Complete the coeff-wise math function table.

1 files changed, 380 insertions, 12 deletions

diff --git a/doc/CoeffwiseMathFunctionsTable.dox b/doc/CoeffwiseMathFunctionsTable.dox
index c466c14c8..ac6e0bd31 100644
--- a/doc/CoeffwiseMathFunctionsTable.dox
+++ b/doc/CoeffwiseMathFunctionsTable.dox
@@ -3,11 +3,11 @@ namespace Eigen {
 /** \eigenManualPage CoeffwiseMathFunctions Catalog of coefficient-wise math functions
 
 
-<span style="font-size:300%; color:red; font-weight: 900;">!WORK IN PROGRESS!</span>
+<!-- <span style="font-size:300%; color:red; font-weight: 900;">!WORK IN PROGRESS!</span> -->
 
 This table presents a catalog of the coefficient-wise math functions supported by %Eigen.
 In this table, \c a, \c b, refer to Array objects or expressions, and \c m refers to a linear algebra Matrix/Vector object. Standard scalar types are abbreviated as follows:
-  - \c int: \c ui32
+  - \c int: \c i32
   - \c float: \c f
   - \c double: \c d
   - \c std::complex<float>: \c cf
@@ -43,7 +43,35 @@ This also means that, unless specified, if the function \c std::foo is available
   using <a href="http://en.cppreference.com/w/cpp/numeric/math/fabs">std::abs</a>; \n
   abs(a[i]);
   </td>
-  <td>SSE2, AVX (ui32,f,d)</td>
+  <td>SSE2, AVX (i32,f,d)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_inverse
+  a.\link ArrayBase::inverse inverse\endlink(); \n
+  \link Eigen::inverse inverse\endlink(a); \n
+  m.\link MatrixBase::cwiseInverse cwiseInverse\endlink();
+  </td>
+  <td>inverse value (\f$ 1/a_i \f$) </td>
+  <td class="code">
+  1/a[i];
+  </td>
+  <td>All engines (f,d,fc,fd)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_conj
+  a.\link ArrayBase::conjugate conjugate\endlink(); \n
+  \link Eigen::conj conj\endlink(a); \n
+  m.\link MatrixBase::conjugate conjugate();
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Complex_conjugate">complex conjugate</a> (\f$ \bar{a_i} \f$),\n
+  no-op for real </td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/complex/conj">std::conj</a>; \n
+  conj(a[i]);
+  </td>
+  <td>All engines (fc,fd)</td>
 </tr>
 <tr>
 <th colspan="4">Exponential functions</th>
@@ -67,12 +95,12 @@ This also means that, unless specified, if the function \c std::foo is available
   a.\link ArrayBase::log log\endlink(); \n
   \link Eigen::log log\endlink(a);
   </td>
-  <td>natural (base \f$ e \f$) logarithm (\f$ ln({a_i}) \f$)</td>
+  <td>natural (base \f$ e \f$) logarithm (\f$ \ln({a_i}) \f$)</td>
   <td class="code">
   using <a href="http://en.cppreference.com/w/cpp/numeric/math/log">std::log</a>; \n
   log(a[i]);
   </td>
-  <td>SSE2, AVX (f,d)</td>
+  <td>SSE2, AVX (f)</td>
 </tr>
 <tr>
   <td class="code">
@@ -80,23 +108,298 @@ This also means that, unless specified, if the function \c std::foo is available
   a.\link ArrayBase::log1p log1p\endlink(); \n
   \link Eigen::log1p log1p\endlink(a);
   </td>
-  <td>natural (base \f$ e \f$) logarithm of 1 plus \n the given number (\f$ ln({1+a_i}) \f$)</td>
+  <td>natural (base \f$ e \f$) logarithm of 1 plus \n the given number (\f$ \ln({1+a_i}) \f$)</td>
   <td>built-in generic implementation based on \c log,\n
   plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/log1p">\c std::log1p </a>; \cpp11</td>
   <td></td>
 </tr>
 <tr>
+  <td class="code">
+  \anchor cwisetable_log10
+  a.\link ArrayBase::log10 log10\endlink(); \n
+  \link Eigen::log10 log10\endlink(a);
+  </td>
+  <td>base 10 logarithm (\f$ \log_{10}({a_i}) \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/log10">std::log10</a>; \n
+  log10(a[i]);
+  </td>
+  <td></td>
+</tr>
+<tr>
 <th colspan="4">Power functions</th>
 </tr>
 <tr>
+  <td class="code">
+  \anchor cwisetable_pow
+  a.\link ArrayBase::pow pow\endlink(b); \n
+  \link Eigen::pow pow\endlink(a,b);
+  </td>
+  <td>raises a number to the given power (\f$ a_i ^ {b_i} \f$) \n \c a and \c b can be either an array or scalar.</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/pow">std::pow</a>; \n
+  pow(a[i],b[i]);\n
+  (plus builtin for integer types)</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_sqrt
+  a.\link ArrayBase::sqrt sqrt\endlink(); \n
+  \link Eigen::sqrt sqrt\endlink(a);\n
+  m.\link MatrixBase::cwiseSqrt cwiseSqrt\endlink();
+  </td>
+  <td>computes square root (\f$ \sqrt a_i \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt">std::sqrt</a>; \n
+  sqrt(a[i]);</td>
+  <td>SSE2, AVX (f,d)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_rsqrt
+  a.\link ArrayBase::rsqrt rsqrt\endlink(); \n
+  \link Eigen::rsqrt rsqrt\endlink(a);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Fast_inverse_square_root">reciprocal square root</a> (\f$ 1/{\sqrt a_i} \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt">std::sqrt</a>; \n
+  1/sqrt(a[i]); \n
+  </td>
+  <td>SSE2, AVX, AltiVec, ZVector (f,d)\n
+  (approx + 1 Newton iteration)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_square
+  a.\link ArrayBase::square square\endlink(); \n
+  \link Eigen::square square\endlink(a);
+  </td>
+  <td>computes square power (\f$ a_i^2 \f$)</td>
+  <td class="code">
+  a[i]*a[i]</td>
+  <td>All (i32,f,d,cf,cd)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_cube
+  a.\link ArrayBase::cube cube\endlink(); \n
+  \link Eigen::cube cube\endlink(a);
+  </td>
+  <td>computes cubic power (\f$ a_i^3 \f$)</td>
+  <td class="code">
+  a[i]*a[i]*a[i]</td>
+  <td>All (i32,f,d,cf,cd)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_abs2
+  a.\link ArrayBase::abs2 abs2\endlink(); \n
+  \link Eigen::abs2 abs2\endlink(a);\n
+  m.\link MatrixBase::cwiseAbs2 cwiseAbs2\endlink();
+  </td>
+  <td>computes the squared absolute value (\f$ |a_i|^2 \f$)</td>
+  <td class="code">
+  real:    a[i]*a[i] \n
+  complex:  real(a[i])*real(a[i]) \n
+  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; + imag(a[i])*imag(a[i])</td>
+  <td>All (i32,f,d)</td>
+</tr>
+<tr>
 <th colspan="4">Trigonometric functions</th>
 </tr>
 <tr>
+  <td class="code">
+  \anchor cwisetable_sin
+  a.\link ArrayBase::sin sin\endlink(); \n
+  \link Eigen::sin sin\endlink(a);
+  </td>
+  <td>computes sine</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/sin">std::sin</a>; \n
+  sin(a[i]);</td>
+  <td>SSE2, AVX (f)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_cos
+  a.\link ArrayBase::cos cos\endlink(); \n
+  \link Eigen::cos cos\endlink(a);
+  </td>
+  <td>computes cosine</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/cos">std::cos</a>; \n
+  cos(a[i]);</td>
+  <td>SSE2, AVX (f)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_tan
+  a.\link ArrayBase::tan tan\endlink(); \n
+  \link Eigen::tan tan\endlink(a);
+  </td>
+  <td>computes tangent</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/tan">std::tan</a>; \n
+  tan(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_asin
+  a.\link ArrayBase::asin asin\endlink(); \n
+  \link Eigen::asin asin\endlink(a);
+  </td>
+  <td>computes arc sine (\f$ \sin^{-1} a_i \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/asin">std::asin</a>; \n
+  asin(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_acos
+  a.\link ArrayBase::acos acos\endlink(); \n
+  \link Eigen::acos acos\endlink(a);
+  </td>
+  <td>computes arc cosine  (\f$ \cos^{-1} a_i \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/acos">std::acos</a>; \n
+  acos(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_atan
+  a.\link ArrayBase::atan tan\endlink(); \n
+  \link Eigen::atan atan\endlink(a);
+  </td>
+  <td>computes arc tangent (\f$ \tan^{-1} a_i \f$)</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/atan">std::atan</a>; \n
+  atan(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
 <th colspan="4">Hyperbolic functions</th>
 </tr>
 <tr>
+  <td class="code">
+  \anchor cwisetable_sinh
+  a.\link ArrayBase::sinh sinh\endlink(); \n
+  \link Eigen::sinh sinh\endlink(a);
+  </td>
+  <td>computes hyperbolic sine</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/sinh">std::sinh</a>; \n
+  sinh(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_cosh
+  a.\link ArrayBase::cosh cohs\endlink(); \n
+  \link Eigen::cosh cosh\endlink(a);
+  </td>
+  <td>computes hyperbolic cosine</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/cosh">std::cosh</a>; \n
+  cosh(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_tanh
+  a.\link ArrayBase::tanh tanh\endlink(); \n
+  \link Eigen::tanh tanh\endlink(a);
+  </td>
+  <td>computes hyperbolic tangent</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/tanh">std::tanh</a>; \n
+  tanh(a[i]);</td>
+  <td></td>
+</tr>
+<tr>
+<th colspan="4">Nearest integer floating point operations</th>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_ceil
+  a.\link ArrayBase::ceil ceil\endlink(); \n
+  \link Eigen::ceil ceil\endlink(a);
+  </td>
+  <td>nearest integer not less than the given value</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/ceil">std::ceil</a>; \n
+  ceil(a[i]);</td>
+  <td>SSE4,AVX,ZVector (f,d)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_floor
+  a.\link ArrayBase::floor floor\endlink(); \n
+  \link Eigen::floor floor\endlink(a);
+  </td>
+  <td>nearest integer not greater than the given value</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/floor">std::floor</a>; \n
+  floor(a[i]);</td>
+  <td>SSE4,AVX,ZVector (f,d)</td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_round
+  a.\link ArrayBase::round round\endlink(); \n
+  \link Eigen::round round\endlink(a);
+  </td>
+  <td>nearest integer, \n rounding away from zero in halfway cases</td>
+  <td>built-in generic implementation \n based on \c floor and \c ceil,\n
+  plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/round">\c std::round </a>; \cpp11</td>
+  <td>SSE4,AVX,ZVector (f,d)</td>
+</tr>
+<tr>
+<th colspan="4">Floating point manipulation functions</th>
+</tr>
+<tr>
+<th colspan="4">Classification and comparison</th>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_isfinite
+  a.\link ArrayBase::isfinite isfinite\endlink(); \n
+  \link Eigen::isfinite isfinite\endlink(a);
+  </td>
+  <td>checks if the given number has finite value</td>
+  <td>built-in generic implementation,\n
+  plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isfinite">\c std::isfinite </a>; \cpp11</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_isinf
+  a.\link ArrayBase::isinf isinf\endlink(); \n
+  \link Eigen::isinf isinf\endlink(a);
+  </td>
+  <td>checks if the given number is infinite</td>
+  <td>built-in generic implementation,\n
+  plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isinf">\c std::isinf </a>; \cpp11</td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_isnan
+  a.\link ArrayBase::isnan isnan\endlink(); \n
+  \link Eigen::isnan isnan\endlink(a);
+  </td>
+  <td>checks if the given number is not a number</td>
+  <td>built-in generic implementation,\n
+  plus \c using <a href="http://en.cppreference.com/w/cpp/numeric/math/isnan">\c std::isnan </a>; \cpp11</td>
+  <td></td>
+</tr>
+<tr>
 <th colspan="4">Error and gamma functions</th>
 </tr>
+<tr> <td colspan="4">  Require \c #include \c <unsupported/Eigen/SpecialFunctions> </td></tr>
 <tr>
   <td class="code">
   \anchor cwisetable_erf
@@ -124,24 +427,89 @@ This also means that, unless specified, if the function \c std::foo is available
   <td></td>
 </tr>
 <tr>
-<th colspan="4">Nearest integer floating point operations</th>
+  <td class="code">
+  \anchor cwisetable_lgamma
+  a.\link ArrayBase::lgamma lgamma\endlink(); \n
+  \link Eigen::lgamma lgamma\endlink(a);
+  </td>
+  <td>natural logarithm of the gamma function</td>
+  <td class="code">
+  using <a href="http://en.cppreference.com/w/cpp/numeric/math/lgamma">std::lgamma</a>; \cpp11 \n
+  lgamma(a[i]);
+  </td>
+  <td></td>
 </tr>
 <tr>
-<th colspan="4">Floating point manipulation functions</th>
+  <td class="code">
+  \anchor cwisetable_digamma
+  a.\link ArrayBase::digamma digamma\endlink(); \n
+  \link Eigen::digamma digamma\endlink(a);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Digamma_function">logarithmic derivative of the gamma function</a></td>
+  <td>
+  built-in for float and double
+  </td>
+  <td></td>
 </tr>
 <tr>
-<th colspan="4">Classification and comparison</th>
+  <td class="code">
+  \anchor cwisetable_igamma
+  \link Eigen::igamma igamma\endlink(a,x);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">lower incomplete gamma integral</a>
+  \n \f$ \gamma(a_i,x_i)= \frac{1}{|a_i|} \int_{0}^{x_i}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td>
+  <td>
+  built-in for float and double,\n but requires \cpp11
+  </td>
+  <td></td>
+</tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_igammac
+  \link Eigen::igammac igammac\endlink(a,x);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">upper incomplete gamma integral</a>
+  \n \f$ \Gamma(a_i,x_i) = \frac{1}{|a_i|} \int_{x_i}^{\infty}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td>
+  <td>
+  built-in for float and double,\n but requires \cpp11
+  </td>
+  <td></td>
+</tr>
+<tr>
+<th colspan="4">Special functions</th>
+</tr>
+<tr> <td colspan="4">  Require \c #include \c <unsupported/Eigen/SpecialFunctions> </td></tr>
+<tr>
+  <td class="code">
+  \anchor cwisetable_polygamma
+  \link Eigen::polygamma polygamma\endlink(n,x);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Polygamma_function">n-th derivative of digamma at x</a></td>
+  <td>
+  built-in generic based on\n <a href="#cwisetable_lgamma">\c lgamma </a>,
+  <a href="#cwisetable_digamma"> \c digamma </a>
+  and <a href="#cwisetable_zeta">\c zeta </a>.
+  </td>
+  <td></td>
 </tr>
 <tr>
-<th colspan="4">Miscellaneous</th>
+  <td class="code">
+  \anchor cwisetable_betainc
+  \link Eigen::betainc betainc\endlink(a,b,x);
+  </td>
+  <td><a href="https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function">Incomplete beta function</a></td>
+  <td>
+  built-in for float and double,\n but requires \cpp11
+  </td>
+  <td></td>
 </tr>
 <tr>
   <td class="code">
   \anchor cwisetable_zeta
-  a.\link ArrayBase::zeta zeta\endlink(b); \n
   \link Eigen::zeta zeta\endlink(a,b);
   </td>
-  <td><a href="https://en.wikipedia.org/wiki/Hurwitz_zeta_function">Hurwitz zeta function</a> \n \f$ \zeta(a_i,b_i)=\sum_{k=0}^{\infty}(b_i+k)^{\text{-}a_i} \f$</td>
+  <td><a href="https://en.wikipedia.org/wiki/Hurwitz_zeta_function">Hurwitz zeta function</a>
+  \n \f$ \zeta(a_i,b_i)=\sum_{k=0}^{\infty}(b_i+k)^{\text{-}a_i} \f$</td>
   <td>
   built-in for float and double
   </td>