@@ -509,7 +509,7 @@ density (``density``), number density resolved by particle spin
509509(``gofr ``), static structure factor (``sk ``), static structure factor
510510(``skall ``), energy density (``energydensity ``), one body reduced
511511density matrix (``dm1b ``), :math: `S(k)` based kinetic energy correction
512- (``chiesa ``), forward walking (`` ForwardWalking ``), and force
512+ (``chiesa ``), and force
513513(``Force ``) estimators. Other estimators are not yet covered.
514514
515515When an ``<estimator/> `` element appears in ``<hamiltonian/> ``, it is
@@ -555,8 +555,6 @@ section (e.g., during VMC only).
555555 +------------------+------------------+-----------------------------------------------------------+
556556 | | Force | Family of "force" estimators (see :ref: `ccz-force-est `) |
557557 +------------------+------------------+-----------------------------------------------------------+
558- | | ForwardWalking | Forward walking values for existing estimators |
559- +------------------+------------------+-----------------------------------------------------------+
560558 | | orbitalimages | Create image files for orbitals, then exit |
561559 +------------------+------------------+-----------------------------------------------------------+
562560 | | flux | Checks sampling of kinetic energy |
@@ -1920,90 +1918,6 @@ Additional information:
19201918 <sposet type="bspline" name="dm_basis" size="50" spindataset="0"/>
19211919 </sposet_builder>
19221920
1923- .. _forward-walking :
1924-
1925- Forward-Walking Estimators
1926- --------------------------
1927-
1928- Forward walking is a method for sampling the pure fixed-node
1929- distribution :math: `\langle \Phi _0 | \Phi _0 \rangle `. Specifically, one
1930- multiplies each walker’s DMC mixed estimate for the observable
1931- :math: `\mathcal {O}`,
1932- :math: `\frac {\mathcal {O}(\mathbf {R})\Psi _T(\mathbf {R})}{\Psi _T(\mathbf {R})}`,
1933- by the weighting factor
1934- :math: `\frac {\Phi _0 (\mathbf {R})}{\Psi _T(\mathbf {R})}`. As it turns out,
1935- this weighting factor for any walker :math: `\mathbf {R}` is proportional
1936- to the total number of descendants the walker will have after a
1937- sufficiently long projection time :math: `\beta `.
1938-
1939- To forward walk on an observable, declare a generic forward-walking
1940- estimator within a ``<hamiltonian> `` block, and then specify the
1941- observables to forward walk on and the forward-walking parameters. Here
1942- is a summary.
1943-
1944- ``estimator type=ForwardWalking `` element:
1945-
1946- +------------------+----------------------+
1947- | parent elements: | ``hamiltonian, qmc `` |
1948- +------------------+----------------------+
1949- | child elements: | ``Observable `` |
1950- +------------------+----------------------+
1951-
1952- attributes:
1953-
1954- +---------------------+--------------+--------------------+-------------+---------------------------+
1955- | **Name ** | **Datatype ** | **Values ** | **Default ** | **Description ** |
1956- +=====================+==============+====================+=============+===========================+
1957- | ``type ``:math:`^r ` | text | **ForwardWalking ** | | Must be "ForwardWalking" |
1958- +---------------------+--------------+--------------------+-------------+---------------------------+
1959- | ``name ``:math:`^r ` | text | *anything * | any | Unique name for estimator |
1960- +---------------------+--------------+--------------------+-------------+---------------------------+
1961-
1962- ``Observable `` element:
1963-
1964- +------------------+---------------------------------+
1965- | parent elements: | ``estimator, hamiltonian, qmc `` |
1966- +------------------+---------------------------------+
1967- | child elements: | *None * |
1968- +------------------+---------------------------------+
1969-
1970- +--------------------------+--------------+---------------+-------------+---------------------------------------------------------------------------------+
1971- | **Name ** | **Datatype ** | **Values ** | **Default ** | **Description ** |
1972- +==========================+==============+===============+=============+=================================================================================+
1973- | ``name ``:math:`^r ` | text | *anything * | any | Registered name of existing estimator on which to forward walk |
1974- +--------------------------+--------------+---------------+-------------+---------------------------------------------------------------------------------+
1975- | ``max ``:math:`^r ` | integer | :math: `>0 ` | | Maximum projection time in steps (``max ``:math:`=\beta/\tau `) |
1976- +--------------------------+--------------+---------------+-------------+---------------------------------------------------------------------------------+
1977- | ``frequency ``:math:`^r ` | text | :math: `\geq 1 `| | Dump data only for every ``frequency ``-th to ``scalar.dat `` file |
1978- +--------------------------+--------------+---------------+-------------+---------------------------------------------------------------------------------+
1979-
1980- Additional information:
1981-
1982- - **Cost **: Because histories of observables up to ``max `` time steps
1983- have to be stored, the memory cost of storing the nonforward-walked
1984- observables variables should be multiplied by :math: `\texttt {max}`.
1985- Although this is not an issue for items such as potential energy, it
1986- could be prohibitive for observables such as density, forces, etc.
1987-
1988- - **Naming Convention **: Forward-walked observables are automatically
1989- named ``FWE_name_i ``, where ``i `` is the forward-walked expectation
1990- value at time step ``i ``, and ``name `` is whatever name appears in
1991- the ``<Observable> `` block. This is also how it will appear in the
1992- ``scalar.dat `` file.
1993-
1994- In the following example case, QMCPACK forward walks on the potential
1995- energy for 300 time steps and dumps the forward-walked value at every
1996- time step.
1997-
1998- .. code-block ::
1999- :caption: Forward-walking estimator element.
2000- :name: Listing 42
2001-
2002- <estimator name="fw" type="ForwardWalking">
2003- <Observable name="LocalPotential" max="300" frequency="1"/>
2004- <!--- Additional Observable blocks go here -->
2005- </estimator>
2006-
20071921 .. _ccz-force-est :
20081922
20091923Chiesa-Ceperley-Zhang Force Estimators
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