Complete the coeff-wise math function table.
diff --git a/doc/CoeffwiseMathFunctionsTable.dox b/doc/CoeffwiseMathFunctionsTable.dox
index c466c14..ac6e0bd 100644
--- a/doc/CoeffwiseMathFunctionsTable.dox
+++ b/doc/CoeffwiseMathFunctionsTable.dox
@@ -3,11 +3,11 @@
/** \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 @@
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$),\n
+ no-op for real </td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/complex/conj">std::conj</a>; \n
+ conj(a[i]);
+ </td>
+ <td>All engines (fc,fd)</td>
</tr>
<tr>
<th colspan="4">Exponential functions</th>
@@ -67,12 +95,12 @@
a.\link ArrayBase::log log\endlink(); \n
\link Eigen::log log\endlink(a);
</td>
- <td>natural (base \f$ e \f$) logarithm (\f$ ln({a_i}) \f$)</td>
+ <td>natural (base \f$ e \f$) logarithm (\f$ \ln({a_i}) \f$)</td>
<td class="code">
using <a href="http://en.cppreference.com/w/cpp/numeric/math/log">std::log</a>; \n
log(a[i]);
</td>
- <td>SSE2, AVX (f,d)</td>
+ <td>SSE2, AVX (f)</td>
</tr>
<tr>
<td class="code">
@@ -80,23 +108,298 @@
a.\link ArrayBase::log1p log1p\endlink(); \n
\link Eigen::log1p log1p\endlink(a);
</td>
- <td>natural (base \f$ 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$)</td>
+ <td class="code">
+ real: a[i]*a[i] \n
+ complex: real(a[i])*real(a[i]) \n
+ + imag(a[i])*imag(a[i])</td>
+ <td>All (i32,f,d)</td>
+</tr>
+<tr>
<th colspan="4">Trigonometric functions</th>
</tr>
<tr>
+ <td class="code">
+ \anchor cwisetable_sin
+ a.\link ArrayBase::sin sin\endlink(); \n
+ \link Eigen::sin sin\endlink(a);
+ </td>
+ <td>computes sine</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/sin">std::sin</a>; \n
+ sin(a[i]);</td>
+ <td>SSE2, AVX (f)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_cos
+ a.\link ArrayBase::cos cos\endlink(); \n
+ \link Eigen::cos cos\endlink(a);
+ </td>
+ <td>computes cosine</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/cos">std::cos</a>; \n
+ cos(a[i]);</td>
+ <td>SSE2, AVX (f)</td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_tan
+ a.\link ArrayBase::tan tan\endlink(); \n
+ \link Eigen::tan tan\endlink(a);
+ </td>
+ <td>computes tangent</td>
+ <td class="code">
+ using <a href="http://en.cppreference.com/w/cpp/numeric/math/tan">std::tan</a>; \n
+ tan(a[i]);</td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_asin
+ a.\link ArrayBase::asin asin\endlink(); \n
+ \link Eigen::asin asin\endlink(a);
+ </td>
+ <td>computes arc sine (\f$ \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 @@
<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$</td>
+ <td>
+ built-in for float and double,\n but requires \cpp11
+ </td>
+ <td></td>
</tr>
<tr>
-<th colspan="4">Miscellaneous</th>
+ <td class="code">
+ \anchor cwisetable_igammac
+ \link Eigen::igammac igammac\endlink(a,x);
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function">upper incomplete gamma integral</a>
+ \n \f$ \Gamma(a_i,x_i) = \frac{1}{|a_i|} \int_{x_i}^{\infty}e^{\text{-}t} t^{a_i-1} \mathrm{d} t \f$</td>
+ <td>
+ built-in for float and double,\n but requires \cpp11
+ </td>
+ <td></td>
+</tr>
+<tr>
+<th colspan="4">Special functions</th>
+</tr>
+<tr> <td colspan="4"> Require \c #include \c <unsupported/Eigen/SpecialFunctions> </td></tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_polygamma
+ \link Eigen::polygamma polygamma\endlink(n,x);
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Polygamma_function">n-th derivative of digamma at x</a></td>
+ <td>
+ built-in generic based on\n <a href="#cwisetable_lgamma">\c lgamma </a>,
+ <a href="#cwisetable_digamma"> \c digamma </a>
+ and <a href="#cwisetable_zeta">\c zeta </a>.
+ </td>
+ <td></td>
+</tr>
+<tr>
+ <td class="code">
+ \anchor cwisetable_betainc
+ \link Eigen::betainc betainc\endlink(a,b,x);
+ </td>
+ <td><a href="https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function">Incomplete beta function</a></td>
+ <td>
+ built-in for float and double,\n but requires \cpp11
+ </td>
+ <td></td>
</tr>
<tr>
<td class="code">
\anchor cwisetable_zeta
- a.\link ArrayBase::zeta zeta\endlink(b); \n
\link Eigen::zeta zeta\endlink(a,b);
</td>
- <td><a href="https://en.wikipedia.org/wiki/Hurwitz_zeta_function">Hurwitz zeta function</a> \n \f$ \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>