float support in doc
This commit is contained in:
1 parent
d8c21582c7
commit
90c37c9ec8
9 files changed
+98
-39
No files matched your search
+3
-3
@@ -119,7 +119,7 @@ scaled). Returns \code{info}.}
|
||||
\lafunc{const NRMat<T> calcsvdinverse(NRMat<T> a, double thr=0, bool do_absadjoint=false)}{Inverse via SVD, $V\,\mathrm{diag}(1/s_i)\,U\Hc$,
|
||||
singular values $s_i<$\code{thr} are treated as zero (pseudoinverse). With \code{do_absadjoint} returns
|
||||
$V\,\mathrm{diag}(\prod_{j\ne i}s_j)\,U\Hc$, the adjugate matrix up to the phase $\det U\det V$. Square matrices only.}
|
||||
\lafunc{NRVec<T> svd_solve(NRMat<T> &a, const NRVec<T> &b, double thres=1e-12, int *nullity=NULL); NRMat<T> svd_solve(NRMat<T> &a, const NRMat<T> &b, double thres=1e-12, int *nullity=NULL)}{Least-squares
|
||||
\lafunc{NRVec<T> svd_solve(NRMat<T> &a, const NRVec<T> &b, normtype thres=LA_precision<normtype>::svd_threshold(), int *nullity=NULL); NRMat<T> svd_solve(NRMat<T> &a, const NRMat<T> &b, normtype thres=LA_precision<normtype>::svd_threshold(), int *nullity=NULL)}{Least-squares
|
||||
solution $x=V\,\mathrm{diag}(1/s_i)\,U\Hc b$ discarding singular values $\le$\code{thres} (no contamination by the null space);
|
||||
the number of discarded ones is stored in \code{*nullity}. Here (unlike \code{linear_solve}) the right-hand sides are the
|
||||
\emph{columns} of the matrix \code{b} ($m\times n_{\mathrm{rhs}}$); \code{a} ($m\times n$, $m\ge n$) is destroyed.}
|
||||
@@ -223,8 +223,8 @@ so they can be used with implicitly defined (``direct'') matrices as in chapter~
|
||||
needs \code{size()}, \code{operator*=}, \code{axpy} and \code{resize()}.
|
||||
|
||||
The exponential uses scaling and squaring: the power $p$ is chosen so that $\|A\|/2^p\lesssim 0.75$
|
||||
(\code{mynextpow2}), the Taylor series of the scaled argument is truncated when the next term would be below $10^{-14}$
|
||||
relative to the norm, and the result is squared $p$ times. The scaling is put into the Taylor coefficients,
|
||||
(\code{mynextpow2}), the Taylor series of the scaled argument is truncated when the next term would be below
|
||||
\code{LA_precision<normtype>::taylor_precision()} ($10^{-14}$ for double, $10^{-7}$ for float) relative to the norm, and the result is squared $p$ times. The scaling is put into the Taylor coefficients,
|
||||
so the argument itself is not copied. \code{maxpower} (if ${}\ge0$) limits $p$, \code{maxtaylor} (if ${}\ge0$) limits
|
||||
the order of the Taylor polynomial, which is useful and exact for nilpotent matrices (e.g.\ coupled-cluster excitation
|
||||
operators).
|
||||
|
||||
Reference in new issue
Block a user