Commit 680caf5a authored by Ben Huber's avatar Ben Huber

fixing more links in documentation

parent 110f85ab
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The `xerus` library is a general purpose library for numerical calculations with higher order tensors, Tensor-Train Decompositions / Matrix Product States and other Tensor Networks.
The focus of development was the simple usability and adaptibility to any setting that requires higher order tensors or decompositions thereof.
For tutorials and a documentation see <a href="http://libxerus.org">the doxygen documentation</a>.
For tutorials and a documentation see <a href="http://libxerus.org">the documentation</a>.
The source code is licenced under the AGPL v3.0. For more details see the LICENSE file.
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......@@ -13,7 +13,7 @@ demonstrate the general layout and is enough for very basic applications. It is
at the more detailed guides for all classes one wishes to use though - or even have a look at the doxygen class documentation for details on all functions.
It is assumed that you have already obtained and compiled the library itself as well as know how to link against it.
If this is not the case, please refer to the [building xerus](building_xerus) page.
If this is not the case, please refer to the [building xerus](/building_xerus) page.
In the following we will solve a FEM equation arising from the heat equation using a QTT decomposition and the ALS algorithm.
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......@@ -12,7 +12,7 @@ In matrix calculus the decomposition of a matrix into the matrix product of seve
into an orthogonal and a triangular matrix (QR) or orthogonal matrices and diagonal of singular values (SVD)) are among the
most powerful tools to devise numerical algorithms. In the case of tensors of higher degree it is necessary to indicate along
which modes the decomposition is supposed to happen, so `xerus` uses the notation of indexed equations explained in the previous
chapter ([Indices and Equations](indices)).
chapter ([Indices and Equations](/indices)).
## QR Decompositions
To provide an intuitive approach to decompositions, `xerus` uses the assignment of multiple tensors with a single operator to
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......@@ -57,12 +57,12 @@ left hand side.
The left hand side (`c` in the above example) is not required to have the right degree or dimensions. The type of `c` on the
other hand does change the meaning of the equation and so has to be set correctly. E.g. if `c` is a `xerus::TensorNetwork`, no
contraction is performed as `A(i,j)*b(j)` is in itself a valid tensor network. See also the tutorials on [TT-Tensors](tttensors)
and [Tensor Networks](tensornetworks) for details on the respective assignments.
contraction is performed as `A(i,j)*b(j)` is in itself a valid tensor network. See also the tutorials on [TT-Tensors](/tttensors)
and [Tensor Networks](/tensornetworks) for details on the respective assignments.
__warnStart
Unless runtime checks have explicitely been disabled during compilation of `xerus` (see [Optimizations](optimization)), invalid
Unless runtime checks have explicitely been disabled during compilation of `xerus` (see [Optimizations](/optimization)), invalid
indexed expressions will produce runtime errors (in the form of `xerus::misc::generic_error`s being thrown as exceptions).
__tabsStart
......@@ -163,7 +163,7 @@ C(i,k) << A(i&1, j) * B(j, k&1)
~~~
__tabsEnd
The division `i/n` is useful for example to write equations with high dimensional operators such as [TT-Operators](tttensors)
The division `i/n` is useful for example to write equations with high dimensional operators such as [TT-Operators](/tttensors)
for which the indices are ordered per default such, that the application of the operator can be written in analogy to
matrix-vector products as:
......@@ -188,7 +188,7 @@ that the degree of `v` is equal to half the degree of `A` and that its dimension
A common use for indexed expressions is to construct tensors in a blockwise fashion. In the following example we were able to
calculate the tensor `comp` whenever the first index was fixed, either by numerical construction (`A` and `B`) or by showing
mathematically, that it is then equal to a well known tensor (here the identity matrix). The full tensor can thus be constructed
with the help of the named constructors of `xerus::Tensor` (see the [Tensor tutorial](tensor)) as follows.
with the help of the named constructors of `xerus::Tensor` (see the [Tensor tutorial](/tensor)) as follows.
__tabsStart
~~~ cpp
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......@@ -11,7 +11,7 @@ __tabsInit
The basic building stone of this library and all Tensor Network methods is the Tensor, represented in the class `xerus::Tensor`.
To simplify the work with these objects, `xerus` contains a number of helper functions that allow the quick creation and
modification of sparse and dense tensors. In the following we will list the most important ones but advise you to also read
the tutorials on [indices and equations](indices) and [decompositions](decompositions) to have the full toolset with which to work on individual
the tutorials on [indices and equations](/indices) and [decompositions](/decompositions) to have the full toolset with which to work on individual
tensors.
## Creation of Tensors
......@@ -194,7 +194,7 @@ V[[1,1]] = 1.0 # equivalently: V[3] = 1.0
~~~
__tabsEnd
Explicitely constructing a tensor similarly in a blockwise fashion will be covered in the tutorial on [indices and equations](indices)
Explicitely constructing a tensor similarly in a blockwise fashion will be covered in the tutorial on [indices and equations](/indices)
## Sparse and Dense Representations
......@@ -376,7 +376,7 @@ __tabsEnd
## Operators and Modifications
We have already seen the most basic method of modifying a tensor via the [operator[]](__doxyref(xerus::Tensor::operator[])). With it
and the index notation presented in the [indices and equations](indices) tutorial, most desired manipulations can be
and the index notation presented in the [indices and equations](/indices) tutorial, most desired manipulations can be
represented. Some of them would still be cumbersome though, so `xerus` includes several helper functions to make your life easier.
The purpose of this section is to present the most important ones.
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