creation of install doc and refactor of doc in general (#1908)

* creation of install doc and refactor of doc in general

* updates based on review comments

* updated based on review comments

* updated readme and contributors markdown

* added extra note to not use -j on its own

* added note about smoke tests and regression tests

* made changes as per Illia's feedback

---------

Co-authored-by: Aviral Goel <aviral.goel@amd.com>

docs/conceptual/Composable-Kernel-math.rst

@@ -0,0 +1,77 @@
+.. meta::
+  :description: Composable Kernel mathematical basis
+  :keywords: composable kernel, CK, ROCm, API, mathematics, algorithm
+
+.. _supported-primitives:
+
+********************************************************************
+Composable Kernel mathematical basis
+********************************************************************
+
+This is an introduction to the math which underpins the algorithms implemented in Composable Kernel.
+
+
+For vectors :math:`x^{(1)}, x^{(2)}, \ldots, x^{(T)}` of size :math:`B` you can decompose the
+softmax of concatenated :math:`x = [ x^{(1)}\ | \ \ldots \ | \ x^{(T)} ]` as,
+
+.. math::
+   :nowrap:
+
+   \begin{align}
+      m(x) & = m( [ x^{(1)}\ | \ \ldots \ | \ x^{(T)} ] ) = \max( m(x^{(1)}),\ldots, m(x^{(T)}) )  \\
+      f(x) & = [\exp( m(x^{(1)}) - m(x) ) f( x^{(1)} )\ | \ \ldots \ | \ \exp( m(x^{(T)}) - m(x) ) f( x^{(T)} )] \\
+      z(x) & = \exp( m(x^{(1)}) - m(x) )\ z(x^{(1)}) + \ldots + \exp( m(x^{(T)}) - m(x) )\ z(x^{(1)}) \\
+      \operatorname{softmax}(x) &= f(x)\ / \ z(x)
+   \end{align}
+
+where :math:`f(x^{(j)}) = \exp( x^{(j)} - m(x^{(j)}) )` is of size :math:`B` and
+:math:`z(x^{(j)}) = f(x_1^{(j)})+ \ldots+ f(x_B^{(j)})` is a scalar.
+
+For a matrix :math:`X` composed of :math:`T_r \times T_c` tiles, :math:`X_{ij}`, of size
+:math:`B_r \times B_c` you can compute the row-wise softmax as follows.
+
+For :math:`j` from :math:`1` to :math:`T_c`, and :math:`i` from :math:`1` to :math:`T_r` calculate,
+
+.. math::
+   :nowrap:
+
+   \begin{align}
+      \tilde{m}_{ij}   &= \operatorname{rowmax}( X_{ij} ) \\
+      \tilde{P}_{ij}   &= \exp(X_{ij} - \tilde{m}_{ij} ) \\
+      \tilde{z}_{ij}   &= \operatorname{rowsum}( P_{ij} ) \\
+   \end{align}
+
+If :math:`j=1`, initialize running max, running sum, and the first column block of the output,
+
+.. math::
+   :nowrap:
+
+   \begin{align}
+      m_i            &= \tilde{m}_{i1} \\
+      z_i            &= \tilde{z}_{i1} \\
+      \tilde{Y}_{i1} &= \diag(\tilde{z}_{ij})^{-1} \tilde{P}_{i1}
+   \end{align}
+
+Else if :math:`j>1`,
+
+1. Update running max, running sum and column blocks :math:`k=1` to :math:`k=j-1`
+
+.. math::
+   :nowrap:
+
+   \begin{align}
+      m^{new}_i &= \max(m_i, \tilde{m}_{ij} ) \\
+      z^{new}_i &= \exp(m_i - m^{new}_i)\ z_i + \exp( \tilde{m}_{ij} - m^{new}_i )\ \tilde{z}_{ij}  \\
+      Y_{ik}    &= \diag(z^{new}_{i})^{-1} \diag(z_{i}) \exp(m_i - m^{new}_i)\ Y_{ik}
+   \end{align}
+
+2. Initialize column block :math:`j` of output and reset running max and running sum variables:
+
+.. math::
+   :nowrap:
+
+   \begin{align}
+      \tilde{Y}_{ij} &= \diag(z^{new}_{i})^{-1} \exp(\tilde{m}_{ij} - m^{new}_i ) \tilde{P}_{ij} \\
+      z_i            &= z^{new}_i \\
+      m_i            &= m^{new}_i \\
+   \end{align}

docs/conceptual/Composable-Kernel-structure.rst

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+.. meta::
+  :description: Composable Kernel structure
+  :keywords: composable kernel, CK, ROCm, API, structure
+
+.. _what-is-ck:
+
+********************************************************************
+Composable Kernel structure
+********************************************************************
+
+The Composable Kernel library uses a tile-based programming model and tensor coordinate transformation to achieve performance portability and code maintainability. Tensor coordinate transformation is a complexity reduction technique for complex machine learning operators.
+  
+
+.. image:: ../data/ck_component.png
+   :alt: CK Components
+
+
+The Composable Kernel library consists of four layers: 
+
+* a templated tile operator layer
+* a templated kernel and invoker layer
+* an instantiated kernel and invoker layer
+* a client API layer.
+
+A wrapper component is included to simplify tensor transform operations.
+
+.. image:: ../data/ck_layer.png
+   :alt: CK Layers
+   

docs/conceptual/what-is-ck.rst

@@ -1,41 +0,0 @@
-.. meta::
-  :description: Composable Kernel documentation and API reference library
-  :keywords: composable kernel, CK, ROCm, API, documentation
-
-.. _what-is-ck:
-
-********************************************************************
-What is the Composable Kernel library
-********************************************************************
-
-
-Methodology
-===========
-
-The Composable Kernel (CK) library provides a programming model for writing performance critical kernels for machine learning workloads across multiple architectures including GPUs and CPUs, through general purpose kernel languages like HIP C++.
-
-CK utilizes two concepts to achieve performance portability and code maintainability:
-
-* A tile-based programming model
-* Algorithm complexity reduction for complex ML operators using an innovative technique called
-  "Tensor Coordinate Transformation".
-
-.. image:: ../data/ck_component.png
-   :alt: CK Components
-
-
-Code Structure
-==============
-
-The CK library is structured into 4 layers:
-
-* "Templated Tile Operators" layer
-* "Templated Kernel and Invoker" layer
-* "Instantiated Kernel and Invoker" layer
-* "Client API" layer
-
-It also includes a simple wrapper component used to perform tensor transform operations more easily and with fewer lines of code.
-
-.. image:: ../data/ck_layer.png
-   :alt: CK Layers
-