diff liboctave/numeric/oct-norm.cc @ 29874:92662b17ef7e

move liboctave xnorm functions inside octave namespace * oct-norm.h (xnorm, xfrobnorm, xcolnorms, xrownorms): Move inside octave namespace. Provide deprecated wrappers for old names. Change uses where needed. * oct-norm.cc: Move templates inside octave namespace. Use octave:: namespace tag where needed. Cast second arg for norm from int to appropriate floating point type where needed. Eliminate OCTAVE_API and extern from definitions of xnorm functions.
author John W. Eaton <jwe@octave.org>
date Tue, 13 Jul 2021 22:56:23 -0400
parents 0a5b15007766
children 6549fa7558ba
line wrap: on
line diff
--- a/liboctave/numeric/oct-norm.cc	Tue Jul 13 15:30:07 2021 -0400
+++ b/liboctave/numeric/oct-norm.cc	Tue Jul 13 22:56:23 2021 -0400
@@ -59,241 +59,244 @@
 #include "mx-fs-fcm.h"
 #include "mx-s-cm.h"
 #include "oct-cmplx.h"
+#include "oct-norm.h"
 #include "quit.h"
 #include "svd.h"
 
-// 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.
+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.
 
-// norm accumulator for the p-norm
-template <typename R>
-class norm_accumulator_p
-{
-  R p,scl,sum;
-public:
-  norm_accumulator_p () { } // we need this one for Array
-  norm_accumulator_p (R pp) : p(pp), scl(0), sum(1) { }
-
-  template <typename U>
-  void accum (U val)
+  // norm accumulator for the p-norm
+  template <typename R>
+  class norm_accumulator_p
   {
-    octave_quit ();
-    R t = std::abs (val);
-    if (scl == t) // we need this to handle Infs properly
-      sum += 1;
-    else if (scl < t)
-      {
-        sum *= std::pow (scl/t, p);
+    R p,scl,sum;
+  public:
+    norm_accumulator_p () { } // we need this one for Array
+    norm_accumulator_p (R pp) : p(pp), scl(0), sum(1) { }
+
+    template <typename U>
+    void accum (U val)
+    {
+      octave_quit ();
+      R t = std::abs (val);
+      if (scl == t) // we need this to handle Infs properly
         sum += 1;
-        scl = t;
-      }
-    else if (t != 0)
-      sum += std::pow (t/scl, p);
-  }
-  operator R () { return scl * std::pow (sum, 1/p); }
-};
+      else if (scl < t)
+        {
+          sum *= std::pow (scl/t, p);
+          sum += 1;
+          scl = t;
+        }
+      else if (t != 0)
+        sum += std::pow (t/scl, p);
+    }
+    operator R () { return scl * std::pow (sum, 1/p); }
+  };
+
+  // norm accumulator for the minus p-pseudonorm
+  template <typename R>
+  class norm_accumulator_mp
+  {
+    R p,scl,sum;
+  public:
+    norm_accumulator_mp () { } // we need this one for Array
+    norm_accumulator_mp (R pp) : p(pp), scl(0), sum(1) { }
 
-// norm accumulator for the minus p-pseudonorm
-template <typename R>
-class norm_accumulator_mp
-{
-  R p,scl,sum;
-public:
-  norm_accumulator_mp () { } // we need this one for Array
-  norm_accumulator_mp (R pp) : p(pp), scl(0), sum(1) { }
+    template <typename U>
+    void accum (U val)
+    {
+      octave_quit ();
+      R t = 1 / std::abs (val);
+      if (scl == t)
+        sum += 1;
+      else if (scl < t)
+        {
+          sum *= std::pow (scl/t, p);
+          sum += 1;
+          scl = t;
+        }
+      else if (t != 0)
+        sum += std::pow (t/scl, p);
+    }
+    operator R () { return scl * std::pow (sum, -1/p); }
+  };
 
-  template <typename U>
-  void accum (U val)
+  // norm accumulator for the 2-norm (euclidean)
+  template <typename R>
+  class norm_accumulator_2
   {
-    octave_quit ();
-    R t = 1 / std::abs (val);
-    if (scl == t)
-      sum += 1;
-    else if (scl < t)
-      {
-        sum *= std::pow (scl/t, p);
+    R scl,sum;
+    static R pow2 (R x) { return x*x; }
+  public:
+    norm_accumulator_2 () : scl(0), sum(1) { }
+
+    void accum (R val)
+    {
+      R t = std::abs (val);
+      if (scl == t)
         sum += 1;
-        scl = t;
-      }
-    else if (t != 0)
-      sum += std::pow (t/scl, p);
-  }
-  operator R () { return scl * std::pow (sum, -1/p); }
-};
+      else if (scl < t)
+        {
+          sum *= pow2 (scl/t);
+          sum += 1;
+          scl = t;
+        }
+      else if (t != 0)
+        sum += pow2 (t/scl);
+    }
+
+    void accum (std::complex<R> val)
+    {
+      accum (val.real ());
+      accum (val.imag ());
+    }
+
+    operator R () { return scl * std::sqrt (sum); }
+  };
+
+  // norm accumulator for the 1-norm (city metric)
+  template <typename R>
+  class norm_accumulator_1
+  {
+    R sum;
+  public:
+    norm_accumulator_1 () : sum (0) { }
+    template <typename U>
+    void accum (U val)
+    {
+      sum += std::abs (val);
+    }
+    operator R () { return sum; }
+  };
 
-// norm accumulator for the 2-norm (euclidean)
-template <typename R>
-class norm_accumulator_2
-{
-  R scl,sum;
-  static R pow2 (R x) { return x*x; }
-public:
-  norm_accumulator_2 () : scl(0), sum(1) { }
+  // norm accumulator for the inf-norm (max metric)
+  template <typename R>
+  class norm_accumulator_inf
+  {
+    R max;
+  public:
+    norm_accumulator_inf () : max (0) { }
+    template <typename U>
+    void accum (U val)
+    {
+      if (octave::math::isnan (val))
+        max = octave::numeric_limits<R>::NaN ();
+      else
+        max = std::max (max, std::abs (val));
+    }
+    operator R () { return max; }
+  };
 
-  void accum (R val)
+  // norm accumulator for the -inf pseudonorm (min abs value)
+  template <typename R>
+  class norm_accumulator_minf
   {
-    R t = std::abs (val);
-    if (scl == t)
-      sum += 1;
-    else if (scl < t)
-      {
-        sum *= pow2 (scl/t);
-        sum += 1;
-        scl = t;
-      }
-    else if (t != 0)
-      sum += pow2 (t/scl);
-  }
+    R min;
+  public:
+    norm_accumulator_minf () : min (octave::numeric_limits<R>::Inf ()) { }
+    template <typename U>
+    void accum (U val)
+    {
+      if (octave::math::isnan (val))
+        min = octave::numeric_limits<R>::NaN ();
+      else
+        min = std::min (min, std::abs (val));
+    }
+    operator R () { return min; }
+  };
 
-  void accum (std::complex<R> val)
+  // norm accumulator for the 0-pseudonorm (hamming distance)
+  template <typename R>
+  class norm_accumulator_0
   {
-    accum (val.real ());
-    accum (val.imag ());
+    unsigned int num;
+  public:
+    norm_accumulator_0 () : num (0) { }
+    template <typename U>
+    void accum (U val)
+    {
+      if (val != static_cast<U> (0)) ++num;
+    }
+    operator R () { return 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;
   }
 
-  operator R () { return scl * std::sqrt (sum); }
-};
-
-// norm accumulator for the 1-norm (city metric)
-template <typename R>
-class norm_accumulator_1
-{
-  R sum;
-public:
-  norm_accumulator_1 () : sum (0) { }
-  template <typename U>
-  void accum (U val)
+  // dense versions
+  template <typename T, typename R, typename ACC>
+  void column_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
   {
-    sum += std::abs (val);
-  }
-  operator R () { return sum; }
-};
+    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));
 
-// norm accumulator for the inf-norm (max metric)
-template <typename R>
-class norm_accumulator_inf
-{
-  R max;
-public:
-  norm_accumulator_inf () : max (0) { }
-  template <typename U>
-  void accum (U val)
-  {
-    if (octave::math::isnan (val))
-      max = octave::numeric_limits<R>::NaN ();
-    else
-      max = std::max (max, std::abs (val));
+        res.xelem (j) = accj;
+      }
   }
-  operator R () { return max; }
-};
 
-// norm accumulator for the -inf pseudonorm (min abs value)
-template <typename R>
-class norm_accumulator_minf
-{
-  R min;
-public:
-  norm_accumulator_minf () : min (octave::numeric_limits<R>::Inf ()) { }
-  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)
   {
-    if (octave::math::isnan (val))
-      min = octave::numeric_limits<R>::NaN ();
-    else
-      min = std::min (min, std::abs (val));
+    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];
   }
-  operator R () { return min; }
-};
-
-// norm accumulator for the 0-pseudonorm (hamming distance)
-template <typename R>
-class norm_accumulator_0
-{
-  unsigned int num;
-public:
-  norm_accumulator_0 () : num (0) { }
-  template <typename U>
-  void accum (U val)
-  {
-    if (val != static_cast<U> (0)) ++num;
-  }
-  operator R () { return 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;
-}
+  // 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));
 
-// 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;
-    }
-}
-
-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));
-    }
+        res.xelem (j) = accj;
+      }
+  }
 
-  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));
+  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));
+      }
 
-      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 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(FUNC_NAME, ARG_TYPE, RES_TYPE)        \
   template <typename T, typename R>                             \
   RES_TYPE FUNC_NAME (const ARG_TYPE& v, R p)                   \
@@ -319,282 +322,291 @@
     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 octave::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 octave::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)
-{
-  R res = 0;
-  if (p == 2)
-    {
-      octave::math::svd<MatrixT> fact
-        (m, octave::math::svd<MatrixT>::Type::sigma_only);
-      res = fact.singular_values () (0,0);
-    }
-  else if (p == 1)
-    res = xcolnorms (m, 1).max ();
-  else if (lo_ieee_isinf (p) && p > 1)
-    res = xrownorms (m, 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)
+      {
+        octave::math::svd<MatrixT> fact
+          (m, octave::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)
-{
-  R res = 0;
-  if (p == 1)
-    res = xcolnorms (m, 1).max ();
-  else if (lo_ieee_isinf (p) && p > 1)
-    res = xrownorms (m, 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_FUNCS(PREFIX, RTYPE)                               \
-  OCTAVE_API RTYPE xnorm (const PREFIX##ColumnVector& x, RTYPE p)       \
+  RTYPE xnorm (const PREFIX##ColumnVector& x, RTYPE p)                  \
   {                                                                     \
     return vector_norm (x, p);                                          \
   }                                                                     \
-  OCTAVE_API RTYPE xnorm (const PREFIX##RowVector& x, RTYPE p)          \
+  RTYPE xnorm (const PREFIX##RowVector& x, RTYPE p)                     \
   {                                                                     \
     return vector_norm (x, p);                                          \
   }                                                                     \
-  OCTAVE_API RTYPE xnorm (const PREFIX##Matrix& x, RTYPE p)             \
+  RTYPE xnorm (const PREFIX##Matrix& x, RTYPE p)                        \
   {                                                                     \
     return svd_matrix_norm (x, p, PREFIX##Matrix ());                   \
   }                                                                     \
-  OCTAVE_API RTYPE xfrobnorm (const PREFIX##Matrix& x)                  \
+  RTYPE xfrobnorm (const PREFIX##Matrix& x)                             \
   {                                                                     \
     return vector_norm (x, static_cast<RTYPE> (2));                     \
   }
 
-DEFINE_XNORM_FUNCS(, double)
-DEFINE_XNORM_FUNCS(Complex, double)
-DEFINE_XNORM_FUNCS(Float, float)
-DEFINE_XNORM_FUNCS(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]);
+  DEFINE_XNORM_FUNCS(, double)
+  DEFINE_XNORM_FUNCS(Complex, double)
+  DEFINE_XNORM_FUNCS(Float, float)
+  DEFINE_XNORM_FUNCS(FloatComplex, float)
 
-  res = acc;
-}
+  // 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]);
 
-#define DEFINE_XNORM_SPARSE_FUNCS(PREFIX, RTYPE)                        \
-  OCTAVE_API RTYPE xnorm (const Sparse##PREFIX##Matrix& x, RTYPE p)     \
-  {                                                                     \
-    return matrix_norm (x, p, PREFIX##Matrix ());                       \
-  }                                                                     \
-  OCTAVE_API RTYPE xfrobnorm (const Sparse##PREFIX##Matrix& x)          \
-  {                                                                     \
-    RTYPE res;                                                          \
-    array_norm_2 (x.data (), x.nnz (), res);                            \
-    return res;                                                         \
+    res = acc;
   }
 
-DEFINE_XNORM_SPARSE_FUNCS(, double)
-DEFINE_XNORM_SPARSE_FUNCS(Complex, double)
+#define DEFINE_XNORM_SPARSE_FUNCS(PREFIX, RTYPE)                \
+  RTYPE xnorm (const Sparse##PREFIX##Matrix& x, RTYPE p)        \
+  {                                                             \
+    return matrix_norm (x, p, PREFIX##Matrix ());               \
+  }                                                             \
+  RTYPE xfrobnorm (const Sparse##PREFIX##Matrix& x)             \
+  {                                                             \
+    RTYPE res;                                                  \
+    array_norm_2 (x.data (), x.nnz (), res);                    \
+    return res;                                                 \
+  }
+
+  DEFINE_XNORM_SPARSE_FUNCS(, double)
+  DEFINE_XNORM_SPARSE_FUNCS(Complex, double)
 
 #define DEFINE_COLROW_NORM_FUNCS(PREFIX, RPREFIX, RTYPE)        \
-  extern OCTAVE_API RPREFIX##RowVector                          \
+  RPREFIX##RowVector                                            \
   xcolnorms (const PREFIX##Matrix& m, RTYPE p)                  \
   {                                                             \
     return column_norms (m, p);                                 \
   }                                                             \
-  extern OCTAVE_API RPREFIX##ColumnVector                       \
+  RPREFIX##ColumnVector                                         \
   xrownorms (const PREFIX##Matrix& m, RTYPE p)                  \
   {                                                             \
     return row_norms (m, p);                                    \
   }                                                             \
 
-DEFINE_COLROW_NORM_FUNCS(, , double)
-DEFINE_COLROW_NORM_FUNCS(Complex, , double)
-DEFINE_COLROW_NORM_FUNCS(Float, Float, float)
-DEFINE_COLROW_NORM_FUNCS(FloatComplex, Float, float)
+  DEFINE_COLROW_NORM_FUNCS(, , double)
+  DEFINE_COLROW_NORM_FUNCS(Complex, , double)
+  DEFINE_COLROW_NORM_FUNCS(Float, Float, float)
+  DEFINE_COLROW_NORM_FUNCS(FloatComplex, Float, float)
 
-DEFINE_COLROW_NORM_FUNCS(Sparse, , double)
-DEFINE_COLROW_NORM_FUNCS(SparseComplex, , double)
+  DEFINE_COLROW_NORM_FUNCS(Sparse, , double)
+  DEFINE_COLROW_NORM_FUNCS(SparseComplex, , double)
+}