README.md

@@ -1,53 +1,54 @@
 # KMath
-Kotlin MATHematics library is intended as a kotlin based analog of numpy python library. Contrary to `numpy`
+The Kotlin MATHematics library is intended as a Kotlin-based analog to Python's `numpy` library. In contrast to `numpy` and `scipy` it is modular and has a lightweight core.
-and `scipy` it is modular and has a lightweight core.
 
 ## Features
 
 * **Algebra**
-    * Mathematical operation entities like rings, spaces and fields with (**TODO** add example to wiki) 
+    * Algebraic structures like rings, spaces and field (**TODO** add example to wiki)
-    * Basic linear algebra operations (summs products, etc) backed by `Space` API.
+    * Basic linear algebra operations (sums, products, etc.), backed by the `Space` API.
-    * Complex numbers backed by `Field` API (meaning that they will be useable in any structures like vectors and NDArrays).
+    * Complex numbers backed by the `Field` API (meaning that they will be usable in any structure like vectors and N-dimensional arrays).
-    * [In progress] advanced linear algebra operations like matrix inversions.
+    * [In progress] advanced linear algebra operations like matrix inversion and LU decomposition.
-* **Array-like structures** Full support of numpy-like ndarray including mixed arithmetic operations and function operations
+* **Array-like structures** Full support of [numpy-like ndarrays](https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.ndarray.html) including mixed arithmetic operations and function operations over arrays and numbers just like in Python (with the added benefit of static type checking).
-on arrays and numbers just like it works in python (with benefit of static type checking).
 
-* **Expressions** Expressions are one of the ultimate goals of kmath. It is planned to be able to write some mathematical
+* **Expressions** Expressions are one of the ultimate goals of KMath. By writing a single mathematical expression
-expression once an then apply it to different types of objects by providing different context. Exception could be used
+once, users will be able to apply different types of objects to the expression by providing a context. Exceptions
-for a wide variety of purposes from high performance calculations to code generation.
+can be used for a wide variety of purposes from high performance calculations to code generation.
 
 ## Planned features
 
 * **Common mathematics** It is planned to gradually wrap most parts of [Apache commons-math](http://commons.apache.org/proper/commons-math/) 
-library in kotlin code and maybe rewrite some parts to better suite kotlin programming paradigm. There is no fixed priority list for that. Feel free
+library in Kotlin code and maybe rewrite some parts to better suit the Kotlin programming paradigm, however there is no fixed roadmap for that. Feel free
-to submit a future request if you want something to be done first.
+to submit a feature request if you want something to be done first.
 
 * **Messaging** A mathematical notation to support multi-language and multi-node communication for mathematical tasks.
 
 ## Multi-platform support
-KMath is developed as a multi-platform library, which means that most of interfaces are declared in common module.
+
-Implementation is also done in common module wherever it is possible. In some cases features are delegated to 
+KMath is developed as a multi-platform library, which means that most of interfaces are declared in the [common module](kmath-core/src/commonMain).
-platform even if they could be done in common module because of platform performance optimization. 
+Implementation is also done in the common module wherever possible. In some cases, features are delegated to
-Currently the main focus of development is the JVM platform, contribution of implementations for Kotlin - Native and
+platform-specific implementations even if they could be done in the common module for performance reasons.
-Kotlin - JS is welcome. 
+Currently, the JVM is the main focus of development, however Kotlin/Native and Kotlin/JS contributions are also welcome.
 
 ## Performance
-The calculation performance is one of major goals of KMath in the future, but in some cases it is not possible to achieve 
+
-both performance and flexibility. We expect to firstly focus on creating convenient universal API and then work on 
+Calculation performance is one of major goals of KMath in the future, but in some cases it is not possible to achieve
-increasing performance for specific cases. We expect the worst KMath performance still be better than natural python,
+both performance and flexibility. We expect to focus on creating convenient universal API first and then work on
-but worse than optimized native/scipy (mostly due to boxing operations on primitive numbers). The best performance 
+increasing performance for specific cases. We expect the worst KMath benchmarks will perform better than native Python,
-of optimized parts should be better than scipy.
+but worse than optimized native/SciPy (mostly due to boxing operations on primitive numbers). The best performance
+of optimized parts should be better than SciPy.
 
 ## Releases
 
-The project is currently in pre-release stage. Nightly builds could be used by adding additional repository to (groovy) gradle config:
+The project is currently in pre-release stage. Nightly builds can be used by adding an additional repository to the Gradle config like so:
+
 ```groovy
 repositories {
     maven { url = "http://npm.mipt.ru:8081/artifactory/gradle-dev" }
     mavenCentral()
 } 
 ```
-or for kotlin gradle dsl:
+
+or for the Gradle Kotlin DSL:
 
 ```kotlin
 repositories {
@@ -56,16 +57,20 @@ repositories {
 } 
 ```
 
-Then use regular dependency like
+Then use a regular dependency like so:
+
 ```groovy
 compile(group: 'scientifik', name: 'kmath-core', version: '0.0.1-SNAPSHOT')
 ```
-or in kotlin
+
+or in the Gradle Kotlin DSL:
+
 ```kotlin
 compile(group = "scientifik", name = "kmath-core", version = "0.0.1-SNAPSHOT")
 ```
 
-Work builds could be obtained with [![](https://jitpack.io/v/altavir/kmath.svg)](https://jitpack.io/#altavir/kmath). 
+Working builds can be obtained here: [![](https://jitpack.io/v/altavir/kmath.svg)](https://jitpack.io/#altavir/kmath).
 
 ## Contributing
-The project requires a lot of additional work. Please fill free to contribute in any way and propose new features.
+
+The project requires a lot of additional work. Please fill free to contribute in any way and propose new features.

doc/contexts.md

@@ -1,50 +1,57 @@
 # Context-oriented mathematics
 
 ## The problem
-A known problem for implementing mathematics in statically-typed languages (and not only in them) is that different 
+A known problem for implementing mathematics in statically-typed languages (but not only in them) is that different
-sets of mathematical operation could be defined on the same mathematical objects. Sometimes there is not single way to
+sets of mathematical operators can be defined on the same mathematical objects. Sometimes there is no single way to
-treat some operations like basic arithmetic operations on Java/Kotlin `Number`. Sometimes there are different ways to do
+treat some operations, including basic arithmetic operations, on a Java/Kotlin `Number`. Sometimes there are different ways to
-the same thing like Euclidean and elliptic geometry vector spaces defined over real vectors. Another problem arises when 
+define the same structure, such as Euclidean and elliptic geometry vector spaces over real vectors. Another problem arises when
-one wants to add some kind of behavior to existing entity. In dynamic languages those problems are usually solved
+one wants to add some kind of behavior to an existing entity. In dynamic languages those problems are usually solved
-by adding dynamic context-specific behaviors in runtime, but this solution has a lot of drawbacks.
+by adding dynamic context-specific behaviors at runtime, but this solution has a lot of drawbacks.
 
 ## Context-oriented approach
-One of possible solutions to those problems is to completely separate object numerical representations from behaviors.
+
-In terms of kotlin it means to have separate class to represent some entity without any operations, 
+One possible solution to these problems is to completely separate numerical representations from behaviors.
+One solution in Kotlin, is to define a separate class which represents some entity without any operations,
 for example a complex number:
 
 ```kotlin
 data class Complex(val re: Double, val im: Double)
 ```
-And a separate class or singleton, representing operation on those complex numbers:
+
+And then define a separate class or singleton, representing an operation on those complex numbers:
+
 ```kotlin
-object: ComplexOperations{
+object ComplexOperations {
     operator fun Complex.plus(other: Complex) = Complex(re + other.re, im + other.im)
     operator fun Complex.minus(other: Complex) = Complex(re - other.re, im - other.im)
 }
 ```
 
-In Java, application of such external operations could be very cumbersome, but Kotlin has a unique feature which allows
+In Java, applying such external operations could be very cumbersome, but Kotlin has a unique feature which allows
-to treat this situation: blocks with receivers. So in kotlin, operation on complex number could beimplemented as:
+to treat this situation: [extensions with receivers](https://kotlinlang.org/docs/reference/extensions.html#extension-functions).
+So in Kotlin, an operation on complex number could be implemented as:
+
 ```kotlin
-with(ComplexOperations){c1 + c2 - c3}
+with(ComplexOperations) { c1 + c2 - c3 }
 ```
+
 Kotlin also allows to create functions with receivers:
+
 ```kotlin
 fun ComplexOperations.doSomethingWithComplex(c1: Complex, c2: Complex, c3: Complex) = c1 + c2 - c3
 
 ComplexOperations.doComethingWithComplex(c1,c2,c3)
 ```
 
-In fact, whole parts of program could run in a mathematical context or even multiple nested contexts. 
+In fact, whole parts of a program may be run within a mathematical context or even multiple nested contexts.
 
-In `kmath` contexts are responsible not only for operations, but also for raw object creation and advanced features.
+In KMath, contexts are responsible not only for operations, but also for raw object creation and advanced features.
 
 ## Other possibilities
 
-An obvious candidate to get more or less the same functionality is type-class feature. It allows to bind a behavior to
+An obvious candidate to get more or less the same functionality is the type-class, which allows one to bind a behavior to
-a specific type without modifying the type itself. On a plus side, type-classes do not require explicit context 
+a specific type without modifying the type itself. On the plus side, type-classes do not require explicit context
 declaration, so the code looks cleaner. On the minus side, if there are different sets of behaviors for the same types,
-it is impossible to combine them in the single module. Also, unlike type-classes, context could have parameters or even
+it is impossible to combine them into one module. Also, unlike type-classes, context can have parameters or even
-state. For example in `kmath`, sizes and strides for `NDElement` or `Matrix` could be moved to context to optimize 
+state. For example in KMath, sizes and strides for `NDElement` or `Matrix` could be moved to context to optimize
-performance in case of large amount of structures.
+performance in case of a large amount of structures.

doc/operations.md

@@ -1,38 +1,40 @@
 ## Spaces and fields
 
-An obvious first choice of mathematical objects to implement in context-oriented style are algebra elements like spaces,
+An obvious first choice of mathematical objects to implement in a context-oriented style are algebraic elements like spaces,
-rings and fields. Those are located in a `scientifik.kmath.operations.Algebra.kt` file. Alongside algebric context
+rings and fields. Those are located in the `scientifik.kmath.operations.Algebra.kt` file. Alongside common contexts, the file includes definitions for algebra elements like `FieldElement`. A `FieldElement` object
-themselves, the file includes definitions for algebra elements such as `FieldElement`. A `FieldElement` object
+stores a reference to the `Field` which contains additive and multiplicative operations, meaning
-stores a reference to the `Field` which contains a additive and multiplicative operations for it, meaning
+it has one fixed context attached and does not require explicit external context. So those `MathElements` can be operated without context:
-it has one fixed context attached to it and does not require explicit external context. So those `MathElements` could be
+
-operated without context:
 ```kotlin
 val c1 = Complex(1.0, 2.0)
 val c2 = ComplexField.i
 val c3 = c1 + c2
 ```
-`ComplexField` also features special operations to mix complex numbers with real numbers like:
+
+`ComplexField` also features special operations to mix complex and real numbers, for example:
+
 ```kotlin
 val c1 = Complex(1.0,2.0)
-val c2 = ComplexField.run{ c1 - 1.0} //returns [re:0.0, im: 2.0]
+val c2 = ComplexField.run{ c1 - 1.0} // Returns: [re:0.0, im: 2.0]
 val c3 = ComplexField.run{ c1 - i*2.0}
 ```
 
 **Note**: In theory it is possible to add behaviors directly to the context, but currently kotlin syntax does not support
-that. Watch [KT-10468](https://youtrack.jetbrains.com/issue/KT-10468) for news.
+that. Watch [KT-10468](https://youtrack.jetbrains.com/issue/KT-10468) for updates.
 
 ## Nested fields
 
-Algebra contexts allow to create more complex structures. For example, it is possible to create a `Matrix` from complex
+Contexts allow one to build more complex structures. For example, it is possible to create a `Matrix` from complex elements like so:
-elements like this:
+
 ```kotlin
 val element = NDElements.create(field = ComplexField, shape = intArrayOf(2,2)){index: IntArray ->
     Complex(index[0] - index[1], index[0] + index[1])
 }
 ```
-The `element` in this example is a member of `Field` of 2-d structures, each element of which is a member of its own
-`ComplexField`. The important thing is that one does not need to create a special nd-structure to hold complex
-numbers and implements operations on it, one need just to provide a field for its elements.
 
-**Note**: Fields themselves do not solve problem of JVM boxing, but it is possible to solve with special contexts like
+The `element` in this example is a member of the `Field` of 2-d structures, each element of which is a member of its own
+`ComplexField`. The important thing is one does not need to create a special n-d class to hold complex
+numbers and implement operations on it, one just needs to provide a field for its elements.
+
+**Note**: Fields themselves do not solve the problem of JVM boxing, but it is possible to solve with special contexts like
 `BufferSpec`. This feature is in development phase.

gradle/wrapper/gradle-wrapper.properties

@@ -0,0 +1,5 @@
+distributionBase=GRADLE_USER_HOME
+distributionPath=wrapper/dists
+distributionUrl=https\://services.gradle.org/distributions/gradle-5.0-bin.zip
+zipStoreBase=GRADLE_USER_HOME
+zipStorePath=wrapper/dists

gradlew

@@ -0,0 +1,172 @@
+#!/usr/bin/env sh
+
+##############################################################################
+##
+##  Gradle start up script for UN*X
+##
+##############################################################################
+
+# Attempt to set APP_HOME
+# Resolve links: $0 may be a link
+PRG="$0"
+# Need this for relative symlinks.
+while [ -h "$PRG" ] ; do
+    ls=`ls -ld "$PRG"`
+    link=`expr "$ls" : '.*-> \(.*\)$'`
+    if expr "$link" : '/.*' > /dev/null; then
+        PRG="$link"
+    else
+        PRG=`dirname "$PRG"`"/$link"
+    fi
+done
+SAVED="`pwd`"
+cd "`dirname \"$PRG\"`/" >/dev/null
+APP_HOME="`pwd -P`"
+cd "$SAVED" >/dev/null
+
+APP_NAME="Gradle"
+APP_BASE_NAME=`basename "$0"`
+
+# Add default JVM options here. You can also use JAVA_OPTS and GRADLE_OPTS to pass JVM options to this script.
+DEFAULT_JVM_OPTS='"-Xmx64m"'
+
+# Use the maximum available, or set MAX_FD != -1 to use that value.
+MAX_FD="maximum"
+
+warn () {
+    echo "$*"
+}
+
+die () {
+    echo
+    echo "$*"
+    echo
+    exit 1
+}
+
+# OS specific support (must be 'true' or 'false').
+cygwin=false
+msys=false
+darwin=false
+nonstop=false
+case "`uname`" in
+  CYGWIN* )
+    cygwin=true
+    ;;
+  Darwin* )
+    darwin=true
+    ;;
+  MINGW* )
+    msys=true
+    ;;
+  NONSTOP* )
+    nonstop=true
+    ;;
+esac
+
+CLASSPATH=$APP_HOME/gradle/wrapper/gradle-wrapper.jar
+
+# Determine the Java command to use to start the JVM.
+if [ -n "$JAVA_HOME" ] ; then
+    if [ -x "$JAVA_HOME/jre/sh/java" ] ; then
+        # IBM's JDK on AIX uses strange locations for the executables
+        JAVACMD="$JAVA_HOME/jre/sh/java"
+    else
+        JAVACMD="$JAVA_HOME/bin/java"
+    fi
+    if [ ! -x "$JAVACMD" ] ; then
+        die "ERROR: JAVA_HOME is set to an invalid directory: $JAVA_HOME
+
+Please set the JAVA_HOME variable in your environment to match the
+location of your Java installation."
+    fi
+else
+    JAVACMD="java"
+    which java >/dev/null 2>&1 || die "ERROR: JAVA_HOME is not set and no 'java' command could be found in your PATH.
+
+Please set the JAVA_HOME variable in your environment to match the
+location of your Java installation."
+fi
+
+# Increase the maximum file descriptors if we can.
+if [ "$cygwin" = "false" -a "$darwin" = "false" -a "$nonstop" = "false" ] ; then
+    MAX_FD_LIMIT=`ulimit -H -n`
+    if [ $? -eq 0 ] ; then
+        if [ "$MAX_FD" = "maximum" -o "$MAX_FD" = "max" ] ; then
+            MAX_FD="$MAX_FD_LIMIT"
+        fi
+        ulimit -n $MAX_FD
+        if [ $? -ne 0 ] ; then
+            warn "Could not set maximum file descriptor limit: $MAX_FD"
+        fi
+    else
+        warn "Could not query maximum file descriptor limit: $MAX_FD_LIMIT"
+    fi
+fi
+
+# For Darwin, add options to specify how the application appears in the dock
+if $darwin; then
+    GRADLE_OPTS="$GRADLE_OPTS \"-Xdock:name=$APP_NAME\" \"-Xdock:icon=$APP_HOME/media/gradle.icns\""
+fi
+
+# For Cygwin, switch paths to Windows format before running java
+if $cygwin ; then
+    APP_HOME=`cygpath --path --mixed "$APP_HOME"`
+    CLASSPATH=`cygpath --path --mixed "$CLASSPATH"`
+    JAVACMD=`cygpath --unix "$JAVACMD"`
+
+    # We build the pattern for arguments to be converted via cygpath
+    ROOTDIRSRAW=`find -L / -maxdepth 1 -mindepth 1 -type d 2>/dev/null`
+    SEP=""
+    for dir in $ROOTDIRSRAW ; do
+        ROOTDIRS="$ROOTDIRS$SEP$dir"
+        SEP="|"
+    done
+    OURCYGPATTERN="(^($ROOTDIRS))"
+    # Add a user-defined pattern to the cygpath arguments
+    if [ "$GRADLE_CYGPATTERN" != "" ] ; then
+        OURCYGPATTERN="$OURCYGPATTERN|($GRADLE_CYGPATTERN)"
+    fi
+    # Now convert the arguments - kludge to limit ourselves to /bin/sh
+    i=0
+    for arg in "$@" ; do
+        CHECK=`echo "$arg"|egrep -c "$OURCYGPATTERN" -`
+        CHECK2=`echo "$arg"|egrep -c "^-"`                                 ### Determine if an option
+
+        if [ $CHECK -ne 0 ] && [ $CHECK2 -eq 0 ] ; then                    ### Added a condition
+            eval `echo args$i`=`cygpath --path --ignore --mixed "$arg"`
+        else
+            eval `echo args$i`="\"$arg\""
+        fi
+        i=$((i+1))
+    done
+    case $i in
+        (0) set -- ;;
+        (1) set -- "$args0" ;;
+        (2) set -- "$args0" "$args1" ;;
+        (3) set -- "$args0" "$args1" "$args2" ;;
+        (4) set -- "$args0" "$args1" "$args2" "$args3" ;;
+        (5) set -- "$args0" "$args1" "$args2" "$args3" "$args4" ;;
+        (6) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" ;;
+        (7) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" ;;
+        (8) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" "$args7" ;;
+        (9) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" "$args7" "$args8" ;;
+    esac
+fi
+
+# Escape application args
+save () {
+    for i do printf %s\\n "$i" | sed "s/'/'\\\\''/g;1s/^/'/;\$s/\$/' \\\\/" ; done
+    echo " "
+}
+APP_ARGS=$(save "$@")
+
+# Collect all arguments for the java command, following the shell quoting and substitution rules
+eval set -- $DEFAULT_JVM_OPTS $JAVA_OPTS $GRADLE_OPTS "\"-Dorg.gradle.appname=$APP_BASE_NAME\"" -classpath "\"$CLASSPATH\"" org.gradle.wrapper.GradleWrapperMain "$APP_ARGS"
+
+# by default we should be in the correct project dir, but when run from Finder on Mac, the cwd is wrong
+if [ "$(uname)" = "Darwin" ] && [ "$HOME" = "$PWD" ]; then
+  cd "$(dirname "$0")"
+fi
+
+exec "$JAVACMD" "$@"

gradlew.bat

@@ -0,0 +1,84 @@
+@if "%DEBUG%" == "" @echo off
+@rem ##########################################################################
+@rem
+@rem  Gradle startup script for Windows
+@rem
+@rem ##########################################################################
+
+@rem Set local scope for the variables with windows NT shell
+if "%OS%"=="Windows_NT" setlocal
+
+set DIRNAME=%~dp0
+if "%DIRNAME%" == "" set DIRNAME=.
+set APP_BASE_NAME=%~n0
+set APP_HOME=%DIRNAME%
+
+@rem Add default JVM options here. You can also use JAVA_OPTS and GRADLE_OPTS to pass JVM options to this script.
+set DEFAULT_JVM_OPTS="-Xmx64m"
+
+@rem Find java.exe
+if defined JAVA_HOME goto findJavaFromJavaHome
+
+set JAVA_EXE=java.exe
+%JAVA_EXE% -version >NUL 2>&1
+if "%ERRORLEVEL%" == "0" goto init
+
+echo.
+echo ERROR: JAVA_HOME is not set and no 'java' command could be found in your PATH.
+echo.
+echo Please set the JAVA_HOME variable in your environment to match the
+echo location of your Java installation.
+
+goto fail
+
+:findJavaFromJavaHome
+set JAVA_HOME=%JAVA_HOME:"=%
+set JAVA_EXE=%JAVA_HOME%/bin/java.exe
+
+if exist "%JAVA_EXE%" goto init
+
+echo.
+echo ERROR: JAVA_HOME is set to an invalid directory: %JAVA_HOME%
+echo.
+echo Please set the JAVA_HOME variable in your environment to match the
+echo location of your Java installation.
+
+goto fail
+
+:init
+@rem Get command-line arguments, handling Windows variants
+
+if not "%OS%" == "Windows_NT" goto win9xME_args
+
+:win9xME_args
+@rem Slurp the command line arguments.
+set CMD_LINE_ARGS=
+set _SKIP=2
+
+:win9xME_args_slurp
+if "x%~1" == "x" goto execute
+
+set CMD_LINE_ARGS=%*
+
+:execute
+@rem Setup the command line
+
+set CLASSPATH=%APP_HOME%\gradle\wrapper\gradle-wrapper.jar
+
+@rem Execute Gradle
+"%JAVA_EXE%" %DEFAULT_JVM_OPTS% %JAVA_OPTS% %GRADLE_OPTS% "-Dorg.gradle.appname=%APP_BASE_NAME%" -classpath "%CLASSPATH%" org.gradle.wrapper.GradleWrapperMain %CMD_LINE_ARGS%
+
+:end
+@rem End local scope for the variables with windows NT shell
+if "%ERRORLEVEL%"=="0" goto mainEnd
+
+:fail
+rem Set variable GRADLE_EXIT_CONSOLE if you need the _script_ return code instead of
+rem the _cmd.exe /c_ return code!
+if  not "" == "%GRADLE_EXIT_CONSOLE%" exit 1
+exit /b 1
+
+:mainEnd
+if "%OS%"=="Windows_NT" endlocal
+
+:omega