operator
-  // returning the intermediate norm.  Reference: Higham, N. "Estimating
-  // the Matrix p-Norm." Numer. Math. 62, 539-555, 1992.
+// Theory: norm accumulator is an object that has an accum method able
+// to handle both real and complex element, and a cast operator
+// returning the intermediate norm.  Reference: Higham, N. "Estimating
+// the Matrix p-Norm." Numer. Math. 62, 539-555, 1992.
 
-  // norm accumulator for the p-norm
-  template <typename R>
-  class norm_accumulator_p
+// norm accumulator for the p-norm
+template <typename R>
+class norm_accumulator_p
+{
+public:
+  norm_accumulator_p () { } // we need this one for Array
+  norm_accumulator_p (R pp) : m_p(pp), m_scl(0), m_sum(1) { }
+
+  template <typename U>
+  void accum (U val)
   {
-  public:
-    norm_accumulator_p () { } // we need this one for Array
-    norm_accumulator_p (R pp) : m_p(pp), m_scl(0), m_sum(1) { }
-
-    template <typename U>
-    void accum (U val)
-    {
-      octave_quit ();
-      R t = std::abs (val);
-      if (m_scl == t) // we need this to handle Infs properly
+    octave_quit ();
+    R t = std::abs (val);
+    if (m_scl == t) // we need this to handle Infs properly
+      m_sum += 1;
+    else if (m_scl < t)
+      {
+        m_sum *= std::pow (m_scl/t, m_p);
         m_sum += 1;
-      else if (m_scl < t)
-        {
-          m_sum *= std::pow (m_scl/t, m_p);
-          m_sum += 1;
-          m_scl = t;
-        }
-      else if (t != 0)
-        m_sum += std::pow (t/m_scl, m_p);
-    }
+        m_scl = t;
+      }
+    else if (t != 0)
+      m_sum += std::pow (t/m_scl, m_p);
+  }
+
+  operator R () { return m_scl * std::pow (m_sum, 1/m_p); }
 
-    operator R () { return m_scl * std::pow (m_sum, 1/m_p); }
+private:
+  R m_p, m_scl, m_sum;
+};
+
+// norm accumulator for the minus p-pseudonorm
+template <typename R>
+class norm_accumulator_mp
+{
+public:
+  norm_accumulator_mp () { } // we need this one for Array
+  norm_accumulator_mp (R pp) : m_p(pp), m_scl(0), m_sum(1) { }
 
-  private:
-    R m_p, m_scl, m_sum;
-  };
-
-  // norm accumulator for the minus p-pseudonorm
-  template <typename R>
-  class norm_accumulator_mp
+  template <typename U>
+  void accum (U val)
   {
-  public:
-    norm_accumulator_mp () { } // we need this one for Array
-    norm_accumulator_mp (R pp) : m_p(pp), m_scl(0), m_sum(1) { }
+    octave_quit ();
+    R t = 1 / std::abs (val);
+    if (m_scl == t)
+      m_sum += 1;
+    else if (m_scl < t)
+      {
+        m_sum *= std::pow (m_scl/t, m_p);
+        m_sum += 1;
+        m_scl = t;
+      }
+    else if (t != 0)
+      m_sum += std::pow (t/m_scl, m_p);
+  }
+
+  operator R () { return m_scl * std::pow (m_sum, -1/m_p); }
 
-    template <typename U>
-    void accum (U val)
-    {
-      octave_quit ();
-      R t = 1 / std::abs (val);
-      if (m_scl == t)
+private:
+  R m_p, m_scl, m_sum;
+};
+
+// norm accumulator for the 2-norm (euclidean)
+template <typename R>
+class norm_accumulator_2
+{
+public:
+  norm_accumulator_2 () : m_scl(0), m_sum(1) { }
+
+  void accum (R val)
+  {
+    R t = std::abs (val);
+    if (m_scl == t)
+      m_sum += 1;
+    else if (m_scl < t)
+      {
+        m_sum *= pow2 (m_scl/t);
         m_sum += 1;
-      else if (m_scl < t)
-        {
-          m_sum *= std::pow (m_scl/t, m_p);
-          m_sum += 1;
-          m_scl = t;
-        }
-      else if (t != 0)
-        m_sum += std::pow (t/m_scl, m_p);
-    }
+        m_scl = t;
+      }
+    else if (t != 0)
+      m_sum += pow2 (t/m_scl);
+  }
+
+  void accum (std::complex<R> val)
+  {
+    accum (val.real ());
+    accum (val.imag ());
+  }
+
+  operator R () { return m_scl * std::sqrt (m_sum); }
+
+private:
+  static inline R pow2 (R x) { return x*x; }
+
+  //--------
+
+  R m_scl, m_sum;
+};
 
-    operator R () { return m_scl * std::pow (m_sum, -1/m_p); }
+// norm accumulator for the 1-norm (city metric)
+template <typename R>
+class norm_accumulator_1
+{
+public:
+  norm_accumulator_1 () : m_sum (0) { }
+  template <typename U>
+  void accum (U val)
+  {
+    m_sum += std::abs (val);
+  }
+
+  operator R () { return m_sum; }
+
+private:
+  R m_sum;
+};
+
+// norm accumulator for the inf-norm (max metric)
+template <typename R>
+class norm_accumulator_inf
+{
+public:
+  norm_accumulator_inf () : m_max (0) { }
+  template <typename U>
+  void accum (U val)
+  {
+    if (math::isnan (val))
+      m_max = numeric_limits<R>::NaN ();
+    else
+      m_max = std::max (m_max, std::abs (val));
+  }
+
+  operator R () { return m_max; }
 
-  private:
-    R m_p, m_scl, m_sum;
-  };
+private:
+  R m_max;
+};
+
+// norm accumulator for the -inf pseudonorm (min abs value)
+template <typename R>
+class norm_accumulator_minf
+{
+public:
+  norm_accumulator_minf () : m_min (numeric_limits<R>::Inf ()) { }
+  template <typename U>
+  void accum (U val)
+  {
+    if (math::isnan (val))
+      m_min = numeric_limits<R>::NaN ();
+    else
+      m_min = std::min (m_min, std::abs (val));
+  }
+
+  operator R () { return m_min; }
+
+private:
+  R m_min;
+};
 
-  // norm accumulator for the 2-norm (euclidean)
-  template <typename R>
-  class norm_accumulator_2
+// norm accumulator for the 0-pseudonorm (hamming distance)
+template <typename R>
+class norm_accumulator_0
+{
+public:
+  norm_accumulator_0 () : m_num (0) { }
+  template <typename U>
+  void accum (U val)
   {
-  public:
-    norm_accumulator_2 () : m_scl(0), m_sum(1) { }
+    if (val != static_cast<U> (0)) ++m_num;
+  }
+
+  operator R () { return m_num; }
+
+private:
+  unsigned int m_num;
+};
+
+// OK, we're armed :) Now let's go for the fun
 
-    void accum (R val)
+template <typename T, typename R, typename ACC>
+inline void vector_norm (const Array<T>& v, R& res, ACC acc)
+{
+  for (octave_idx_type i = 0; i < v.numel (); i++)
+    acc.accum (v(i));
+
+  res = acc;
+}
+
+// dense versions
+template <typename T, typename R, typename ACC>
+void column_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
+{
+  res = MArray<R> (dim_vector (1, m.columns ()));
+  for (octave_idx_type j = 0; j < m.columns (); j++)
     {
-      R t = std::abs (val);
-      if (m_scl == t)
-        m_sum += 1;
-      else if (m_scl < t)
-        {
-          m_sum *= pow2 (m_scl/t);
-          m_sum += 1;
-          m_scl = t;
-        }
-      else if (t != 0)
-        m_sum += pow2 (t/m_scl);
+      ACC accj = acc;
+      for (octave_idx_type i = 0; i < m.rows (); i++)
+        accj.accum (m(i, j));
+
+      res.xelem (j) = accj;
     }
-
-    void accum (std::complex<R> val)
-    {
-      accum (val.real ());
-      accum (val.imag ());
-    }
+}
 
-    operator R () { return m_scl * std::sqrt (m_sum); }
-
-  private:
-    static inline R pow2 (R x) { return x*x; }
-
-    //--------
-
-    R m_scl, m_sum;
-  };
-
-  // norm accumulator for the 1-norm (city metric)
-  template <typename R>
-  class norm_accumulator_1
-  {
-  public:
-    norm_accumulator_1 () : m_sum (0) { }
-    template <typename U>
-    void accum (U val)
+template <typename T, typename R, typename ACC>
+void row_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
+{
+  res = MArray<R> (dim_vector (m.rows (), 1));
+  std::vector<ACC> acci (m.rows (), acc);
+  for (octave_idx_type j = 0; j < m.columns (); j++)
     {
-      m_sum += std::abs (val);
+      for (octave_idx_type i = 0; i < m.rows (); i++)
+        acci[i].accum (m(i, j));
     }
 
-    operator R () { return m_sum; }
-
-  private:
-    R m_sum;
-  };
-
-  // norm accumulator for the inf-norm (max metric)
-  template <typename R>
-  class norm_accumulator_inf
-  {
-  public:
-    norm_accumulator_inf () : m_max (0) { }
-    template <typename U>
-    void accum (U val)
-    {
-      if (math::isnan (val))
-        m_max = numeric_limits<R>::NaN ();
-      else
-        m_max = std::max (m_max, std::abs (val));
-    }
-
-    operator R () { return m_max; }
-
-  private:
-    R m_max;
-  };
+  for (octave_idx_type i = 0; i < m.rows (); i++)
+    res.xelem (i) = acci[i];
+}
 
-  // norm accumulator for the -inf pseudonorm (min abs value)
-  template <typename R>
-  class norm_accumulator_minf
-  {
-  public:
-    norm_accumulator_minf () : m_min (numeric_limits<R>::Inf ()) { }
-    template <typename U>
-    void accum (U val)
+// sparse versions
+template <typename T, typename R, typename ACC>
+void column_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
+{
+  res = MArray<R> (dim_vector (1, m.columns ()));
+  for (octave_idx_type j = 0; j < m.columns (); j++)
     {
-      if (math::isnan (val))
-        m_min = numeric_limits<R>::NaN ();
-      else
-        m_min = std::min (m_min, std::abs (val));
-    }
+      ACC accj = acc;
+      for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
+        accj.accum (m.data (k));
 
-    operator R () { return m_min; }
-
-  private:
-    R m_min;
-  };
+      res.xelem (j) = accj;
+    }
+}
 
-  // norm accumulator for the 0-pseudonorm (hamming distance)
-  template <typename R>
-  class norm_accumulator_0
-  {
-  public:
-    norm_accumulator_0 () : m_num (0) { }
-    template <typename U>
-    void accum (U val)
+template <typename T, typename R, typename ACC>
+void row_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
+{
+  res = MArray<R> (dim_vector (m.rows (), 1));
+  std::vector<ACC> acci (m.rows (), acc);
+  for (octave_idx_type j = 0; j < m.columns (); j++)
     {
-      if (val != static_cast<U> (0)) ++m_num;
+      for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
+        acci[m.ridx (k)].accum (m.data (k));
     }
 
-    operator R () { return m_num; }
-
-  private:
-    unsigned int m_num;
-  };
-
-  // OK, we're armed :) Now let's go for the fun
-
-  template <typename T, typename R, typename ACC>
-  inline void vector_norm (const Array<T>& v, R& res, ACC acc)
-  {
-    for (octave_idx_type i = 0; i < v.numel (); i++)
-      acc.accum (v(i));
-
-    res = acc;
-  }
-
-  // dense versions
-  template <typename T, typename R, typename ACC>
-  void column_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
-  {
-    res = MArray<R> (dim_vector (1, m.columns ()));
-    for (octave_idx_type j = 0; j < m.columns (); j++)
-      {
-        ACC accj = acc;
-        for (octave_idx_type i = 0; i < m.rows (); i++)
-          accj.accum (m(i, j));
-
-        res.xelem (j) = accj;
-      }
-  }
+  for (octave_idx_type i = 0; i < m.rows (); i++)
+    res.xelem (i) = acci[i];
+}
 
-  template <typename T, typename R, typename ACC>
-  void row_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
-  {
-    res = MArray<R> (dim_vector (m.rows (), 1));
-    std::vector<ACC> acci (m.rows (), acc);
-    for (octave_idx_type j = 0; j < m.columns (); j++)
-      {
-        for (octave_idx_type i = 0; i < m.rows (); i++)
-          acci[i].accum (m(i, j));
-      }
-
-    for (octave_idx_type i = 0; i < m.rows (); i++)
-      res.xelem (i) = acci[i];
-  }
-
-  // sparse versions
-  template <typename T, typename R, typename ACC>
-  void column_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
-  {
-    res = MArray<R> (dim_vector (1, m.columns ()));
-    for (octave_idx_type j = 0; j < m.columns (); j++)
-      {
-        ACC accj = acc;
-        for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
-          accj.accum (m.data (k));
-
-        res.xelem (j) = accj;
-      }
-  }
-
-  template <typename T, typename R, typename ACC>
-  void row_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
-  {
-    res = MArray<R> (dim_vector (m.rows (), 1));
-    std::vector<ACC> acci (m.rows (), acc);
-    for (octave_idx_type j = 0; j < m.columns (); j++)
-      {
-        for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
-          acci[m.ridx (k)].accum (m.data (k));
-      }
-
-    for (octave_idx_type i = 0; i < m.rows (); i++)
-      res.xelem (i) = acci[i];
-  }
-
-  // now the dispatchers
+// now the dispatchers
 #define DEFINE_DISPATCHER(FCN_NAME, ARG_TYPE, RES_TYPE)         \
   template <typename T, typename R>                             \
   RES_TYPE FCN_NAME (const ARG_TYPE& v, R p)                    \
@@ -345,224 +345,224 @@
     return res;                                                 \
   }
 
-  DEFINE_DISPATCHER (vector_norm, MArray<T>, R)
-  DEFINE_DISPATCHER (column_norms, MArray<T>, MArray<R>)
-  DEFINE_DISPATCHER (row_norms, MArray<T>, MArray<R>)
-  DEFINE_DISPATCHER (column_norms, MSparse<T>, MArray<R>)
-  DEFINE_DISPATCHER (row_norms, MSparse<T>, MArray<R>)
+DEFINE_DISPATCHER (vector_norm, MArray<T>, R)
+DEFINE_DISPATCHER (column_norms, MArray<T>, MArray<R>)
+DEFINE_DISPATCHER (row_norms, MArray<T>, MArray<R>)
+DEFINE_DISPATCHER (column_norms, MSparse<T>, MArray<R>)
+DEFINE_DISPATCHER (row_norms, MSparse<T>, MArray<R>)
 
-  // The approximate subproblem in Higham's method.  Find lambda and mu such
-  // that norm ([lambda, mu], p) == 1 and norm (y*lambda + col*mu, p) is
-  // maximized.
-  // Real version.  As in Higham's paper.
-  template <typename ColVectorT, typename R>
-  static void
-  higham_subp (const ColVectorT& y, const ColVectorT& col,
-               octave_idx_type nsamp, R p, R& lambda, R& mu)
-  {
-    R nrm = 0;
-    for (octave_idx_type i = 0; i < nsamp; i++)
-      {
-        octave_quit ();
-        R fi = i * static_cast<R> (M_PI) / nsamp;
-        R lambda1 = cos (fi);
-        R mu1 = sin (fi);
-        R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
-                           std::pow (std::abs (mu1), p), 1/p);
-        lambda1 /= lmnr; mu1 /= lmnr;
-        R nrm1 = vector_norm (lambda1 * y + mu1 * col, p);
-        if (nrm1 > nrm)
-          {
-            lambda = lambda1;
-            mu = mu1;
-            nrm = nrm1;
-          }
-      }
-  }
+// The approximate subproblem in Higham's method.  Find lambda and mu such
+// that norm ([lambda, mu], p) == 1 and norm (y*lambda + col*mu, p) is
+// maximized.
+// Real version.  As in Higham's paper.
+template <typename ColVectorT, typename R>
+static void
+higham_subp (const ColVectorT& y, const ColVectorT& col,
+             octave_idx_type nsamp, R p, R& lambda, R& mu)
+{
+  R nrm = 0;
+  for (octave_idx_type i = 0; i < nsamp; i++)
+    {
+      octave_quit ();
+      R fi = i * static_cast<R> (M_PI) / nsamp;
+      R lambda1 = cos (fi);
+      R mu1 = sin (fi);
+      R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
+                         std::pow (std::abs (mu1), p), 1/p);
+      lambda1 /= lmnr; mu1 /= lmnr;
+      R nrm1 = vector_norm (lambda1 * y + mu1 * col, p);
+      if (nrm1 > nrm)
+        {
+          lambda = lambda1;
+          mu = mu1;
+          nrm = nrm1;
+        }
+    }
+}
 
-  // Complex version.  Higham's paper does not deal with complex case, so we
-  // use a simple extension.  First, guess the magnitudes as in real version,
-  // then try to rotate lambda to improve further.
-  template <typename ColVectorT, typename R>
-  static void
-  higham_subp (const ColVectorT& y, const ColVectorT& col,
-               octave_idx_type nsamp, R p,
-               std::complex<R>& lambda, std::complex<R>& mu)
-  {
-    typedef std::complex<R> CR;
-    R nrm = 0;
-    lambda = 1.0;
-    CR lamcu = lambda / std::abs (lambda);
-    // Probe magnitudes
-    for (octave_idx_type i = 0; i < nsamp; i++)
-      {
-        octave_quit ();
-        R fi = i * static_cast<R> (M_PI) / nsamp;
-        R lambda1 = cos (fi);
-        R mu1 = sin (fi);
-        R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
-                           std::pow (std::abs (mu1), p), 1/p);
-        lambda1 /= lmnr; mu1 /= lmnr;
-        R nrm1 = vector_norm (lambda1 * lamcu * y + mu1 * col, p);
-        if (nrm1 > nrm)
-          {
-            lambda = lambda1 * lamcu;
-            mu = mu1;
-            nrm = nrm1;
-          }
-      }
-    R lama = std::abs (lambda);
-    // Probe orientation
-    for (octave_idx_type i = 0; i < nsamp; i++)
-      {
-        octave_quit ();
-        R fi = i * static_cast<R> (M_PI) / nsamp;
-        lamcu = CR (cos (fi), sin (fi));
-        R nrm1 = vector_norm (lama * lamcu * y + mu * col, p);
-        if (nrm1 > nrm)
-          {
-            lambda = lama * lamcu;
-            nrm = nrm1;
-          }
-      }
-  }
+// Complex version.  Higham's paper does not deal with complex case, so we
+// use a simple extension.  First, guess the magnitudes as in real version,
+// then try to rotate lambda to improve further.
+template <typename ColVectorT, typename R>
+static void
+higham_subp (const ColVectorT& y, const ColVectorT& col,
+             octave_idx_type nsamp, R p,
+             std::complex<R>& lambda, std::complex<R>& mu)
+{
+  typedef std::complex<R> CR;
+  R nrm = 0;
+  lambda = 1.0;
+  CR lamcu = lambda / std::abs (lambda);
+  // Probe magnitudes
+  for (octave_idx_type i = 0; i < nsamp; i++)
+    {
+      octave_quit ();
+      R fi = i * static_cast<R> (M_PI) / nsamp;
+      R lambda1 = cos (fi);
+      R mu1 = sin (fi);
+      R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
+                         std::pow (std::abs (mu1), p), 1/p);
+      lambda1 /= lmnr; mu1 /= lmnr;
+      R nrm1 = vector_norm (lambda1 * lamcu * y + mu1 * col, p);
+      if (nrm1 > nrm)
+        {
+          lambda = lambda1 * lamcu;
+          mu = mu1;
+          nrm = nrm1;
+        }
+    }
+  R lama = std::abs (lambda);
+  // Probe orientation
+  for (octave_idx_type i = 0; i < nsamp; i++)
+    {
+      octave_quit ();
+      R fi = i * static_cast<R> (M_PI) / nsamp;
+      lamcu = CR (cos (fi), sin (fi));
+      R nrm1 = vector_norm (lama * lamcu * y + mu * col, p);
+      if (nrm1 > nrm)
+        {
+          lambda = lama * lamcu;
+          nrm = nrm1;
+        }
+    }
+}
 
-  // the p-dual element (should work for both real and complex)
-  template <typename T, typename R>
-  inline T elem_dual_p (T x, R p)
-  {
-    return math::signum (x) * std::pow (std::abs (x), p-1);
-  }
+// the p-dual element (should work for both real and complex)
+template <typename T, typename R>
+inline T elem_dual_p (T x, R p)
+{
+  return math::signum (x) * std::pow (std::abs (x), p-1);
+}
 
-  // the VectorT is used for vectors, but actually it has to be
-  // a Matrix type to allow all the operations.  For instance SparseMatrix
-  // does not support multiplication with column/row vectors.
-  // the dual vector
-  template <typename VectorT, typename R>
-  VectorT dual_p (const VectorT& x, R p, R q)
-  {
-    VectorT res (x.dims ());
-    for (octave_idx_type i = 0; i < x.numel (); i++)
-      res.xelem (i) = elem_dual_p (x(i), p);
-    return res / vector_norm (res, q);
-  }
+// the VectorT is used for vectors, but actually it has to be
+// a Matrix type to allow all the operations.  For instance SparseMatrix
+// does not support multiplication with column/row vectors.
+// the dual vector
+template <typename VectorT, typename R>
+VectorT dual_p (const VectorT& x, R p, R q)
+{
+  VectorT res (x.dims ());
+  for (octave_idx_type i = 0; i < x.numel (); i++)
+    res.xelem (i) = elem_dual_p (x(i), p);
+  return res / vector_norm (res, q);
+}
 
-  // Higham's hybrid method
-  template <typename MatrixT, typename VectorT, typename R>
-  R higham (const MatrixT& m, R p, R tol, int maxiter,
-            VectorT& x)
-  {
-    x.resize (m.columns (), 1);
-    // the OSE part
-    VectorT y(m.rows (), 1, 0), z(m.rows (), 1);
-    typedef typename VectorT::element_type RR;
-    RR lambda = 0;
-    RR mu = 1;
-    for (octave_idx_type k = 0; k < m.columns (); k++)
-      {
-        octave_quit ();
-        VectorT col (m.column (k));
-        if (k > 0)
-          higham_subp (y, col, 4*k, p, lambda, mu);
-        for (octave_idx_type i = 0; i < k; i++)
-          x(i) *= lambda;
-        x(k) = mu;
-        y = lambda * y + mu * col;
-      }
+// Higham's hybrid method
+template <typename MatrixT, typename VectorT, typename R>
+R higham (const MatrixT& m, R p, R tol, int maxiter,
+          VectorT& x)
+{
+  x.resize (m.columns (), 1);
+  // the OSE part
+  VectorT y(m.rows (), 1, 0), z(m.rows (), 1);
+  typedef typename VectorT::element_type RR;
+  RR lambda = 0;
+  RR mu = 1;
+  for (octave_idx_type k = 0; k < m.columns (); k++)
+    {
+      octave_quit ();
+      VectorT col (m.column (k));
+      if (k > 0)
+        higham_subp (y, col, 4*k, p, lambda, mu);
+      for (octave_idx_type i = 0; i < k; i++)
+        x(i) *= lambda;
+      x(k) = mu;
+      y = lambda * y + mu * col;
+    }
 
-    // the PM part
-    x = x / vector_norm (x, p);
-    R q = p/(p-1);
+  // the PM part
+  x = x / vector_norm (x, p);
+  R q = p/(p-1);
 
-    R gamma = 0, gamma1;
-    int iter = 0;
-    while (iter < maxiter)
-      {
-        octave_quit ();
-        y = m*x;
-        gamma1 = gamma;
-        gamma = vector_norm (y, p);
-        z = dual_p (y, p, q);
-        z = z.hermitian ();
-        z = z * m;
+  R gamma = 0, gamma1;
+  int iter = 0;
+  while (iter < maxiter)
+    {
+      octave_quit ();
+      y = m*x;
+      gamma1 = gamma;
+      gamma = vector_norm (y, p);
+      z = dual_p (y, p, q);
+      z = z.hermitian ();
+      z = z * m;
 
-        if (iter > 0 && (vector_norm (z, q) <= gamma
-                         || (gamma - gamma1) <= tol*gamma))
-          break;
+      if (iter > 0 && (vector_norm (z, q) <= gamma
+                       || (gamma - gamma1) <= tol*gamma))
+        break;
 
-        z = z.hermitian ();
-        x = dual_p (z, q, p);
-        iter++;
-      }
+      z = z.hermitian ();
+      x = dual_p (z, q, p);
+      iter++;
+    }
 
-    return gamma;
-  }
+  return gamma;
+}
 
-  // derive column vector and SVD types
+// derive column vector and SVD types
 
-  static const char *p_less1_gripe = "xnorm: p must be >= 1";
+static const char *p_less1_gripe = "xnorm: p must be >= 1";
 
-  // Static constant to control the maximum number of iterations.  100 seems to
-  // be a good value.  Eventually, we can provide a means to change this
-  // constant from Octave.
-  static int max_norm_iter = 100;
+// Static constant to control the maximum number of iterations.  100 seems to
+// be a good value.  Eventually, we can provide a means to change this
+// constant from Octave.
+static int max_norm_iter = 100;
 
-  // version with SVD for dense matrices
-  template <typename MatrixT, typename VectorT, typename R>
-  R svd_matrix_norm (const MatrixT& m, R p, VectorT)
-  {
-    // NOTE: The octave:: namespace tags are needed for the following
-    // function calls until the deprecated inline functions are removed
-    // from oct-norm.h.
+// version with SVD for dense matrices
+template <typename MatrixT, typename VectorT, typename R>
+R svd_matrix_norm (const MatrixT& m, R p, VectorT)
+{
+  // NOTE: The octave:: namespace tags are needed for the following
+  // function calls until the deprecated inline functions are removed
+  // from oct-norm.h.
 
-    R res = 0;
-    if (p == 2)
-      {
-        math::svd<MatrixT> fact (m, math::svd<MatrixT>::Type::sigma_only);
-        res = fact.singular_values () (0, 0);
-      }
-    else if (p == 1)
-      res = octave::xcolnorms (m, static_cast<R> (1)).max ();
-    else if (lo_ieee_isinf (p) && p > 1)
-      res = octave::xrownorms (m, static_cast<R> (1)).max ();
-    else if (p > 1)
-      {
-        VectorT x;
-        const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
-        res = higham (m, p, sqrteps, max_norm_iter, x);
-      }
-    else
-      (*current_liboctave_error_handler) ("%s", p_less1_gripe);
+  R res = 0;
+  if (p == 2)
+    {
+      math::svd<MatrixT> fact (m, math::svd<MatrixT>::Type::sigma_only);
+      res = fact.singular_values () (0, 0);
+    }
+  else if (p == 1)
+    res = octave::xcolnorms (m, static_cast<R> (1)).max ();
+  else if (lo_ieee_isinf (p) && p > 1)
+    res = octave::xrownorms (m, static_cast<R> (1)).max ();
+  else if (p > 1)
+    {
+      VectorT x;
+      const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
+      res = higham (m, p, sqrteps, max_norm_iter, x);
+    }
+  else
+    (*current_liboctave_error_handler) ("%s", p_less1_gripe);
 
-    return res;
-  }
+  return res;
+}
 
-  // SVD-free version for sparse matrices
-  template <typename MatrixT, typename VectorT, typename R>
-  R matrix_norm (const MatrixT& m, R p, VectorT)
-  {
-    // NOTE: The octave:: namespace tags are needed for the following
-    // function calls until the deprecated inline functions are removed
-    // from oct-norm.h.
+// SVD-free version for sparse matrices
+template <typename MatrixT, typename VectorT, typename R>
+R matrix_norm (const MatrixT& m, R p, VectorT)
+{
+  // NOTE: The octave:: namespace tags are needed for the following
+  // function calls until the deprecated inline functions are removed
+  // from oct-norm.h.
 
-    R res = 0;
-    if (p == 1)
-      res = octave::xcolnorms (m, static_cast<R> (1)).max ();
-    else if (lo_ieee_isinf (p) && p > 1)
-      res = octave::xrownorms (m, static_cast<R> (1)).max ();
-    else if (p > 1)
-      {
-        VectorT x;
-        const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
-        res = higham (m, p, sqrteps, max_norm_iter, x);
-      }
-    else
-      (*current_liboctave_error_handler) ("%s", p_less1_gripe);
+  R res = 0;
+  if (p == 1)
+    res = octave::xcolnorms (m, static_cast<R> (1)).max ();
+  else if (lo_ieee_isinf (p) && p > 1)
+    res = octave::xrownorms (m, static_cast<R> (1)).max ();
+  else if (p > 1)
+    {
+      VectorT x;
+      const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
+      res = higham (m, p, sqrteps, max_norm_iter, x);
+    }
+  else
+    (*current_liboctave_error_handler) ("%s", p_less1_gripe);
 
-    return res;
-  }
+  return res;
+}
 
-  // and finally, here's what we've promised in the header file
+// and finally, here's what we've promised in the header file
 
 #define DEFINE_XNORM_FCNS(PREFIX, RTYPE)                                \
   RTYPE xnorm (const PREFIX##ColumnVector& x, RTYPE p)                  \
@@ -582,21 +582,21 @@
     return vector_norm (x, static_cast<RTYPE> (2));                     \
   }
 
-  DEFINE_XNORM_FCNS(, double)
-  DEFINE_XNORM_FCNS(Complex, double)
-  DEFINE_XNORM_FCNS(Float, float)
-  DEFINE_XNORM_FCNS(FloatComplex, float)
+DEFINE_XNORM_FCNS(, double)
+DEFINE_XNORM_FCNS(Complex, double)
+DEFINE_XNORM_FCNS(Float, float)
+DEFINE_XNORM_FCNS(FloatComplex, float)
 
-  // this is needed to avoid copying the sparse matrix for xfrobnorm
-  template <typename T, typename R>
-  inline void array_norm_2 (const T *v, octave_idx_type n, R& res)
-  {
-    norm_accumulator_2<R> acc;
-    for (octave_idx_type i = 0; i < n; i++)
-      acc.accum (v[i]);
+// this is needed to avoid copying the sparse matrix for xfrobnorm
+template <typename T, typename R>
+inline void array_norm_2 (const T *v, octave_idx_type n, R& res)
+{
+  norm_accumulator_2<R> acc;
+  for (octave_idx_type i = 0; i < n; i++)
+    acc.accum (v[i]);
 
-    res = acc;
-  }
+  res = acc;
+}
 
 #define DEFINE_XNORM_SPARSE_FCNS(PREFIX, RTYPE)                 \
   RTYPE xnorm (const Sparse##PREFIX##Matrix& x, RTYPE p)        \
@@ -610,8 +610,8 @@
     return res;                                                 \
   }
 
-  DEFINE_XNORM_SPARSE_FCNS(, double)
-  DEFINE_XNORM_SPARSE_FCNS(Complex, double)
+DEFINE_XNORM_SPARSE_FCNS(, double)
+DEFINE_XNORM_SPARSE_FCNS(Complex, double)
 
 #define DEFINE_COLROW_NORM_FCNS(PREFIX, RPREFIX, RTYPE)         \
   RPREFIX##RowVector                                            \
@@ -625,12 +625,12 @@
     return row_norms (m, p);                                    \
   }                                                             \
 
-  DEFINE_COLROW_NORM_FCNS(, , double)
-  DEFINE_COLROW_NORM_FCNS(Complex, , double)
-  DEFINE_COLROW_NORM_FCNS(Float, Float, float)
-  DEFINE_COLROW_NORM_FCNS(FloatComplex, Float, float)
+DEFINE_COLROW_NORM_FCNS(,, double)
+DEFINE_COLROW_NORM_FCNS(Complex,, double)
+DEFINE_COLROW_NORM_FCNS(Float, Float, float)
+DEFINE_COLROW_NORM_FCNS(FloatComplex, Float, float)
 
-  DEFINE_COLROW_NORM_FCNS(Sparse, , double)
-  DEFINE_COLROW_NORM_FCNS(SparseComplex, , double)
+DEFINE_COLROW_NORM_FCNS(Sparse,, double)
+DEFINE_COLROW_NORM_FCNS(SparseComplex,, double)
 
 OCTAVE_END_NAMESPACE(octave)