improving examples, and fixed bug in Python histogram constructor, now all axis types are recognized

doc/getting_started.qbk

@@ -1,9 +1,11 @@
 [section Getting started]
 
-To get you started, here are some commented usage examples.
+To get you started quickly, here are some heavily commented examples to copy paste from. If you prefer a more traditional, structured exposition, check out the [link histogram.guide full user guide].
 
 [section Make and use a static 1d-histogram in C++]
 
+If possible, use the static histogram. It is faster and user errors are caught at compile time.
+
 [c++]``
 #include <boost/histogram.hpp>
 #include <iostream>
@@ -12,13 +14,15 @@ int main(int, char**) {
     namespace bh = boost::histogram;
     using namespace bh::literals; // enables _c suffix
 
-    // create static 1d-histogram with 10 equidistant bins from -1.0 to 2.0,
+    /*
-    // with axis of histogram labeled as "x"
+        create a static 1d-histogram with an axis that has 10 equidistant
+        bins on the real line from -1.0 to 2.0, and label it as "x"
+    */
     auto h = bh::make_static_histogram(
         bh::axis::regular<>(10, -1.0, 2.0, "x")
     );
 
-    // fill histogram with data
+    // fill histogram with data, typically this would happen in a loop
     h.fill(-1.5); // put in underflow bin
     h.fill(-1.0); // included in first bin, bin interval is semi-open
     h.fill(-0.5);
@@ -29,37 +33,50 @@ int main(int, char**) {
     h.fill(20.0); // put in overflow bin
 
     /*
-        instead of calling h.fill(...) with same argument N times,
+        use bh::count(N) if you would otherwise call h.fill(...) with
-        use bh::count, which accepts an integer argument N
+        *same* argument N times, N is an integer argument
     */
     h.fill(1.0, bh::count(4));
 
     /*
-        to fill a weighted entry, use bh::weight, which accepts a double
+        do a weighted fill using bh::weight, which accepts a double
-        argument; don't confuse with bh::count, it has a different effect
+        - don't mix this with bh::count, both have a different effect on the
-        on the variance (see Rationale for a section explaining weighted fills)
+          variance (see Rationale for an explanation regarding weights)
+        - if you don't know what this is good for, use bh::count instead,
+          it is most likeliy what you want and it is more efficient
     */
     h.fill(0.1, bh::weight(2.5));
 
     /*
         iterate over bins, loop excludes under- and overflow bins
-        - index 0_c is a compile-time number to make axis(...) return
+        - index 0_c is a compile-time number, the only way in C++ to make
-          a different type for each axis
+          axis(...) to return a different type for each index
-        - for-loop yields std::pair<[bin index], [bin type]>, where
+        - for-loop yields instances of `std::pair<int, bin_type>`, where
-          [bin type] usually is a semi-open interval representing the bin,
+          `bin_type` usually is a semi-open interval representing the bin,
-          whose edges can be accessed with methods lower() and upper(), but
+          whose edges can be accessed with methods `lower()` and `upper()`,
-          the [bin type] depends on the axis and could be something else
+          but the [bin type] depends on the axis, look it up in the reference
-        - value(index) method returns the bin count at index,
+        - `value(index)` method returns the bin count at index
-        - variance(index) method returns a variance estimate of the bin count
+        - `variance(index)` method returns a variance estimate of the bin
-          at index (see Rationale for a section explaining the variance)
+          count at index (see Rationale section for what this means)
     */
     for (const auto& bin : h.axis(0_c)) {
-        std::cout << "bin " << bin.first
+        std::cout << "bin " << bin.first << " x in ["
-                  << " x in [" << bin.second.lower() << ", " << bin.second.upper() << "): "
+                  << bin.second.lower() << ", " << bin.second.upper() << "): "
-                  << h.value(bin.first) << " +/- " << std::sqrt(h.variance(bin.first))
+                  << h.value(bin.first) << " +/- "
+                  << std::sqrt(h.variance(bin.first))
                   << std::endl;
     }
 
+    // accessing under- and overflow bins is easy, use indices -1 and 10
+    std::cout << "underflow bin [" << h.axis(0_c)[-1].lower()
+              << ", " << h.axis(0_c)[-1].upper() << "): "
+              << h.value(-1) << " +/- " << std::sqrt(h.variance(-1))
+              << std::endl;
+    std::cout << "overflow  bin [" << h.axis(0_c)[10].lower()
+              << ", " << h.axis(0_c)[10].upper() << "): "
+              << h.value(10) << " +/- " << std::sqrt(h.variance(10))
+              << std::endl;
+
     /* program output:
 
     bin 0 x in [-1, -0.7): 1 +/- 1
@@ -72,6 +89,8 @@ int main(int, char**) {
     bin 7 x in [1.1, 1.4): 1 +/- 1
     bin 8 x in [1.4, 1.7): 0 +/- 0
     bin 9 x in [1.7, 2): 1 +/- 1
+    underflow bin [-inf, -1): 1 +/- 1
+    overflow  bin [2, inf): 2 +/- 1.41421
 
     */
 }
@@ -79,57 +98,71 @@ int main(int, char**) {
 
 [endsect]
 
-[section Make and use a dynamic 2d-histogram in C++]
+[section Make and use a dynamic 3d-histogram in C++]
 
-Here we fill the histogram with some random numbers.
+Dynamic histograms are a bit slower than static histograms, but still faster than other libraries. Use a dynamic histogram when you only know at runtime how to layout the histogram, for example, because you wrote a graphical user interface that uses Boost.Histogram underneath.
 
 [c++]``
 #include <boost/histogram.hpp>
 #include <boost/random/mersenne_twister.hpp>
 #include <boost/random/normal_distribution.hpp>
 #include <cstdlib>
+#include <string>
 
 namespace br = boost::random;
 namespace bh = boost::histogram;
 
 int main() {
     /*
-        create dynamic histogram using `make_dynamic_histogram`
+        create a dynamic histogram with the factory `make_dynamic_histogram`
-        - axis can be passed directly, just like for `make_static_histogram`
+        - axis can be passed directly just like for `make_static_histogram`
-        - in addition, also accepts iterators over a sequence of axes
+        - in addition, the factory also accepts iterators over a sequence of
+          axis::any, the polymorphic type that can hold concrete axis types
     */
-    std::vector<bh::axis::any<>> axes = {bh::axis::regular<>(5, -5, 5, "x"),
+    std::vector<bh::axis::any<>> axes;
-                                         bh::axis::regular<>(5, -5, 5, "y")};
+    axes.emplace_back(bh::axis::category<std::string>({"red", "blue"}));
+    axes.emplace_back(bh::axis::regular<>(5, -5, 5, "x"));
+    axes.emplace_back(bh::axis::regular<>(5, -5, 5, "y"));
     auto h = bh::make_dynamic_histogram(axes.begin(), axes.end());
 
-    // fill histogram, random numbers are generated on the fly
+    // fill histogram with random numbers
     br::mt19937 gen;
     br::normal_distribution<> norm;
     for (int i = 0; i < 1000; ++i)
-        h.fill(norm(gen), norm(gen));
+        h.fill(i % 2 ? "red" : "blue", norm(gen), norm(gen));
 
     /*
-        print histogram
+        print dynamic histogram by iterating over bins
         - for most axis types, the for loop looks just like for a static
           histogram, except that we can pass runtime numbers, too
-        - in contrast to the static histogram, we need to cast axis::any
+        - if the [bin type] of the axis is not convertible to a
-          to the held axis type before looping, if the [bin type] is not
+          double interval, one needs to cast axis::any before looping;
-          convertible to a double interval
+          this is here the case for the category axis
     */
-    for (const auto& ybin : h.axis(1)) { // rows
+    using cas = bh::axis::category<std::string>;
-        for (const auto& xbin : h.axis(0)) { // columns
+    for (const auto& cbin : bh::axis::cast<cas>(h.axis(0))) {
-            std::printf("%3.0f ", h.value(xbin.first, ybin.first));
+        std::printf("%s\n", cbin.second.c_str());
+        for (const auto& ybin : h.axis(2)) { // rows
+            for (const auto& xbin : h.axis(1)) { // columns
+                std::printf("%3.0f ", h.value(cbin.first, xbin.first, ybin.first));
+            }
+            std::printf("\n");
         }
-        std::printf("\n");
     }
 }
 ``
+[note
+If you care about maximum performance: In this example, `axis::category<std::string>` is used with two string labels "red" and "blue". It is faster to use an enum, `enum { red, blue };` and a `axis::category<>` axis.
+]
+
+[endsect]
 
 [section Make and use a 2d-histogram in Python]
 
 You need to build the library with Numpy support to run this example.
 
-[python]`import histogram as hg
+[python]``
+import histogram as hg
 import numpy as np
 
 # create 2d-histogram with two axes with 10 equidistant bins from -3 to 3
@@ -153,7 +186,7 @@ y = np.array(h.axis(1))
 # creates a view of the counts (no copy involved)
 count_matrix = np.asarray(h)
 
-# cut off the under- and overflow bins (no copy involved)
+# cut off the under- and overflow bins to not confuse matplotib (no copy)
 reduced_count_matrix = count_matrix[:-2,:-2]
 
 try:
@@ -164,8 +197,44 @@ try:
     plt.ylabel(h.axis(1).label)
     plt.savefig("example_2d_python.png")
 except ImportError:
-    # ok, no matplotlib, then just print it
+    # ok, no matplotlib, then just print the full count matrix
     print count_matrix
+
+    # output of the print looks something like this, the two right-most rows
+    # and two down-most columns represent under-/overflow bins
+    # [[ 0  0  0  1  5  0  0  1  0  0  0  0]
+    #  [ 0  0  0  1 17 11  6  0  0  0  0  0]
+    #  [ 0  0  0  5 31 26  4  1  0  0  0  0]
+    #  [ 0  0  3 20 59 62 26  4  0  0  0  0]
+    #  [ 0  0  1 26 96 89 16  1  0  0  0  0]
+    #  [ 0  0  4 21 86 84 20  1  0  0  0  0]
+    #  [ 0  0  1 24 71 50 15  2  0  0  0  0]
+    #  [ 0  0  0  6 26 37  7  0  0  0  0  0]
+    #  [ 0  0  0  0 11 10  2  0  0  0  0  0]
+    #  [ 0  0  0  1  2  3  1  0  0  0  0  0]
+    #  [ 0  0  0  0  0  2  0  0  0  0  0  0]
+    #  [ 0  0  0  0  0  1  0  0  0  0  0  0]]
+``
+
+[endsect]
+
+[section Make and use a 1d-histogram in Python without Numpy]
+
+Building the library with Numpy support is highly recommended, but just for completeness, here is an example on how to use the library without Numpy support.
+
+[python]``
+import histogram as hg
+
+# make 1-d histogram with 10 logarithmic bins from 1e0 to 1e5
+h = hg.histogram(hg.axis.regular_log(10, 1e0, 1e5, "x"))
+
+# fill histogram with numbers
+for x in (1e0, 1e1, 1e2, 1e3, 1e4):
+    h.fill(x)
+
+# iterate over bins
+for idx, (lower, upper) in enumerate(h.axis(0)):
+    print "bin %i x in [%g, %g): %g +/- %g" % (idx, lower, upper, h.value(idx), h.variance(idx) ** 0.5)
 ``
 
 [endsect]

doc/guide.qbk

@@ -1,4 +1,4 @@
-[section User guide]
+[section:guide User guide]
 
 How to create and work with histograms is described here. This library is designed to make simple things simple, yet complex things possible. For a quick start, you don't need to read the complete user guide; have a look into the tutorial and the examples instead. This guide covers the basic and more advanced usage of the library.
 
@@ -72,7 +72,6 @@ ranges from `begin` to `end`, where `end` is also not included.
 When you work with [classref boost::histogram::histogram<Dynamic,...>], you can also create a histogram from a run-time compiled collection of axis objects:
 
 [c++]``
-// also see examples/create_dynamic_histogram.cpp
 #include <boost/histogram.hpp>
 #include <vector>
 
@@ -131,7 +130,6 @@ int main() {
 Here is a second example which using a weighted fill in a functional programming style. The input values are taken from a container:
 
 [c++]``
-// also see examples/create_dynamic_histogram.cpp
 #include <boost/histogram.hpp>
 #include <algorithm>
 #include <vector>

examples/create_dynamic_histogram.cpp

@@ -1,51 +0,0 @@
-#include <boost/histogram.hpp>
-#include <boost/histogram/histogram_ostream_operators.hpp>
-#include <vector>
-#include <cstdlib>
-
-namespace bh = boost::histogram;
-
-/*
-  command line usage: cmd [i a b|r n x y]
-    a,b,n: integers
-    x,y  : floats
-*/
-
-int main(int argc, char** argv) {
-    auto v = std::vector<bh::axis::any<>>();
-
-    // parse arguments
-    auto argi = 1;
-    while (argi < argc) {
-        switch (argv[argi][0]) {
-            case 'i': {
-                ++argi;
-                auto a = std::atoi(argv[argi]);
-                ++argi;
-                auto b = std::atoi(argv[argi]);
-                ++argi;
-                v.push_back(bh::axis::integer<>(a, b));
-            }
-            break;
-            case 'r': {
-                ++argi;
-                auto n = std::atoi(argv[argi]);
-                ++argi;
-                auto x = std::atof(argv[argi]);
-                ++argi;
-                auto y = std::atof(argv[argi]);
-                ++argi;
-                v.push_back(bh::axis::regular<>(n, x, y));
-            }
-            break;
-            default:
-                std::cerr << "unknown argument " << argv[argi] << std::endl;
-                return 1;
-        }
-    }
-
-    auto h = bh::histogram<bh::Dynamic, bh::axis::builtins>(v.begin(), v.end());
-
-    // do something with h
-    std::cout << "you created the following histogram:\n" << h << std::endl;
-}

examples/getting_started_listing_1.cpp

@@ -5,13 +5,15 @@ int main(int, char**) {
     namespace bh = boost::histogram;
     using namespace bh::literals; // enables _c suffix
 
-    // create static 1d-histogram with 10 equidistant bins from -1.0 to 2.0,
+    /*
-    // with axis of histogram labeled as "x"
+        create a static 1d-histogram with an axis that has 10 equidistant
+        bins on the real line from -1.0 to 2.0, and label it as "x"
+    */
     auto h = bh::make_static_histogram(
         bh::axis::regular<>(10, -1.0, 2.0, "x")
     );
 
-    // fill histogram with data
+    // fill histogram with data, typically this would happen in a loop
     h.fill(-1.5); // put in underflow bin
     h.fill(-1.0); // included in first bin, bin interval is semi-open
     h.fill(-0.5);
@@ -22,37 +24,50 @@ int main(int, char**) {
     h.fill(20.0); // put in overflow bin
 
     /*
-        instead of calling h.fill(...) with same argument N times,
+        use bh::count(N) if you would otherwise call h.fill(...) with
-        use bh::count, which accepts an integer argument N
+        *same* argument N times, N is an integer argument
     */
     h.fill(1.0, bh::count(4));
 
     /*
-        to fill a weighted entry, use bh::weight, which accepts a double
+        do a weighted fill using bh::weight, which accepts a double
-        argument; don't confuse with bh::count, it has a different effect
+        - don't mix this with bh::count, both have a different effect on the
-        on the variance (see Rationale for a section explaining weighted fills)
+          variance (see Rationale for an explanation regarding weights)
+        - if you don't know what this is good for, use bh::count instead,
+          it is most likeliy what you want and it is more efficient
     */
     h.fill(0.1, bh::weight(2.5));
 
     /*
         iterate over bins, loop excludes under- and overflow bins
-        - index 0_c is a compile-time number to make axis(...) return
+        - index 0_c is a compile-time number, the only way in C++ to make
-          a different type for each axis
+          axis(...) to return a different type for each index
-        - for-loop yields std::pair<[bin index], [bin type]>, where
+        - for-loop yields instances of `std::pair<int, bin_type>`, where
-          [bin type] usually is a semi-open interval representing the bin,
+          `bin_type` usually is a semi-open interval representing the bin,
-          whose edges can be accessed with methods lower() and upper(), but
+          whose edges can be accessed with methods `lower()` and `upper()`,
-          the [bin type] depends on the axis and could be something else
+          but the [bin type] depends on the axis, look it up in the reference
-        - value(index) method returns the bin count at index,
+        - `value(index)` method returns the bin count at index
-        - variance(index) method returns a variance estimate of the bin count
+        - `variance(index)` method returns a variance estimate of the bin
-          at index (see Rationale for a section explaining the variance)
+          count at index (see Rationale section for what this means)
     */
     for (const auto& bin : h.axis(0_c)) {
-        std::cout << "bin " << bin.first
+        std::cout << "bin " << bin.first << " x in ["
-                  << " x in [" << bin.second.lower() << ", " << bin.second.upper() << "): "
+                  << bin.second.lower() << ", " << bin.second.upper() << "): "
-                  << h.value(bin.first) << " +/- " << std::sqrt(h.variance(bin.first))
+                  << h.value(bin.first) << " +/- "
+                  << std::sqrt(h.variance(bin.first))
                   << std::endl;
     }
 
+    // accessing under- and overflow bins is easy, use indices -1 and 10
+    std::cout << "underflow bin [" << h.axis(0_c)[-1].lower()
+              << ", " << h.axis(0_c)[-1].upper() << "): "
+              << h.value(-1) << " +/- " << std::sqrt(h.variance(-1))
+              << std::endl;
+    std::cout << "overflow  bin [" << h.axis(0_c)[10].lower()
+              << ", " << h.axis(0_c)[10].upper() << "): "
+              << h.value(10) << " +/- " << std::sqrt(h.variance(10))
+              << std::endl;
+
     /* program output:
 
     bin 0 x in [-1, -0.7): 1 +/- 1
@@ -65,6 +80,8 @@ int main(int, char**) {
     bin 7 x in [1.1, 1.4): 1 +/- 1
     bin 8 x in [1.4, 1.7): 0 +/- 0
     bin 9 x in [1.7, 2): 1 +/- 1
+    underflow bin [-inf, -1): 1 +/- 1
+    overflow  bin [2, inf): 2 +/- 1.41421
 
     */
 }

examples/getting_started_listing_2.cpp

@@ -2,38 +2,46 @@
 #include <boost/random/mersenne_twister.hpp>
 #include <boost/random/normal_distribution.hpp>
 #include <cstdlib>
+#include <string>
 
 namespace br = boost::random;
 namespace bh = boost::histogram;
 
 int main() {
     /*
-        create dynamic histogram using `make_dynamic_histogram`
+        create a dynamic histogram with the factory `make_dynamic_histogram`
-        - axis can be passed directly, just like for `make_static_histogram`
+        - axis can be passed directly just like for `make_static_histogram`
-        - in addition, also accepts iterators over a sequence of axes
+        - in addition, the factory also accepts iterators over a sequence of
+          axis::any, the polymorphic type that can hold concrete axis types
     */
-    std::vector<bh::axis::any<>> axes = {bh::axis::regular<>(5, -5, 5, "x"),
+    std::vector<bh::axis::any<>> axes;
-                                         bh::axis::regular<>(5, -5, 5, "y")};
+    axes.emplace_back(bh::axis::category<std::string>({"red", "blue"}));
+    axes.emplace_back(bh::axis::regular<>(5, -5, 5, "x"));
+    axes.emplace_back(bh::axis::regular<>(5, -5, 5, "y"));
     auto h = bh::make_dynamic_histogram(axes.begin(), axes.end());
 
-    // fill histogram, random numbers are generated on the fly
+    // fill histogram with random numbers
     br::mt19937 gen;
     br::normal_distribution<> norm;
     for (int i = 0; i < 1000; ++i)
-        h.fill(norm(gen), norm(gen));
+        h.fill(i % 2 ? "red" : "blue", norm(gen), norm(gen));
 
     /*
-        print histogram
+        print dynamic histogram by iterating over bins
         - for most axis types, the for loop looks just like for a static
           histogram, except that we can pass runtime numbers, too
-        - in contrast to the static histogram, we need to cast axis::any
+        - if the [bin type] of the axis is not convertible to a
-          to the held axis type before looping, if the [bin type] is not
+          double interval, one needs to cast axis::any before looping;
-          convertible to a double interval
+          this is here the case for the category axis
     */
-    for (const auto& ybin : h.axis(1)) { // rows
+    using cas = bh::axis::category<std::string>;
-        for (const auto& xbin : h.axis(0)) { // columns
+    for (const auto& cbin : bh::axis::cast<cas>(h.axis(0))) {
-            std::printf("%3.0f ", h.value(xbin.first, ybin.first));
+        std::printf("%s\n", cbin.second.c_str());
+        for (const auto& ybin : h.axis(2)) { // rows
+            for (const auto& xbin : h.axis(1)) { // columns
+                std::printf("%3.0f ", h.value(cbin.first, xbin.first, ybin.first));
+            }
+            std::printf("\n");
         }
-        std::printf("\n");
     }
 }

examples/getting_started_listing_3.py

@@ -22,7 +22,7 @@ y = np.array(h.axis(1))
 # creates a view of the counts (no copy involved)
 count_matrix = np.asarray(h)
 
-# cut off the under- and overflow bins (no copy involved)
+# cut off the under- and overflow bins to not confuse matplotib (no copy)
 reduced_count_matrix = count_matrix[:-2,:-2]
 
 try:
@@ -33,5 +33,20 @@ try:
     plt.ylabel(h.axis(1).label)
     plt.savefig("example_2d_python.png")
 except ImportError:
-    # ok, no matplotlib, then just print it
+    # ok, no matplotlib, then just print the full count matrix
     print count_matrix
+
+    # output of the print looks something like this, the two right-most rows
+    # and two down-most columns represent under-/overflow bins
+    # [[ 0  0  0  1  5  0  0  1  0  0  0  0]
+    #  [ 0  0  0  1 17 11  6  0  0  0  0  0]
+    #  [ 0  0  0  5 31 26  4  1  0  0  0  0]
+    #  [ 0  0  3 20 59 62 26  4  0  0  0  0]
+    #  [ 0  0  1 26 96 89 16  1  0  0  0  0]
+    #  [ 0  0  4 21 86 84 20  1  0  0  0  0]
+    #  [ 0  0  1 24 71 50 15  2  0  0  0  0]
+    #  [ 0  0  0  6 26 37  7  0  0  0  0  0]
+    #  [ 0  0  0  0 11 10  2  0  0  0  0  0]
+    #  [ 0  0  0  1  2  3  1  0  0  0  0  0]
+    #  [ 0  0  0  0  0  2  0  0  0  0  0  0]
+    #  [ 0  0  0  0  0  1  0  0  0  0  0  0]]

examples/guide_listing_5.cpp

@@ -1,4 +1,3 @@
-// also see examples/create_dynamic_histogram.cpp
 #include <boost/histogram.hpp>
 #include <vector>
 

examples/guide_listing_7.cpp

@@ -1,4 +1,3 @@
-// also see examples/create_dynamic_histogram.cpp
 #include <boost/histogram.hpp>
 #include <algorithm>
 #include <vector>

examples/guide_listing_8.cpp

@@ -1,4 +1,3 @@
-// also see examples/create_dynamic_histogram.cpp
 #include <boost/histogram.hpp>
 #include <algorithm>
 #include <vector>

examples/python_example_1d.py

@@ -1,19 +0,0 @@
-import histogram as hg
-import numpy as np
-
-h = hg.histogram(hg.axis.regular(10, -3, 3, "x"))
-h.fill(np.random.randn(1000))
-
-x = np.array(h.axis(0)) # axis instances behave like sequences
-y = np.asarray(h)       # creates a view (no copy involved)
-y = y[:len(h.axis(0))]  # cut off underflow/overflow bins; y[:-2] also works
-y = np.append(y, [0])   # extra zero needed by matplotlib's plot(...) function
-
-try:
-    import matplotlib.pyplot as plt
-    plt.plot(x, y, drawstyle="steps-post")
-    plt.xlabel(h.axis(0).label)
-    plt.ylabel("counts")
-    plt.savefig("example_1d_python.png")
-except ImportError:
-    pass

include/boost/histogram/axis.hpp

@@ -41,66 +41,33 @@ namespace axis {
 
 enum class uoflow { off = false, on = true };
 
-namespace detail {
-// similar to boost::reference_wrapper, but with default ctor
-template <typename T> class cref {
-public:
-  cref() = default;
-  cref(const cref &o) : ptr_(o.ptr_) {}
-  cref &operator=(const cref &o) {
-    ptr_ = o.ptr_;
-    return *this;
-  }
-  cref(const T &t) : ptr_(&t) {}
-  cref &operator=(const T &t) {
-    ptr_ = &t;
-    return *this;
-  }
-  operator const T &() const { return *ptr_; }
-
-private:
-  const T *ptr_ = nullptr;
-};
-
-template <typename Axis>
-using axis_iterator_value_t = std::pair<
-    int, typename conditional<
-             is_reference<typename Axis::bin_type>::value,
-             cref<typename remove_reference<typename Axis::bin_type>::type>,
-             typename Axis::bin_type>::type>;
-} // namespace detail
-
 template <typename Axis>
 class axis_iterator
     : public iterator_facade<axis_iterator<Axis>,
-                             detail::axis_iterator_value_t<Axis>,
+                             std::pair<int, typename Axis::bin_type>,
-                             random_access_traversal_tag> {
+                             random_access_traversal_tag,
+                             std::pair<int, typename Axis::bin_type>> {
 public:
-  using value_type = detail::axis_iterator_value_t<Axis>;
+  explicit axis_iterator(const Axis &axis, int idx) : axis_(axis), idx_(idx) {}
-
-  explicit axis_iterator(const Axis &axis, int idx) : axis_(axis) {
-    value_.first = idx;
-  }
 
   axis_iterator(const axis_iterator &o) = default;
   axis_iterator &operator=(const axis_iterator &o) = default;
 
 private:
-  void increment() noexcept { ++value_.first; }
+  void increment() noexcept { ++idx_; }
-  void decrement() noexcept { --value_.first; }
+  void decrement() noexcept { --idx_; }
-  void advance(int n) noexcept { value_.first += n; }
+  void advance(int n) noexcept { idx_ += n; }
   int distance_to(const axis_iterator &other) const noexcept {
-    return other.value_.first - value_.first;
+    return other.idx_ - idx_;
   }
   bool equal(const axis_iterator &other) const noexcept {
-    return value_.first == other.value_.first;
+    return idx_ == other.idx_;
   }
-  value_type &dereference() const {
+  std::pair<int, typename Axis::bin_type> dereference() const {
-    value_.second = axis_[value_.first];
+    return std::make_pair(idx_, axis_[idx_]);
-    return value_;
   }
-  const Axis &axis_;
+  const Axis& axis_;
-  mutable value_type value_;
+  int idx_;
   friend class boost::iterator_core_access;
 };
 
@@ -552,7 +519,7 @@ template <typename T> class category : public axis_base {
 
 public:
   using value_type = T;
-  using bin_type = const value_type &;
+  using bin_type = T;
   using const_iterator = axis_iterator<category<T>>;
 
   category() = default;

src/python/histogram.cpp

@@ -15,6 +15,7 @@
 #include <boost/shared_ptr.hpp>
 #include <boost/variant/apply_visitor.hpp>
 #include <boost/variant/static_visitor.hpp>
+#include <boost/mpl/for_each.hpp>
 #ifdef HAVE_NUMPY
 #include <boost/python/numpy.hpp>
 namespace np = boost::python::numpy;
@@ -121,6 +122,22 @@ struct axis_visitor : public static_visitor<python::object> {
   }
 };
 
+struct axes_appender {
+  python::object obj;
+  std::vector<dynamic_histogram::any_axis_type>& axes;
+  bool& success;
+  axes_appender(python::object o, std::vector<dynamic_histogram::any_axis_type>& a,
+                bool& s) : obj(o), axes(a), success(s) {}
+  template <typename A> void operator()(const A&) const {
+    if (success) return;
+    python::extract<const A&> get_axis(obj);
+    if (get_axis.check()) {
+      axes.emplace_back(get_axis());
+      success = true;
+    }
+  }
+};
+
 python::object histogram_axis(const dynamic_histogram &self, int i) {
   if (i < 0)
     i += self.dim();
@@ -147,35 +164,16 @@ python::object histogram_init(python::tuple args, python::dict kwargs) {
   std::vector<dynamic_histogram::any_axis_type> axes;
   for (unsigned i = 0; i < dim; ++i) {
     python::object pa = args[i + 1];
-    python::extract<axis::regular<>> er(pa);
+    bool success = false;
-    if (er.check()) {
+    mpl::for_each<dynamic_histogram::any_axis_type::types>(
-      axes.push_back(er());
+      axes_appender(pa, axes, success)
-      continue;
+    );
+    if (!success) {
+      std::string msg = "require an axis object, got ";
+      msg += python::extract<std::string>(pa.attr("__class__"))();
+      PyErr_SetString(PyExc_TypeError, msg.c_str());
+      python::throw_error_already_set();
     }
-    python::extract<axis::circular<>> ep(pa);
-    if (ep.check()) {
-      axes.push_back(ep());
-      continue;
-    }
-    python::extract<axis::variable<>> ev(pa);
-    if (ev.check()) {
-      axes.push_back(ev());
-      continue;
-    }
-    python::extract<axis::integer<>> ei(pa);
-    if (ei.check()) {
-      axes.push_back(ei());
-      continue;
-    }
-    python::extract<axis::category<>> ec(pa);
-    if (ec.check()) {
-      axes.push_back(ec());
-      continue;
-    }
-    std::string msg = "require an axis object, got ";
-    msg += python::extract<std::string>(pa.attr("__class__").attr("__name__"))();
-    PyErr_SetString(PyExc_TypeError, msg.c_str());
-    python::throw_error_already_set();
   }
   dynamic_histogram h(axes.begin(), axes.end());
   return pyinit(h);