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When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{\texttip{b^2-4ac}{descriminant}} \over 2a}.$$


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package words
- Alphabetic
- Public
- All
Type Members
-
final
class
BeWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
orMustMatchers
for an overview of the matchers DSL.Class
BeWord
contains anapply
method that takes aSymbol
, which uses reflection to find and access aBoolean
property and determine if it istrue
. If the symbol passed is'empty
, for example, theapply
method will use reflection to look for a public Java field named "empty", a public method named "empty", or a public method named "isEmpty". If a field, it must be of typeBoolean
. If a method, it must take no parameters and returnBoolean
. If multiple candidates are found, theapply
method will select based on the following algorithm:Field Method "is" Method Result Throws TestFailedException
, because no candidates foundisEmpty()
Invokes isEmpty()
empty()
Invokes empty()
empty()
isEmpty()
Invokes empty()
(this can occur whenBeanProperty
annotation is used)empty
Accesses field empty
empty
isEmpty()
Invokes isEmpty()
empty
empty()
Invokes empty()
empty
empty()
isEmpty()
Invokes empty()
(this can occur whenBeanProperty
annotation is used) -
final
class
BehaveWord
extends AnyRef
Class that supports shared test registration via instances referenced from the
behave
field ofFunSpec
s,FlatSpec
s, andWordSpec
s as well as instance of their sister traits,fixture.FunSpec
,fixture.FlatSpec
, andfixture.WordSpec
.Class that supports shared test registration via instances referenced from the
behave
field ofFunSpec
s,FlatSpec
s, andWordSpec
s as well as instance of their sister traits,fixture.FunSpec
,fixture.FlatSpec
, andfixture.WordSpec
.This class, via the
behave
field, enables syntax such as the following inFunSpec
s,FlatSpec
s,fixture.FunSpec
s, andfixture.FlatSpec
s:it should behave like nonFullStack(stackWithOneItem) ^
It also enables syntax such as the following syntax in
WordSpec
s andfixture.WordSpec
s:behave like nonEmptyStack(lastValuePushed) ^
For more information and examples of the use of <cod>behave, see the Shared tests section in the main documentation for trait
FunSpec
,FlatSpec
, orWordSpec
. -
trait
CanVerb
extends AnyRef
Provides an implicit conversion that adds
can
methods toString
to support the syntax ofFlatSpec
,WordSpec
,org.scalatest.fixture.FlatSpec
, andfixture.WordSpec
.Provides an implicit conversion that adds
can
methods toString
to support the syntax ofFlatSpec
,WordSpec
,org.scalatest.fixture.FlatSpec
, andfixture.WordSpec
.For example, this trait enables syntax such as the following test registration in
FlatSpec
andfixture.FlatSpec
:"A Stack (when empty)" can "be empty" in { ... } ^
It also enables syntax such as the following shared test registration in
FlatSpec
andfixture.FlatSpec
:"A Stack (with one item)" can behave like nonEmptyStack(stackWithOneItem, lastValuePushed) ^
In addition, it supports the registration of subject descriptions in
WordSpec
andfixture.WordSpec
, such as:"A Stack (when empty)" can { ... ^
And finally, it also supportds the registration of subject descriptions with after words in
WordSpec
andfixture.WordSpec
. For example:def provide = afterWord("provide") "The ScalaTest Matchers DSL" can provide { ^
The reason this implicit conversion is provided in a separate trait, instead of being provided directly in
FlatSpec
,WordSpec
,fixture.FlatSpec
, andfixture.WordSpec
, is primarily for design symmetry withShouldVerb
andMustVerb
. BothShouldVerb
andMustVerb
must exist as a separate trait because an implicit conversion provided directly would conflict with the implicit conversion that providesshould
ormust
methods onString
in theMatchers
andMustMatchers
traits. -
final
class
CompileWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ContainWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
DefinedWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
EmptyWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
EndWithWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ExistWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
FullyMatchWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
HaveWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
IncludeWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
LengthWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
MatchPatternWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
trait
MatcherWords
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
trait
MustVerb
extends AnyRef
Provides an implicit conversion that adds
must
methods toString
to support the syntax ofFlatSpec
,WordSpec
,fixture.FlatSpec
, andfixture.WordSpec
.Provides an implicit conversion that adds
must
methods toString
to support the syntax ofFlatSpec
,WordSpec
,fixture.FlatSpec
, andfixture.WordSpec
.For example, this trait enables syntax such as the following test registration in
FlatSpec
andfixture.FlatSpec
:"A Stack (when empty)" must "be empty" in { ... } ^
It also enables syntax such as the following shared test registration in
FlatSpec
andfixture.FlatSpec
:"A Stack (with one item)" must behave like nonEmptyStack(stackWithOneItem, lastValuePushed) ^
In addition, it supports the registration of subject descriptions in
WordSpec
andfixture.WordSpec
, such as:"A Stack (when empty)" must { ... ^
And finally, it also supportds the registration of subject descriptions with after words in
WordSpec
andfixture.WordSpec
. For example:def provide = afterWord("provide") "The ScalaTest Matchers DSL" must provide { ^
The reason this implicit conversion is provided in a separate trait, instead of being provided directly in
FlatSpec
,WordSpec
,fixture.FlatSpec
, andfixture.WordSpec
, is because an implicit conversion provided directly would conflict with the implicit conversion that providesmust
methods onString
in theMustMatchers
trait. By contrast, there is no conflict with the separateMustVerb
trait approach, because:FlatSpec
,WordSpec
,fixture.FlatSpec
, andfixture.WordSpec
mix inMustVerb
directly, andMustMatchers
extendsMustVerb
, overriding theconvertToStringMustWrapper
implicit conversion function.
So whether or not a
FlatSpec
,WordSpec
,fixture.FlatSpec
, orfixture.WordSpec
mixes inMustMatchers
, there will only be one implicit conversion in scope that addsmust
methods toString
s.Also, because the class of the result of the overriding
convertToStringMustWrapper
implicit conversion method provided inMustMatchers
extends this trait'sStringMustWrapperForVerb
class, the four uses ofmust
provided here are still available. These fourmust
are in fact available to any class that mixes inMustMatchers
, but each takes an implicit parameter that is provided only inFlatSpec
andfixture.FlatSpec
, orWordSpec
andfixture.WordSpec
. -
final
class
NoExceptionWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
NotWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. - final class PleaseUseNoExceptionShouldSyntaxInstead extends AnyRef
-
final
class
ReadableWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
RegexWithGroups
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfATypeInvocation
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfAWordToAMatcherApplication
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfAWordToBePropertyMatcherApplication
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfAWordToSymbolApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfAfterWordApplication
extends AnyRef
Class that supports the use of after words in
WordSpec
andfixture.WordSpec
.Class that supports the use of after words in
WordSpec
andfixture.WordSpec
.A
ResultOfAfterWordApplication
, which encapsulates the text of the after word and a block, is accepted bywhen
,should
,must
,can
, andthat
methods. For more information, see the main documentation for traitWordSpec
. -
class
ResultOfAllElementsOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfAllOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfAnTypeInvocation
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfAnWordToAnMatcherApplication
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfAnWordToBePropertyMatcherApplication
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfAnWordToSymbolApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfAtLeastOneElementOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfAtLeastOneOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfAtMostOneElementOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfAtMostOneOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfBeThrownBy
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfBeWordForAType
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfBeWordForAnType
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfBeWordForNoException
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfContainWord
[L] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfDefinedAt
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfGreaterThanComparison
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfGreaterThanOrEqualToComparison
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfInOrderApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfInOrderElementsOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfInOrderOnlyApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfKeyWordApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfLengthWordApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfLessThanComparison
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfLessThanOrEqualToComparison
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfMessageWordApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfNoElementsOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfNoneOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfNotExist
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfNotWordForAny
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfOfTypeInvocation
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfOneElementOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfOneOfApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfOnlyApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfRegexWordApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL.The primary constructor enables the following syntax (with a passed
scala.util.matching.Regex
):"eight" should not fullyMatch regex ("""(-)?(\d+)(\.\d*)?""".r) ^
-
final
class
ResultOfSizeWordApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
abstract
class
ResultOfStringPassedToVerb
extends AnyRef
Abstract class that supports test registration in
FlatSpec
andfixture.FlatSpec
.Abstract class that supports test registration in
FlatSpec
andfixture.FlatSpec
.For example, this class enables syntax such as the following pending test registration in
FlatSpec
andfixture.FlatSpec
:"A Stack (when empty)" should "be empty" is (pending) ^
For example, this class enables syntax such as the following tagged test registration in
FlatSpec
andfixture.FlatSpec
:"A Stack (when empty)" should "be empty" taggedAs(SlowTet) in { ... } ^
This class also indirectly enables syntax such as the following regular test registration in
FlatSpec
andfixture.FlatSpec
:"A Stack (when empty)" should "be empty" in { ... } ^
However, this class does not declare any methods named
in
, because the type passed toin
differs in aFlatSpec
and afixture.FlatSpec
. Afixture.FlatSpec
needs twoin
methods, one that takes a no-arg test function and another that takes a one-arg test function (a test that takes aFixture
as its parameter). By constrast, aFlatSpec
needs only onein
method that takes a by-name parameter. As a result,FlatSpec
andfixture.FlatSpec
each provide an implicit conversion fromResultOfStringPassedToVerb
to a type that provides the appropriatein
methods. -
abstract
class
ResultOfTaggedAsInvocation
extends AnyRef
Supports the registration of tagged tests in shorthand form in
FlatSpec
andfixture.FlatSpec
.Supports the registration of tagged tests in shorthand form in
FlatSpec
andfixture.FlatSpec
.For example, this class enables syntax such as the following tagged, pending test registration in shorthand form:
"A Stack (when empty)" should "be empty" taggedAs() is (pending) ^
In addition, this class indirectly enables syntax such as the following tagged test registration in shorthand form:
"A Stack (when empty)" should "be empty" taggedAs() in { ... } ^
Rather than provide
in
andignore
methods directly, these methods are provided aftertaggedAs()
by implicit conversions because the type passed toin
(andignore
) differs in aFlatSpec
and afixture.FlatSpec
. Afixture.FlatSpec
needs twoin
methods, one that takes a no-arg test function and another that takes a one-arg test function (a test that takes aFixture
as its parameter). By constrast, aFlatSpec
needs only onein
method that takes a by-name parameter. As a result,FlatSpec
andfixture.FlatSpec
each provide an implicit conversion fromResultOfTaggedAsInvocation
to a type that provides the appropriatein
methods. -
class
ResultOfTheSameElementsAsApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
class
ResultOfTheSameElementsInOrderAsApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfTheSameInstanceAsApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfTheTypeInvocation
[T] extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfThrownByApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
ResultOfValueWordApplication
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
trait
ShouldVerb
extends AnyRef
Provides an implicit conversion that adds
should
methods toString
to support the syntax ofFlatSpec
,WordSpec
,fixture.FlatSpec
, andfixture.WordSpec
.Provides an implicit conversion that adds
should
methods toString
to support the syntax ofFlatSpec
,WordSpec
,fixture.FlatSpec
, andfixture.WordSpec
.For example, this trait enables syntax such as the following test registration in
FlatSpec
andfixture.FlatSpec
:"A Stack (when empty)" should "be empty" in { ... } ^
It also enables syntax such as the following shared test registration in
FlatSpec
andfixture.FlatSpec
:"A Stack (with one item)" should behave like nonEmptyStack(stackWithOneItem, lastValuePushed) ^
In addition, it supports the registration of subject descriptions in
WordSpec
andfixture.WordSpec
, such as:"A Stack (when empty)" should { ... ^
And finally, it also supportds the registration of subject descriptions with after words in
WordSpec
andfixture.WordSpec
. For example:def provide = afterWord("provide") "The ScalaTest Matchers DSL" should provide { ^
The reason this implicit conversion is provided in a separate trait, instead of being provided directly in
FlatSpec
,WordSpec
,fixture.FlatSpec
, andfixture.WordSpec
, is because an implicit conversion provided directly would conflict with the implicit conversion that providesshould
methods onString
in theMatchers
trait. By contrast, there is no conflict with the separateShouldVerb
trait approach, because:FlatSpec
,WordSpec
,fixture.FlatSpec
, andfixture.WordSpec
mix inShouldVerb
directly, andMatchers
extendsShouldVerb
, overriding theconvertToStringShouldWrapper
implicit conversion function.
So whether or not a
FlatSpec
,WordSpec
,fixture.FlatSpec
, orfixture.WordSpec
mixes inMatchers
, there will only be one implicit conversion in scope that addsshould
methods toString
s.Also, because the class of the result of the overriding
convertToStringShouldWrapper
implicit conversion method provided inMatchers
extends this trait'sStringShouldWrapperForVerb
class, the four uses ofshould
provided here are still available. These fourshould
are in fact available to any class that mixes inMatchers
, but each takes an implicit parameter that is provided only inFlatSpec
andfixture.FlatSpec
, orWordSpec
andfixture.WordSpec
. -
final
class
SizeWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
SortedWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
StartWithWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
abstract
class
StringVerbBehaveLikeInvocation
extends AnyRef
Class that provides a role-specific type for an implicit conversion used to support the registration of subject descriptions in
FlatSpec
andFreeSpec
styles.Class that provides a role-specific type for an implicit conversion used to support the registration of subject descriptions in
FlatSpec
andFreeSpec
styles.For example, this class enables syntax such as the following in
WordSpec
andfixture.WordSpec
:"A Stack (when empty)" should { ... ^
This
should
method, which is provided inShouldVerb
, needs an implicit parameter of typeStringVerbBlockRegistration
. -
abstract
class
StringVerbBlockRegistration
extends AnyRef
Class that provides a role-specific type for an implicit conversion used to support the registration of subject descriptions in
WordSpec
andfixture.WordSpec
.Class that provides a role-specific type for an implicit conversion used to support the registration of subject descriptions in
WordSpec
andfixture.WordSpec
.For example, this class enables syntax such as the following in
WordSpec
andfixture.WordSpec
:"A Stack (when empty)" should { ... ^
This
should
method, which is provided inShouldVerb
, needs an implicit parameter of typeStringVerbBlockRegistration
. -
abstract
class
StringVerbStringInvocation
extends AnyRef
Class that provides a role-specific type for an implicit conversion used to support the registration of subject descriptions in
FlatSpec
andFreeSpec
styles.Class that provides a role-specific type for an implicit conversion used to support the registration of subject descriptions in
FlatSpec
andFreeSpec
styles.For example, this class enables syntax such as the following in
WordSpec
andfixture.WordSpec
:"A Stack (when empty)" should { ... ^
This
should
method, which is provided inShouldVerb
, needs an implicit parameter of typeStringVerbBlockRegistration
. -
abstract
class
SubjectWithAfterWordRegistration
extends AnyRef
Class that provides a role-specific type for an implicit conversion used to support the registration of subject descriptions in
FlatSpec
andFreeSpec
styles.Class that provides a role-specific type for an implicit conversion used to support the registration of subject descriptions in
FlatSpec
andFreeSpec
styles.For example, this class enables syntax such as the following in
WordSpec
andfixture.WordSpec
:"A Stack (when empty)" should { ... ^
This
should
method, which is provided inShouldVerb
, needs an implicit parameter of typeStringVerbBlockRegistration
. -
final
class
TypeCheckWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL. -
final
class
WritableWord
extends AnyRef
This class is part of the ScalaTest matchers DSL.
This class is part of the ScalaTest matchers DSL. Please see the documentation for
Matchers
for an overview of the matchers DSL.
Value Members
- object MatcherWords extends MatcherWords


INFLUENCE OF RESOURCE DISTRIBUTION AND
ABUNDANCE ON BUTTERFLY POPULATION STRUCTURE
A DISSERTATION SUBMITTED TO THE DEPARTMENT OF BIOLOGICAL SCIENCES AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PRILOSOPHY
By Lawrence Edmund Gilbert, Jr.
May 1971.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.


Right of the way gonna say that doing it on Saturday just because didn’t feel like doing it at all. This task is based on Mondays one and consists of two parts. Task is here, latest solution is here.
So with regular task I came pretty quickly and there is really nothing special comparing with easy one.
(def wire-rules {:s0 {\w :s1, \r :s2} :s1 {\w :s2, \o :s3} :s2 {\b :s3, \r :s0} :s3 {\b :s3, \o :s4, \g :s5} :s4 {\g :exit} :s5 {\o :exit}}) (defn end?
...
Read more


\
Please check back with oidc-gen. \
In case of an error call oidc-gen with the following command:\
\
oidc-gen --state='%s'\
\
\
\
"


Object: Action: $nbspPerform Action
Domain:
Camera:  Get Rover Photos
Person: Action: Perform Action
Animal:


{% extends "base.html" %} {% block content %}
We take pride in our work, and it shows. Every time you order a beverage from us, we guarantee that it will be an experience worth having. Whether it's our world famous Venezuelan Cappuccino, a refreshing iced herbal tea, or something as simple as a cup of speciality sourced black coffee, you will be coming back for more.
{{ item.description }}
{{ item.description }}
{{ item.description }}
caramel, chocolate, citrus, and floral
$7{{item["name"]}}, {{item["quantity"]}}
{% endfor %}


public class IndexSearcher extends Searcher
Applications usually need only call the inherited
search(Query,int)
or
search(Query,Filter,int)
methods. For
performance reasons, if your index is unchanging, you
should share a single IndexSearcher instance across
multiple searches instead of creating a new one
per-search. If your index has changed and you wish to
see the changes reflected in searching, you should
use
IndexReader.openIfChanged(org.apache.lucene.index.IndexReader)
to obtain a new reader and
then create a new IndexSearcher from that. Also, for
low-latency turnaround it's best to use a near-real-time
reader (
IndexReader.open(IndexWriter,boolean)
).
Once you have a new
IndexReader
, it's relatively
cheap to create a new IndexSearcher from it.
NOTE
:
instances are completely
thread safe, meaning multiple threads can call any of its
methods, concurrently. If your application requires
external synchronization, you should
not
synchronize on the
IndexSearcher
IndexSearcher
instance;
use your own (non-Lucene) objects instead.
| Modifier and Type | Field and Description |
|---|---|
protected int[]
|
docStarts
|
protected
IndexReader
[]
|
subReaders
|
protected
IndexSearcher
[]
|
subSearchers
|
| Constructor and Description |
|---|
IndexSearcher
(
Directory
path)
Deprecated.
use
IndexSearcher(IndexReader)
instead.
|
IndexSearcher
(
Directory
path,
boolean readOnly)
Deprecated.
Use
IndexSearcher(IndexReader)
instead.
|
IndexSearcher
(
IndexReader
r)
Creates a searcher searching the provided index.
|
IndexSearcher
(
IndexReader
r,
ExecutorService
executor)
Runs searches for each segment separately, using the
provided ExecutorService.
|
IndexSearcher
(
IndexReader
reader,
IndexReader
[] subReaders,
int[] docStarts)
Expert: directly specify the reader, subReaders and
their docID starts.
|
IndexSearcher
(
IndexReader
reader,
IndexReader
[] subReaders,
int[] docStarts,
ExecutorService
executor)
Expert: directly specify the reader, subReaders and
their docID starts, and an ExecutorService.
|
| Modifier and Type | Method and Description |
|---|---|
void
|
close
()
Note that the underlying IndexReader is not closed, if
IndexSearcher was constructed with IndexSearcher(IndexReader r).
|
Weight
|
createNormalizedWeight
(
Query
query)
Creates a normalized weight for a top-level
Query
.
|
Document
|
doc
(int docID)
Returns the stored fields of document
i
.
|
Document
|
doc
(int docID,
FieldSelector
fieldSelector)
Get the
Document
at the
n
th
position.
|
int
|
docFreq
(
Term
term)
Returns total docFreq for this term.
|
Explanation
|
explain
(
Query
query,
int doc)
Returns an Explanation that describes how
doc
scored against
query
.
|
Explanation
|
explain
(
Weight
weight,
int doc)
Expert: low-level implementation method
Returns an Explanation that describes how
doc
scored against
weight
.
|
protected void
|
gatherSubReaders
(
List
<
IndexReader
> allSubReaders,
IndexReader
r)
|
IndexReader
|
getIndexReader
()
Return the
IndexReader
this searches.
|
Similarity
|
getSimilarity
()
Expert: Return the Similarity implementation used by this Searcher.
|
IndexReader
[]
|
getSubReaders
()
Returns the atomic subReaders used by this searcher.
|
int
|
maxDoc
()
Expert: Returns one greater than the largest possible document number.
|
Query
|
rewrite
(
Query
original)
Expert: called to re-write queries into primitive queries.
|
void
|
search
(
Query
query,
Collector
results)
Lower-level search API.
|
void
|
search
(
Query
query,
Filter
filter,
Collector
results)
Lower-level search API.
|
TopDocs
|
search
(
Query
query,
Filter
filter,
int n)
Finds the top
n
hits for
query
, applying
filter
if non-null.
|
TopFieldDocs
|
search
(
Query
query,
Filter
filter,
int n,
Sort
sort)
Search implementation with arbitrary sorting.
|
TopDocs
|
search
(
Query
query,
int n)
Finds the top
n
hits for
query
.
|
TopFieldDocs
|
search
(
Query
query,
int n,
Sort
sort)
Search implementation with arbitrary sorting and no filter.
|
void
|
search
(
Weight
weight,
Filter
filter,
Collector
collector)
Lower-level search API.
|
TopDocs
|
search
(
Weight
weight,
Filter
filter,
int nDocs)
Expert: Low-level search implementation.
|
TopFieldDocs
|
search
(
Weight
weight,
Filter
filter,
int nDocs,
Sort
sort)
Expert: Low-level search implementation with arbitrary sorting.
|
protected
TopFieldDocs
|
search
(
Weight
weight,
Filter
filter,
int nDocs,
Sort
sort,
boolean fillFields)
Just like
search(Weight, Filter, int, Sort)
, but you choose
whether or not the fields in the returned
FieldDoc
instances should
be set by specifying fillFields.
|
protected
TopDocs
|
search
(
Weight
weight,
Filter
filter,
ScoreDoc
after,
int nDocs)
Expert: Low-level search implementation.
|
TopDocs
|
searchAfter
(
ScoreDoc
after,
Query
query,
Filter
filter,
int n)
Finds the top
n
hits for
query
, applying
filter
if non-null,
where all results are after a previous result (
after
).
|
TopDocs
|
searchAfter
(
ScoreDoc
after,
Query
query,
int n)
Finds the top
n
hits for
query
where all results are after a previous
result (
after
).
|
void
|
setDefaultFieldSortScoring
(boolean doTrackScores,
boolean doMaxScore)
By default, no scores are computed when sorting by
field (using
search(Query,Filter,int,Sort)
).
|
void
|
setSimilarity
(
Similarity
similarity)
Expert: Set the Similarity implementation used by this Searcher.
|
String
|
toString
()
|
createWeight
,
docFreqs
protected final IndexReader [] subReaders
protected final int[] docStarts
protected final IndexSearcher [] subSearchers
@Deprecated public IndexSearcher( Directory path) throws CorruptIndexException , IOException
IndexSearcher(IndexReader)
instead.
path
- directory where IndexReader will be opened
CorruptIndexException
- if the index is corrupt
IOException
- if there is a low-level IO error
@Deprecated public IndexSearcher( Directory path, boolean readOnly) throws CorruptIndexException , IOException
IndexSearcher(IndexReader)
instead.
path
- directory where IndexReader will be opened
readOnly
- if true, the underlying IndexReader
will be opened readOnly
CorruptIndexException
- if the index is corrupt
IOException
- if there is a low-level IO error
public IndexSearcher( IndexReader r)
public IndexSearcher( IndexReader r, ExecutorService executor)
NIOFSDirectory
, do not use
the shutdownNow method of ExecutorService as this uses
Thread.interrupt under-the-hood which can silently
close file descriptors (see
LUCENE-2239
).
public IndexSearcher( IndexReader reader, IndexReader [] subReaders, int[] docStarts)
public IndexSearcher( IndexReader reader, IndexReader [] subReaders, int[] docStarts, ExecutorService executor)
NIOFSDirectory
, do not use
the shutdownNow method of ExecutorService as this uses
Thread.interrupt under-the-hood which can silently
close file descriptors (see
LUCENE-2239
).
protected void gatherSubReaders( List < IndexReader > allSubReaders, IndexReader r)
public IndexReader getIndexReader()
IndexReader
this searches.
public IndexReader [] getSubReaders()
public int maxDoc()
maxDoc
in interface
Searchable
maxDoc
in class
Searcher
IndexReader.maxDoc()
public int docFreq( Term term) throws IOException
docFreq
in interface
Searchable
docFreq
in class
Searcher
IOException
IndexReader.docFreq(Term)
public Document doc(int docID) throws CorruptIndexException , IOException
Searchable
i
.
doc
in interface
Searchable
doc
in class
Searcher
CorruptIndexException
- if the index is corrupt
IOException
- if there is a low-level IO error
IndexReader.document(int)
public Document doc(int docID, FieldSelector fieldSelector) throws CorruptIndexException , IOException
Searchable
Document
at the
n
th
position. The
FieldSelector
may be used to determine what
Field
s to load and how they should be loaded.
NOTE:
If the underlying Reader (more specifically, the underlying
FieldsReader
) is closed before the lazy
Field
is
loaded an exception may be thrown. If you want the value of a lazy
Field
to be available after closing you must
explicitly load it or fetch the Document again with a new loader.
doc
in interface
Searchable
doc
in class
Searcher
docID
- Get the document at the
n
th
position
fieldSelector
- The
FieldSelector
to use to determine what Fields should be loaded on the Document. May be null, in which case all Fields will be loaded.
Document
at the nth position
CorruptIndexException
- if the index is corrupt
IOException
- if there is a low-level IO error
IndexReader.document(int, FieldSelector)
,
Fieldable
,
FieldSelector
,
SetBasedFieldSelector
,
LoadFirstFieldSelector
public void setSimilarity( Similarity similarity)
setSimilarity
in class
Searcher
Similarity.setDefault(Similarity)
public Similarity getSimilarity()
Searcher
This defaults to the current value of
Similarity.getDefault()
.
getSimilarity
in class
Searcher
public void close() throws IOException
close
in interface
Closeable
close
in interface
Searchable
close
in class
Searcher
IOException
public TopDocs searchAfter( ScoreDoc after, Query query, int n) throws IOException
n
hits for
query
where all results are after a previous
result (
after
).
By passing the bottom result from a previous page as
after
,
this method can be used for efficient 'deep-paging' across potentially
large result sets.
public TopDocs searchAfter( ScoreDoc after, Query query, Filter filter, int n) throws IOException
n
hits for
query
, applying
filter
if non-null,
where all results are after a previous result (
after
).
By passing the bottom result from a previous page as
after
,
this method can be used for efficient 'deep-paging' across potentially
large result sets.
public TopDocs search( Query query, int n) throws IOException
n
hits for
query
.
search
in class
Searcher
BooleanQuery.TooManyClauses
IOException
public TopDocs search( Query query, Filter filter, int n) throws IOException
n
hits for
query
, applying
filter
if non-null.
search
in class
Searcher
BooleanQuery.TooManyClauses
IOException
public void search( Query query, Filter filter, Collector results) throws IOException
Collector.collect(int)
is called for every matching
document.
Collector-based access to remote indexes is discouraged.
Applications should only use this if they need
all
of the
matching documents. The high-level search API (
Searcher.search(Query, Filter, int)
) is usually more efficient, as it skips
non-high-scoring hits.
search
in class
Searcher
query
- to match documents
filter
- if non-null, used to permit documents to be collected.
results
- to receive hits
BooleanQuery.TooManyClauses
IOException
public void search( Query query, Collector results) throws IOException
Collector.collect(int)
is called for every matching document.
Applications should only use this if they need
all
of the
matching documents. The high-level search API (
Searcher.search(Query, int)
) is usually more efficient, as it skips
non-high-scoring hits.
Note: The
score
passed to this method is a raw score.
In other words, the score will not necessarily be a float whose value is
between 0 and 1.
search
in class
Searcher
BooleanQuery.TooManyClauses
IOException
public TopFieldDocs search( Query query, Filter filter, int n, Sort sort) throws IOException
n
hits for
query
, applying
filter
if non-null, and sorting the hits by the criteria in
sort
.
NOTE: this does not compute scores by default; use
setDefaultFieldSortScoring(boolean, boolean)
to
enable scoring.
search
in class
Searcher
BooleanQuery.TooManyClauses
IOException
public TopFieldDocs search( Query query, int n, Sort sort) throws IOException
search
in class
Searcher
query
- The query to search for
n
- Return only the top n results
sort
- The
Sort
object
Sort
instance
IOException
public TopDocs search( Weight weight, Filter filter, int nDocs) throws IOException
n
hits for
query
, applying
filter
if non-null.
Applications should usually call
Searcher.search(Query,int)
or
Searcher.search(Query,Filter,int)
instead.
search
in interface
Searchable
search
in class
Searcher
BooleanQuery.TooManyClauses
IOException
protected TopDocs search( Weight weight, Filter filter, ScoreDoc after, int nDocs) throws IOException
n
hits for
query
, applying
filter
if non-null,
returning results after
after
.
public TopFieldDocs search( Weight weight, Filter filter, int nDocs, Sort sort) throws IOException
n
hits for
query
, applying
filter
if non-null, and sorting the hits by the criteria in
sort
.
Applications should usually call
Searcher.search(Query,Filter,int,Sort)
instead.
search
in interface
Searchable
search
in class
Searcher
BooleanQuery.TooManyClauses
IOException
protected TopFieldDocs search( Weight weight, Filter filter, int nDocs, Sort sort, boolean fillFields) throws IOException
search(Weight, Filter, int, Sort)
, but you choose
whether or not the fields in the returned
FieldDoc
instances should
be set by specifying fillFields.
NOTE: this does not compute scores by default. If you
need scores, create a
TopFieldCollector
instance by calling
TopFieldCollector.create(org.apache.lucene.search.Sort, int, boolean, boolean, boolean, boolean)
and
then pass that to
search(Weight, Filter,
Collector)
.
IOException
public void search( Weight weight, Filter filter, Collector collector) throws IOException
Collector.collect(int)
is called for every document.
Collector-based access to remote indexes is discouraged.
Applications should only use this if they need
all
of the matching
documents. The high-level search API (
Searcher.search(Query,int)
) is
usually more efficient, as it skips non-high-scoring hits.
search
in interface
Searchable
search
in class
Searcher
weight
- to match documents
filter
- if non-null, used to permit documents to be collected.
collector
- to receive hits
BooleanQuery.TooManyClauses
IOException
public Query rewrite( Query original) throws IOException
rewrite
in interface
Searchable
rewrite
in class
Searcher
BooleanQuery.TooManyClauses
IOException
public Explanation explain( Query query, int doc) throws IOException
doc
scored against
query
.
This is intended to be used in developing Similarity implementations, and, for good performance, should not be displayed with every hit. Computing an explanation is as expensive as executing the query over the entire index.
explain
in class
Searcher
IOException
public Explanation explain( Weight weight, int doc) throws IOException
doc
scored against
weight
.
This is intended to be used in developing Similarity implementations, and, for good performance, should not be displayed with every hit. Computing an explanation is as expensive as executing the query over the entire index.
Applications should call
Searcher.explain(Query, int)
.
explain
in interface
Searchable
explain
in class
Searcher
BooleanQuery.TooManyClauses
IOException
public void setDefaultFieldSortScoring(boolean doTrackScores, boolean doMaxScore)
search(Query,Filter,int,Sort)
).
You can change that, per IndexSearcher instance, by
calling this method. Note that this will incur a CPU
cost.
doTrackScores
- If true, then scores are
returned for every matching document in
TopFieldDocs
.
doMaxScore
- If true, then the max score for all
matching docs is computed.
public Weight createNormalizedWeight( Query query) throws IOException
Query
.
The query is rewritten by this method and
Query.createWeight(org.apache.lucene.search.Searcher)
called,
afterwards the
Weight
is normalized. The returned
Weight
can then directly be used to get a
Scorer
.
createNormalizedWeight
in class
Searcher
IOException


Security configuration
We set up SSH key-only login on non-standard port, with root login forbidden. We then set up ufw
firewall, fail2ban
, and tripwire
.
- Configure an SSH key login. Next, Create a user, add to sudoers, and then disable root login.. Edits
/etc/ssh/sshd_config
:
- Disabling root logins. (We’ll need to add ourselves to sudo first: (
adduser
, edit/etc/sudoers
) - Change ssh port from default to something else.
- Whitelist user login ids
Additionally, let’s be sure to disable password authentication: Add PasswordAuthentication no
to /etc/ssh/sshd_config
. (editing PermitRootLogin only doesn’t do this).
Locally add an entry in ~/.ssh/config
to alias the host and port to avoid having to remember these numbers for login. Run ssh-copy-id <droplet-ip>
to enable key-based login for the user.
- Install and configure
ufw
firewall. As we’re not using the defaultssh
port, we need to explicitly tellufw
which ssh port to allow.
sudo ufw allow <PORT>/tcp
(The /tcp
part is optional, saying only allow tcp
protocol over that port, not other protocols.)
We must also tell ufw to allow Docker: In /etc/default/ufw
change DEFAULT_FORWARD_POLICY
to ACCEPT, then:
sudo ufw reload
sudo ufw allow 2375/tcp
and similarly allow any ports we export for our various services (Gitlab, Drone, etc).
Install and configure
fail2ban
. Prevents brute force password attacks. Be sure to assign the config to match chosen ssh port.Install and configure
tripwire
(intrusion detection).Update software:
sudo apt-get -q update && sudo apt-get -qy dist-upgrade
and then also update tripwire log:
sudo tripwire --check --interactive
Note: Clearly all these steps need to be running on the server itself, not merely in a container image deployed on server so that they are securing access to the actual host.
Additional configuration
While we’re doing things, add user to the docker group for convenience: sudo addgroup cboettig docker
Enable swap on a small instance. Here we set up 1GB of swap (setting swap at twice the available RAM is the recommended rule-of-thumb, though makes less sense once RAM is large)
sudo fallocate -l 1G /swapfile
sudo chmod 600 /swapfile
sudo mkswap /swapfile
sudo swapon /swapfile
To make this persistant on reboot edit /etc/fstab
:
sudo echo "/swapfile none swap sw 0 0" >> /etc/fstab
For better performance, we might tweak swappiness to 10 (default is 60 out of 100, where 0 is never swap and 1 is swap frequently):
echo 10 | sudo tee /proc/sys/vm/swappiness
echo vm.swappiness = 10 | sudo tee -a /etc/sysctl.conf
Set ownership
sudo chown root:root /swapfile
sudo chmod 0600 /swapfile
Server modules
Running different services as their own docker containers offers serveral advantages:
Containers often make it easier to install and deploy existing services, since the necessary configuration is scripted in the Dockerfile and we can often find Dockerfiles already made on Docker Hub for common services. This note illustrates several examples.
Containers may provide an added level of stability, since they run largely in isolation from each other.
Containers can be resource limited, e.g.
docker run -it -m 100m -c 100 ubuntu /bin/bash
would provide the container with 100 MB of RAM and 100 “shares” of CPU (acts kind of like a niceness, where the default share of a container is 1024. On multicore machines you can also pass --cpuset "0"
or --cpuset "0,1"
etc, which is a list of which cpus (numbered 0 to n-1, as in /proc/cpuinfo
) the container is permitted to use.
As noted in the link, restricting disk space is more tricky, though might become easier down the road.
ssh server:
Permit users to ssh directly into a container rather than access the server itself. Despite its simplicity, I found this a bit tricky to set up correctly, particularly in managing users.
Here’s the basic Dockerfile for an image we’ll call ssh
. This creates a user given by the environmental variable. A few tricks:
- We use
adduser
instead ofuseradd
so that we get the home directory for the user created and granted the correct permissions automaticalliy. We need the--gecos
information so that we’re not prompted to enter the user’s full name etc. We use--disabled-password
rather than set a password here. - Login is still possible through ssh key (as well as through nsenter on the host machine). We go ahead and add the ssh key now, though this could be done after the container is running by using nsenter.
- In this dockerfile, we’ve added the user to
sudo
ers group for root access on the container (installing software, etc). This won’t be active until the user has a password.
FROM ubuntu:14.04
ENV USER cboettig
RUN apt-get update && apt-get install -y openssh-server
RUN mkdir /var/run/sshd
RUN adduser --disabled-password --gecos "" $USER
RUN adduser $USER sudo
ADD authorized_keys /home/$USER/.ssh/authorized_keys
RUN chown $USER /home/$USER/.ssh/authorized_keys
EXPOSE 22
CMD ["/usr/sbin/sshd", "-D"]
When building the image, note that a copy of authorized_keys
(contains the contents of the id_rda.pub
public key) file must be found in the same directory as the Dockerfile so that it can be added to the image.
Start the ssh server on port 2200:
docker run -d -p 2200:22 --name="ssh" ssh
Add to the firewall permissions
sudo ufw add 2200/tcp
From here I can now ssh in from the computer housing the private key pair to the public key that is added to the image here. However, that user doesn’t have root access since we haven’t provided a password.
Use nsenter
to enter the instance:
docker run -v /usr/local/bin:/target jpetazzo/nsenter
nsenter -m -u -n -i -p -t `docker inspect --format '' ssh` /bin/bash
Create a password for the user to enable root access:
echo '$USER:<password>' | chpasswd
We can create other users and add them to sudoers or not as desired, e.g. add interactively using:
useradd <username>
users can later change their passwords once they log in.
Restoring containers when restarting
A certain times we need to power cycle the server (e.g. after certain software updates), using the sudo reboot now
command or the DigitalOcean console. Any running containers will be automatically stopped. Once the machine is back up and we log back in, these containers can be brought back up with docker restart <container_id>
(or <container_name>
), and then everything is back to normal.
Note that while we can stop and restart a container, it seems we cannot simply save a container (e.g. with docker commit
or docker save
and re-run it and expect the server functionality to be restored after the container is destroyed (e.g. by docker rm -f
). (See previous notes 2014-09-05) for an illustration of this problem. This occurs because the container image does not include the volume where it writes its data, and that volume address is generated uniquely each time a container is run.
Consequently, a different (probably more traditional) approach is needed to backup the configuration of a server such as Gitlab or Drone-CI even when running in a container. Will explore this later.
Meanwhile, remember remove unneeded containers with
docker rm $(docker ps -a | grep Exited | awk '{print $1}')
and not with -f
(destroying running containers!)
Key security
We can largely avoid needing a private ssh key for the server, though may use https authentication to let us use git (rather than, say, rsync) to develop and save changes made remotely (say, through RStudio server).
Backing up keys
Probably unnecessary to have a backup of the ssh private RSA key, as we can access the DigitalOcean Server or Github through the web consoles and add a new public key and replace our private key.


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It is a learning environment that requires you to be comfortable with your vulnerability, understand yourself, your limits, your capacity to learn and create. By DBC/EDA providing tools and allowing space for these experiences to happen alongside content being taught by highly skilled teachers, it allows for rapid learning and personal growth.
My impressions have been positive. Based on my own experiences and styles of learning, I know it is important that I work alongside people with similar social values and I have been really enjoyed the conversations about EDA’s culture. From what I have seen and heard, I understand it is going to be challenging and rewarding. It is exciting and scary to know I will experience a spectrum of emotions to come away from EDA with a great set of skills and friendships.
I think initially I will be observing how other people are engaging until I become more familiar and participate more openly. I have the tendancy to be quite shy before I’m ready to contribute. I work well alongside other people in team environments and I think I will enjoy the experience of partnering with different people throughout the course.
Yes they have. After I watching this video and visiting the EDA campus for the first time, I now know I will need to be more emotionally and physically commited to Phase 0, more so than what I had thought. I don’t think I realised how much this will contribute to my own and the cohort’s learning experience.
I am both excited and nervous to be in this learning environment! It’s a strange feeling to be at the start, anticipating the intensity and workload. I’m really excited to learn so much in a short amount of time, as well as experiencing it alongside other people, who I will no doubt become good friends with. I’m excited to meet new people! I’m nervous already but I’m very pleased to be scared and to be taking a risk.


This section discusses a number of problems that may arise when using MPI in a Fortran program. It is intended as advice to users, and clarifies how MPI interacts with Fortran. It does not add to the standard, but is intended to clarify the standard.
As noted in the original MPI specification, the interface violates the Fortran standard in several ways. While these cause few problems for Fortran 77 programs, they become more significant for Fortran 90 programs, so that users must exercise care when using new Fortran 90 features. The violations were originally adopted and have been retained because they are important for the usability of MPI. The rest of this section describes the potential problems in detail. It supersedes and replaces the discussion of Fortran bindings in the original MPI specification (for Fortran 90, not Fortran 77).
The following MPI features are inconsistent with Fortran 90.
Additionally, MPI is inconsistent with Fortran 77 in a number of
ways, as noted below.
MPI-1 contained several routines that take address-sized information
as input or return address-sized information as output. In C
such arguments were of type MPI_Aint and in Fortran of
type INTEGER. On machines where integers are smaller than
addresses, these routines can lose information. In MPI-2 the
use of these functions has been deprecated
and they have been replaced by
routines taking INTEGER arguments of KIND=MPI_ADDRESS_KIND.
A number of new MPI-2 functions also take INTEGER arguments
of non-default KIND. See Section Language Binding
on page Language Binding
and
Section Type Constructors with Explicit Addresses
on page Type Constructors with Explicit Addresses
for more information.
All MPI functions with choice arguments associate actual arguments
of different Fortran datatypes with the same dummy argument. This is
not allowed by Fortran 77, and in Fortran 90 is technically
only allowed if the function is overloaded with a different function
for each type. In C, the use of void* formal arguments avoids these
problems.
The following code fragment is technically illegal and may
generate a compile-time error.
It is also technically illegal in Fortran to pass a scalar actual
argument to an array dummy argument. Thus the following code fragment
may generate an error since the buf argument to
MPI_SEND is declared as an assumed-size array
<type> buf(*).
In the event that you run into one of the problems related to
type checking, you may be able to work around it by using a compiler
flag, by compiling separately, or by using an MPI implementation
with Extended Fortran Support as described in Section
Extended Fortran Support
.
An alternative that will usually work with variables local to a
routine but not with arguments to a function or subroutine is to use
the EQUIVALENCE statement to create another variable with a type
accepted by the compiler.
( End of advice to users.)
Implicit in MPI is the idea of a contiguous chunk of memory accessible
through a linear address space. MPI copies data to and from this
memory. An MPI program specifies the location of data by providing
memory addresses and offsets. In the C language, sequence association
rules plus pointers provide all the necessary low-level structure.
In Fortran 90, user data is not necessarily stored contiguously. For
example, the array section A(1:N:2) involves only the elements of
A with
indices 1, 3, 5, ... . The same is true for a pointer array whose
target is such a section. Most compilers ensure that an array that is a
dummy argument is held in contiguous memory if it is declared with an
explicit shape (e.g., B(N)) or is of assumed size (e.g., B(*)). If
necessary, they do this by making a copy of the array into contiguous
memory. Both Fortran 77 and Fortran 90 are carefully worded to allow
such copying to occur, but few Fortran 77 compilers do
it.*
Because MPI dummy buffer arguments are assumed-size arrays, this leads
to a serious problem for a nonblocking call: the compiler copies the
temporary array back on return but MPI continues to copy data to the
memory that held it. For example, consider the following code fragment:
Most Fortran 90 compilers do not make a copy if the actual argument is
the whole of an explicit-shape or assumed-size array or is a `simple'
section such as A(1:N) of such an array. (We define `simple' more fully
in the next paragraph.) Also, many compilers treat allocatable arrays
the same as they treat explicit-shape arrays in this regard (though we know of one that
does not). However, the same is not true for assumed-shape and pointer
arrays; since they may be discontiguous, copying is often done. It is
this copying that causes problems for MPI as described in the previous
paragraph.
Our formal definition of a `simple' array section is
The same problem can occur with a scalar argument. Some compilers, even for
Fortran 77, make a copy of some scalar dummy arguments within
a called procedure. That this can cause a problem is illustrated by the
example
Note that copying will almost certainly occur for an argument that is a
non-trivial expression (one with at least one operator or function
call), a section that does not select a contiguous part of its parent
(e.g., A(1:n:2)), a pointer whose target is such a section, or an
assumed-shape array that is (directly or indirectly) associated with
such a section.
If there is a compiler option that inhibits copying of arguments,
in either the calling or called procedure, this should be employed.
If a compiler makes copies in the calling procedure of arguments that
are explicit-shape or assumed-size arrays, simple array sections of
such arrays, or scalars, and if there is no compiler option to inhibit
this, then the compiler cannot be used for applications that use
MPI_GET_ADDRESS, or any nonblocking MPI routine. If a
compiler copies scalar arguments in the called procedure and there is no
compiler option to inhibit this, then this compiler cannot be used for
applications that use memory references across subroutine calls as
in the example above.
2.2
MPI requires a number of special ``constants'' that cannot be
implemented as normal Fortran constants, e.g.,
MPI_BOTTOM. The complete list can be found in Section
Named Constants
on page Named Constants
.
In C, these are implemented as constant pointers, usually as
NULL and are used where the function prototype calls for a pointer to
a variable, not the variable itself.
In Fortran the implementation of these special constants may require the
use of language constructs that are outside the Fortran
standard. Using special values for the constants (e.g., by defining
them through parameter statements) is not possible because an
implementation cannot distinguish these values from legal
data. Typically these constants are implemented as predefined
static variables (e.g., a variable in an MPI-declared COMMON
block), relying on the fact that the target compiler passes data by
address. Inside the subroutine, this address can be extracted by some
mechanism outside the Fortran standard (e.g., by Fortran extensions or
by implementing the function in C).
MPI does not explicitly support passing Fortran 90 derived
types to choice dummy arguments. Indeed, for MPI implementations
that provide explicit interfaces through the mpi module
a compiler will reject derived type actual arguments at compile time. Even when
no explicit interfaces are given,
users should be aware that Fortran 90 provides no guarantee of
sequence association for derived types or arrays of derived
types. For instance, an array of a derived type consisting
of two elements may be implemented as an array of the first
elements followed by an array of the second. Use
of the SEQUENCE attribute may help here, somewhat.
The following code fragment shows one possible way to send a derived
type in Fortran. The example assumes that all data is passed by address.
MPI provides operations that may be hidden from the user code
and run concurrently with it, accessing the same memory as user
code. Examples include the data transfer for an
MPI_IRECV.
The optimizer of a compiler will assume that
it can recognize periods when a copy of a variable can be kept
in a register without reloading from or storing to memory. When
the user code is working with a register copy of some variable
while the hidden operation reads or writes the memory copy, problems
occur. This section discusses register optimization pitfalls.
When a variable is local to a Fortran subroutine (i.e., not in
a module or COMMON block), the compiler will assume that it cannot be modified
by a called subroutine unless it is an actual argument of the
call. In the most common linkage convention, the subroutine is
expected to save and restore certain registers. Thus, the optimizer
will assume that a register which held a valid copy of such a
variable before the call will still hold a valid copy on return.
Normally users are not afflicted with this.
But the user should pay attention to this section if in his/her
program a buffer argument to an MPI_SEND, MPI_RECV
etc., uses a name which hides the actual variables involved.
MPI_BOTTOM with an
MPI_Datatype containing absolute addresses is one example. Creating
a datatype which uses one variable as an anchor and brings along
others by using MPI_GET_ADDRESS to determine their offsets from
the anchor is another. The anchor variable would be the only one
mentioned in the call. Also attention must be paid if MPI operations
are used that run in parallel with the user's application.
Example 13
shows what Fortran compilers are allowed to do.
Example 13
shows extreme, but allowed, possibilities.
To prevent instruction reordering or the allocation of a buffer in
a register there are two possibilities in portable Fortran code:
(assuming that buf has type INTEGER). The compiler may be similarly
prevented from moving a reference to a variable across a call to an MPI
subroutine.
In the case of a nonblocking call, as in the above call of MPI_WAIT,
no reference to the buffer is permitted until it has been verified
that the transfer has been completed. Therefore, in this case, the
extra call ahead of the MPI call is not necessary, i.e., the call
of MPI_WAIT in the example might be replaced by
In C, subroutines which modify variables that are not in the argument
list will not cause register optimization problems. This is because
taking pointers to storage objects by using the & operator and
later referencing the objects by way of the pointer is an integral
part of the language.
A C compiler understands the implications,
so that the problem should not occur, in general. However,
some compilers do offer optional aggressive optimization levels which may not
be safe.
Up: Fortran Support
Next: Problems Due to Strong Typing
Previous: Overview
313.1. Problems Due to Strong Typing
Up: Problems With Fortran Bindings for MPI
Next: Problems Due to Data Copying and Sequence Association
Previous: Problems With Fortran Bindings for MPI
integer i(5)
real x(5)
...
call mpi_send(x, 5, MPI_REAL, ...)
call mpi_send(i, 5, MPI_INTEGER, ...)
In practice, it is rare for compilers to do more than issue a
warning, though there is concern that Fortran 90 compilers are more likely
to return errors.
integer a
call mpi_send(a, 1, MPI_INTEGER, ...)
Advice to users.
Up: Problems With Fortran Bindings for MPI
Next: Problems Due to Data Copying and Sequence Association
Previous: Problems With Fortran Bindings for MPI
313.2. Problems Due to Data Copying and Sequence Association
Up: Problems With Fortran Bindings for MPI
Next: Special Constants
Previous: Problems Due to Strong Typing
real a(100)
call MPI_IRECV(a(1:100:2), MPI_REAL, 50, ...)
Since the first dummy argument to MPI_IRECV is an assumed-size
array ( <type> buf(*)), the array section a(1:100:2) is copied to
a temporary before being passed to MPI_IRECV, so that it is
contiguous in memory. MPI_IRECV returns immediately, and data is
copied from the temporary back into the array a. Sometime later, MPI
may write to the address of the deallocated temporary.
Copying is also a problem for MPI_ISEND since the temporary
array may be deallocated before the data has all been sent from it.
name ( [:,]... [<subscript>]:[<subscript>] [,<subscript>]... )
That is, there are zero or more dimensions that are selected in full,
then one dimension selected without a stride, then zero or more
dimensions that are selected with a simple subscript. Examples are
A(1:N), A(:,N), A(:,1:N,1), A(1:6,N), A(:,:,1:N)
Because of Fortran's column-major ordering, where the first index
varies fastest, a simple section of a contiguous array will also be
contiguous.*
call user1(a,rq)
call MPI_WAIT(rq,status,ierr)
write (*,*) a
subroutine user1(buf,request)
call MPI_IRECV(buf,...,request,...)
end
If a is copied, MPI_IRECV will alter the copy when it completes the
communication and will not alter a itself.
Up: Problems With Fortran Bindings for MPI
Next: Special Constants
Previous: Problems Due to Strong Typing
313.3. Special Constants
Up: Problems With Fortran Bindings for MPI
Next: Fortran 90 Derived Types
Previous: Problems Due to Data Copying and Sequence Association
Up: Problems With Fortran Bindings for MPI
Next: Fortran 90 Derived Types
Previous: Problems Due to Data Copying and Sequence Association
313.4. Fortran 90 Derived Types
Up: Problems With Fortran Bindings for MPI
Next: A Problem with Register Optimization
Previous: Special Constants
type mytype
integer i
real x
double precision d
end type mytype
type(mytype) foo
integer blocklen(3), type(3)
integer(MPI_ADDRESS_KIND) disp(3), base
call MPI_GET_ADDRESS(foo%i, disp(1), ierr)
call MPI_GET_ADDRESS(foo%x, disp(2), ierr)
call MPI_GET_ADDRESS(foo%d, disp(3), ierr)
base = disp(1)
disp(1) = disp(1) - base
disp(2) = disp(2) - base
disp(3) = disp(3) - base
blocklen(1) = 1
blocklen(2) = 1
blocklen(3) = 1
type(1) = MPI_INTEGER
type(2) = MPI_REAL
type(3) = MPI_DOUBLE_PRECISION
call MPI_TYPE_CREATE_STRUCT(3, blocklen, disp, type, newtype, ierr)
call MPI_TYPE_COMMIT(newtype, ierr)
! unpleasant to send foo%i instead of foo, but it works for scalar
! entities of type mytype
call MPI_SEND(foo%i, 1, newtype, ...)
Up: Problems With Fortran Bindings for MPI
Next: A Problem with Register Optimization
Previous: Special Constants
313.5. A Problem with Register Optimization
Up: Problems With Fortran Bindings for MPI
Next: Basic Fortran Support
Previous: Fortran 90 Derived Types
Example
Fortran 90 register optimization.
This source ... can be compiled as:
call MPI_GET_ADDRESS(buf,bufaddr, call MPI_GET_ADDRESS(buf,...)
ierror)
call MPI_TYPE_CREATE_STRUCT(1,1, call MPI_TYPE_CREATE_STRUCT(...)
bufaddr,
MPI_REAL,type,ierror)
call MPI_TYPE_COMMIT(type,ierror) call MPI_TYPE_COMMIT(...)
val_old = buf register = buf
val_old = register
call MPI_RECV(MPI_BOTTOM,1,type,...) call MPI_RECV(MPI_BOTTOM,...)
val_new = buf val_new = register
The compiler does not invalidate the register because it cannot
see that MPI_RECV changes the value of buf.
The access of buf is hidden by the use of
MPI_GET_ADDRESS and MPI_BOTTOM.
Example
Fortran 90 register optimization -- extreme.
 But the compiler cannot see any possibility that
buf can be changed after MPI_IRECV has returned,
and may schedule the load of buf earlier than
typed in the source. It has no reason to avoid using a register to
hold buf across the call to MPI_WAIT. It also
may reorder the instructions as in the case on the right.
call DD(buf)
call MPI_RECV(MPI_BOTTOM,...)
call DD(buf)
with the separately compiled
subroutine DD(buf)
integer buf
end
call MPI_WAIT(req,..)
call DD(buf)
2.2
The VOLATILE attribute, available in later versions of Fortran,
gives the buffer or variable the properties needed, but it may inhibit
optimization of any code containing the buffer or variable.
Up: Problems With Fortran Bindings for MPI
Next: Basic Fortran Support
Previous: Fortran 90 Derived Types
Return to MPI-2.2 Standard Index
Return to MPI Forum Home Page
(Unofficial) MPI-2.2 of September 4, 2009
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Dana PlatoDana Michelle Plato (1964-1999) endured a roller coaster life of career sabotage, drug addiction, pornography, armed robbery, and Gary Coleman. Placed up for adoption by a sixteen year-old, baby Dana was taken in by an overachieving southern California mother who gently guided her as best she could toward an acting career. Starting at the age of seven, Dana was regularly thrust before the camera, appearing in over one hundred ads for Kentucky Fried Chicken, Noxema, Arco, Hallmark and other high-profile sponsors. During numerous retakes of one commercial for Dole fruit cocktail, Plato ended up extremely ill after consuming eighty-two bananas which expanded in her stomach.Shortly thereafter, she was enthusiastically hired for the lead role in The Exorcist, but her adoptive mother refused to allow Dana's participation in "that kind of movie". As Linda Blair enjoyed overnight superstardom, Dana plodded through roles in Beyond the Bermuda Triangle. During a brief appearance on The Gong Show, Dana was spotted by a producer who helped her land the role of Kimberly Drummond, the older sister on TV's Diff'rent Strokes. Her character served a dual purpose: she'd cast disapproving glances at the crazy schemes of her younger brothers, and she'd periodically proclaim she was no longer using the bathroom. Regardless, this part earned the child star tremendous fame and the unprecedented salary of $22,000 per episode between 1978 and 1984. Her role was terminated after she became pregnant in real life, a condition Diff'rent Strokes writers and producers ruled impossible to reconcile with the virginal, goody-two-shoes character of Kimberly. Plato then married guitarist Lanny Lambert, and named their son Tyler. Lambert divorced her in 1990, winning custody. Everything associated with Diff'rent Strokes became an obscure novelty. Her co-stars Todd Bridges and Gary Coleman had problems with both the law and their personal lives. Their names became punch lines in the public discourse, and privately Dana began to express an interest in developing an identity wholly separate from them. She wanted to exhibit the real Dana. She believed a five-page spread in the June 1989 issue of Playboy magazine might lead to some positive attention, but her pictorial was overshadowed by the centerfold: Playmate of the Year Kimberly Conrad, Hugh Hefner's new bride. Two Kimberlys were bad enough, but Conrad [Bain] was the name of the actor who played Kimberly's father on Diff'rent Strokes. It all proved too confusing for American masturbators, and Plato's career seemed permanently shelved. Leads were drying up, and she found herself unable to pay the rent. She was even developing a cocaine addiction. Had the Just-Say-No episode featuring First Lady Nancy Reagan all been a dream? In 1991, she was arrested for the armed robbery of a Las Vegas video store while wearing a clumsy disguise consisting of a curly blonde wig and jumbo-sized dark sunglasses. Dana pointed a pellet gun at the clerk, walked out with $164, removed the disguise, and immediately returned to the video store as though nothing had happened. Astonishingly, it was legendary entertainer Wayne Newton who posted her $15,000 bail bond. Plato was given five years' probation. News of her arrest, coupled with a timely increase in America's warmed-over kitschy nostalgia for all things Diff'rent Strokes, garnered her more publicity than ever. She was able to enjoy roles like the scantily-clad victim in the video-based interactive game Night Trap, and a string of B-grade movies like Bikini Beach Race. "If I hadn't gotten caught, it could have been the worst thing that happened to me because I could have died of a drug overdose," she mused. Later that year, she was arrested after forging prescriptions for Valium. As this was a direct violation of her armed robbery parole arrangement, she served thirty days in jail. This was to be the first of numerous arrests, jail terms, and drug-and-alcohol treatment centers for Plato, who ultimately exited her last prison sentence a lesbian, according to a 1998 issue of the Sapphic pride magazine Girlfriends. This was less of a revelation, since one year earlier she'd starred in an X-rated film cleverly titled Diff'rent Strokes.  Says Plato, "When the role came along I was very happy to do it because this is life. It's something people need to see and recognize and get healthy about. In my opinion it's not about gay or straight or bi; but attracted to spirits whatever body they're in. There's other reasons too, but that's how I see it. With women and women I think there´s an understanding.  We are the nurturers and there are times when we need to be nurtured." Paul Petersen (The Donna Reed Show) over time observed Plato had become far too hyperactive and way too thin. He relates an encounter which took place backstage at a Sally Jesse Raphael broadcast about former child stars:
Just before we taped I was walking past the women's bathroom when a harried Dana came busting out the door. She apologized wildly for a collision that was no one's fault. I took her arm and held her fast. She had the cocaine user's tell-tale ring around the collar. Dana, I said to her. Wipe your nose. In less than ten minutes she was in front of the camera telling everyone she was clean and sober. Dana Plato's last public appearance took place May 8th, 1999, on the Howard Stern radio and television program, to clear up "misunderstandings" that she was a drug-addicted lesbian. Plato replied that she'd been sober for ten years. Then she wept. She volunteered a strand of hair for a drug test, only to plead with Howard to return it. Even the King of all Media seemed taken aback. He exhibited sympathy and restrained his remarks, avoiding easy pot-shots. She announced that she'd never been happier in her life.
The next day, coroner officials at an Oklahoma trailer park would be ruling her death a suicide; the result of an intentional overdose on a toxic combination of Valium and Loritab. She died peacefully in her sleep at the age of thirty-four, and didn't leave a note.
Timeline
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Professional Summary
Full Stuck Web Developer
Full stack web developer with advanced knowledge in various web development libraries, frameworks, open source software, design techniques, security standards and database management.
Technology Summary
HTML, CSS, bootstrap, JavaScript, JQuery, AngularJS, PHP, Laravel, MySQL, Python, Java, C++
NanaBooks Kenya ( Lead Programmer), Bitdax Group ( Lead Programmer ), The Programmer's Hub ( Co-founder, Teacher, Lead Programmer ), Good Foundation School ( Programmer ), Pickmovement Inc. ( Co-founder, Lead Programmer )


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Simple img
<img> srcset 1.5x, 2x, 3x
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Picture (resize your browser)
Container intersect
You can fire code on intersect container div
Container InView/OutView
You can use as container "InView" observer
See you console logs on scroll


svn - Revision 62: /hms/web/js/color_picker/images
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Kendal:
It was really horrible. They were tortured, abused, killed. That's how it was. Beleth is evil, and so is Darion. Hmph. Go teach them a lesson!


We'll go through the generic Gradient Descent algorithm, and then explain and illustrate possible optimizations, in order to speed-up the convergence, especially in the scope of very big data sets.
Let us first set some vocabulary and notations. Gradient descent is a method to find the minimizer of an objective function , usually noted: $$ \begin{align*} J & : & \mathbb{R}^d \longrightarrow & \mathbb{R}^n \\ & & \theta \longmapsto & J(\theta) \end{align*} $$ Where \( \theta \) is the vector of the model's parameters, \( d\) is the dimension of the input space, and \( n \) the dimension of the objective function output space, usually 1.
This minimizer is found by updating the parameters \( \theta \) in the opposite direction of the gradient at \( \theta \), i.e. \( \nabla J(\theta)\), controlled by a learning rate \( \eta \) that gives the size of the steps during the descent. \( t \) will be the step number in the following paragraphs.
Gradient descent is a first-order iterative optimization algorithm.
- First order means that the first derivative of the function to be minimized is involved.
- Iterative means each step is supposed to make an improvement.
Batch Gradient Descent
The batch gradient descent updates the parameter vector \( \theta \) like this: $$ \begin{align*} \theta_t = \theta_{t-1} - \eta_t \nabla J(\theta_{t-1}) \end{align*} $$ In Python code, batch gradient descent looks something like this:import numpy as np # From calculation, it is expected that the local minimum occurs at x=9/4 x_old = 0 # The value does not matter as long as abs(x_new - x_old) > precision x_new = 6 # The algorithm starts at x=6 gamma = 0.01 # step size precision = 0.00001 def df(x): y = 4 * x**3 - 9 * x**2 return y while abs(x_new - x_old) > precision: x_old = x_new x_new += -gamma * df(x_old) print("The local minimum occurs at %f" % x_new)In a Machine Learning context, and using this method, we need to calculate the gradients for the entire dataset to perform each update; this is a big limitation for very large datasets (defined for \( n \), number of observations very large and \(d\), dimension of the observations, very large). This algorithm is also not suitable for online updates. The convergence rate is in \( \mathcal{O} (1 / t)\) for convex functions, and the iteration complexity is linear in \( n\).


First page Back Continue Last page Overview Graphics
forGL as an Application
Enable Beginning Programmers :
Simple things done in a simple way.
Full control of forGL options.
Options have usable defaults.
Display intermediate results as wanted.
Intermediate results help with
Understanding AND Debugging.
Informative Warnings and Errors.
Use Color to show: Nouns, Verbs, etc.
Overall ... use Best Known Practices.


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Add your name and press the button to get the weather in the target city!


Because our digital story started with our dreams integrated manually.
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Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged.
Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged.
Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged.
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