public abstract class StringUtils extends Object
String
utility methods.
Mainly for internal use within the framework; consider
Apache's Commons Lang
for a more comprehensive suite of String
utilities.
This class delivers some simple functionality that should really be
provided by the core Java String
and StringBuilder
classes. It also provides easy-to-use methods to convert between
delimited strings, such as CSV strings, and collections and arrays.
Constructor and Description |
---|
StringUtils() |
Modifier and Type | Method and Description |
---|---|
static String[] |
addStringToArray(String[] array,
String str)
Append the given
String to the given String array,
returning a new array consisting of the input array contents plus
the given String . |
static String |
applyRelativePath(String path,
String relativePath)
Apply the given relative path to the given Java resource path,
assuming standard Java folder separation (i.e.
|
static String |
arrayToCommaDelimitedString(Object[] arr)
Convert a
String array into a comma delimited String
(i.e., CSV). |
static String |
arrayToDelimitedString(Object[] arr,
String delim)
Convert a
String array into a delimited String (e.g. |
static String |
capitalize(String str)
Capitalize a
String , changing the first letter to
upper case as per Character.toUpperCase(char) . |
static String |
cleanPath(String path)
Normalize the path by suppressing sequences like "path/.." and
inner simple dots.
|
static String |
collectionToCommaDelimitedString(Collection<?> coll)
Convert a
Collection into a delimited String (e.g., CSV). |
static String |
collectionToDelimitedString(Collection<?> coll,
String delim)
Convert a
Collection into a delimited String (e.g. |
static String |
collectionToDelimitedString(Collection<?> coll,
String delim,
String prefix,
String suffix)
Convert a
Collection to a delimited String (e.g. |
static Set<String> |
commaDelimitedListToSet(String str)
Convert a comma delimited list (e.g., a row from a CSV file) into a set.
|
static String[] |
commaDelimitedListToStringArray(String str)
Convert a comma delimited list (e.g., a row from a CSV file) into an
array of strings.
|
static String[] |
concatenateStringArrays(String[] array1,
String[] array2)
Concatenate the given
String arrays into one,
with overlapping array elements included twice. |
static boolean |
containsWhitespace(CharSequence str)
Check whether the given
CharSequence contains any whitespace characters. |
static boolean |
containsWhitespace(String str)
Check whether the given
String contains any whitespace characters. |
static int |
countOccurrencesOf(String str,
String sub)
Count the occurrences of the substring
sub in string str . |
static String |
delete(String inString,
String pattern)
Delete all occurrences of the given substring.
|
static String |
deleteAny(String inString,
String charsToDelete)
Delete any character in a given
String . |
static String[] |
delimitedListToStringArray(String str,
String delimiter)
Take a
String that is a delimited list and convert it into a
String array. |
static String[] |
delimitedListToStringArray(String str,
String delimiter,
String charsToDelete)
Take a
String that is a delimited list and convert it into
a String array. |
static boolean |
endsWithIgnoreCase(String str,
String suffix)
Test if the given
String ends with the specified suffix,
ignoring upper/lower case. |
static String |
getFilename(String path)
Extract the filename from the given Java resource path,
e.g.
|
static String |
getFilenameExtension(String path)
Extract the filename extension from the given Java resource path,
e.g.
|
static boolean |
hasLength(CharSequence str)
Check that the given
CharSequence is neither null nor
of length 0. |
static boolean |
hasLength(String str)
Check that the given
String is neither null nor of length 0. |
static boolean |
hasText(CharSequence str)
Check whether the given
CharSequence contains actual text. |
static boolean |
hasText(String str)
Check whether the given
String contains actual text. |
static boolean |
isEmpty(Object str)
Deprecated.
as of 5.3, in favor of
hasLength(String) and
hasText(String) (or ObjectUtils.isEmpty(Object) ) |
static boolean |
matchesCharacter(String str,
char singleCharacter)
Test if the given
String matches the given single character. |
static String[] |
mergeStringArrays(String[] array1,
String[] array2)
Deprecated.
as of 4.3.15, in favor of manual merging via
LinkedHashSet
(with every entry included at most once, even entries within the first array) |
static Locale |
parseLocale(String localeValue)
Parse the given
String value into a Locale , accepting
the Locale.toString() format as well as BCP 47 language tags as
specified by Locale.forLanguageTag(java.lang.String) . |
static Locale |
parseLocaleString(String localeString)
Parse the given
String representation into a Locale . |
static TimeZone |
parseTimeZoneString(String timeZoneString)
Parse the given
timeZoneString value into a TimeZone . |
static boolean |
pathEquals(String path1,
String path2)
Compare two paths after normalization of them.
|
static String |
quote(String str)
Quote the given
String with single quotes. |
static Object |
quoteIfString(Object obj)
Turn the given Object into a
String with single quotes
if it is a String ; keeping the Object as-is else. |
static String[] |
removeDuplicateStrings(String[] array)
Remove duplicate strings from the given array.
|
static String |
replace(String inString,
String oldPattern,
String newPattern)
Replace all occurrences of a substring within a string with another string.
|
static String[] |
sortStringArray(String[] array)
Sort the given
String array if necessary. |
static String[] |
split(String toSplit,
String delimiter)
Split a
String at the first occurrence of the delimiter. |
static Properties |
splitArrayElementsIntoProperties(String[] array,
String delimiter)
Take an array of strings and split each element based on the given delimiter.
|
static Properties |
splitArrayElementsIntoProperties(String[] array,
String delimiter,
String charsToDelete)
Take an array of strings and split each element based on the given delimiter.
|
static boolean |
startsWithIgnoreCase(String str,
String prefix)
Test if the given
String starts with the specified prefix,
ignoring upper/lower case. |
static String |
stripFilenameExtension(String path)
Strip the filename extension from the given Java resource path,
e.g.
|
static boolean |
substringMatch(CharSequence str,
int index,
CharSequence substring)
Test whether the given string matches the given substring
at the given index.
|
static String[] |
tokenizeToStringArray(String str,
String delimiters)
|
static String[] |
tokenizeToStringArray(String str,
String delimiters,
boolean trimTokens,
boolean ignoreEmptyTokens)
|
static String |
toLanguageTag(Locale locale)
Deprecated.
as of 5.0.4, in favor of
Locale.toLanguageTag() |
static String[] |
toStringArray(Collection<String> collection)
Copy the given
Collection into a String array. |
static String[] |
toStringArray(Enumeration<String> enumeration)
Copy the given
Enumeration into a String array. |
static CharSequence |
trimAllWhitespace(CharSequence str)
Trim all whitespace from the given
CharSequence :
leading, trailing, and in between characters. |
static String |
trimAllWhitespace(String str)
Trim all whitespace from the given
String :
leading, trailing, and in between characters. |
static String[] |
trimArrayElements(String[] array)
Trim the elements of the given
String array, calling
String.trim() on each non-null element. |
static String |
trimLeadingCharacter(String str,
char leadingCharacter)
Trim all occurrences of the supplied leading character from the given
String . |
static String |
trimLeadingWhitespace(String str)
Trim leading whitespace from the given
String . |
static String |
trimTrailingCharacter(String str,
char trailingCharacter)
Trim all occurrences of the supplied trailing character from the given
String . |
static String |
trimTrailingWhitespace(String str)
Trim trailing whitespace from the given
String . |
static String |
trimWhitespace(String str)
Trim leading and trailing whitespace from the given
String . |
static String |
truncate(CharSequence charSequence)
Truncate the supplied
CharSequence . |
static String |
truncate(CharSequence charSequence,
int threshold)
Truncate the supplied
CharSequence . |
static String |
uncapitalize(String str)
Uncapitalize a
String , changing the first letter to
lower case as per Character.toLowerCase(char) . |
static String |
unqualify(String qualifiedName)
Unqualify a string qualified by a '.' dot character.
|
static String |
unqualify(String qualifiedName,
char separator)
Unqualify a string qualified by a separator character.
|
static String |
uriDecode(String source,
Charset charset)
Decode the given encoded URI component value.
|
@Deprecated public static boolean isEmpty(@Nullable Object str)
hasLength(String)
and
hasText(String)
(or ObjectUtils.isEmpty(Object)
)String
) is empty.
This is effectively a shortcut for !hasLength(String)
.
This method accepts any Object as an argument, comparing it to
null
and the empty String. As a consequence, this method
will never return true
for a non-null non-String object.
The Object signature is useful for general attribute handling code that commonly deals with Strings but generally has to iterate over Objects since attributes may e.g. be primitive value objects as well.
Note: If the object is typed to String
upfront, prefer
hasLength(String)
or hasText(String)
instead.
str
- the candidate object (possibly a String
)public static boolean hasLength(@Nullable CharSequence str)
CharSequence
is neither null
nor
of length 0.
Note: this method returns true
for a CharSequence
that purely consists of whitespace.
StringUtils.hasLength(null) = false StringUtils.hasLength("") = false StringUtils.hasLength(" ") = true StringUtils.hasLength("Hello") = true
str
- the CharSequence
to check (may be null
)true
if the CharSequence
is not null
and has lengthhasLength(String)
,
hasText(CharSequence)
public static boolean hasLength(@Nullable String str)
String
is neither null
nor of length 0.
Note: this method returns true
for a String
that
purely consists of whitespace.
str
- the String
to check (may be null
)true
if the String
is not null
and has lengthhasLength(CharSequence)
,
hasText(String)
public static boolean hasText(@Nullable CharSequence str)
CharSequence
contains actual text.
More specifically, this method returns true
if the
CharSequence
is not null
, its length is greater than
0, and it contains at least one non-whitespace character.
StringUtils.hasText(null) = false StringUtils.hasText("") = false StringUtils.hasText(" ") = false StringUtils.hasText("12345") = true StringUtils.hasText(" 12345 ") = true
str
- the CharSequence
to check (may be null
)true
if the CharSequence
is not null
,
its length is greater than 0, and it does not contain whitespace onlyhasText(String)
,
hasLength(CharSequence)
,
Character.isWhitespace(char)
public static boolean hasText(@Nullable String str)
String
contains actual text.
More specifically, this method returns true
if the
String
is not null
, its length is greater than 0,
and it contains at least one non-whitespace character.
str
- the String
to check (may be null
)true
if the String
is not null
, its
length is greater than 0, and it does not contain whitespace onlyhasText(CharSequence)
,
hasLength(String)
,
Character.isWhitespace(char)
public static boolean containsWhitespace(@Nullable CharSequence str)
CharSequence
contains any whitespace characters.str
- the CharSequence
to check (may be null
)true
if the CharSequence
is not empty and
contains at least 1 whitespace characterCharacter.isWhitespace(char)
public static boolean containsWhitespace(@Nullable String str)
String
contains any whitespace characters.str
- the String
to check (may be null
)true
if the String
is not empty and
contains at least 1 whitespace charactercontainsWhitespace(CharSequence)
public static String trimWhitespace(String str)
String
.str
- the String
to checkString
Character.isWhitespace(char)
public static CharSequence trimAllWhitespace(CharSequence str)
CharSequence
:
leading, trailing, and in between characters.str
- the CharSequence
to checkCharSequence
trimAllWhitespace(String)
,
Character.isWhitespace(char)
public static String trimAllWhitespace(String str)
String
:
leading, trailing, and in between characters.str
- the String
to checkString
trimAllWhitespace(CharSequence)
,
Character.isWhitespace(char)
public static String trimLeadingWhitespace(String str)
String
.str
- the String
to checkString
Character.isWhitespace(char)
public static String trimTrailingWhitespace(String str)
String
.str
- the String
to checkString
Character.isWhitespace(char)
public static String trimLeadingCharacter(String str, char leadingCharacter)
String
.str
- the String
to checkleadingCharacter
- the leading character to be trimmedString
public static String trimTrailingCharacter(String str, char trailingCharacter)
String
.str
- the String
to checktrailingCharacter
- the trailing character to be trimmedString
public static boolean matchesCharacter(@Nullable String str, char singleCharacter)
String
matches the given single character.str
- the String
to checksingleCharacter
- the character to compare topublic static boolean startsWithIgnoreCase(@Nullable String str, @Nullable String prefix)
String
starts with the specified prefix,
ignoring upper/lower case.str
- the String
to checkprefix
- the prefix to look forString.startsWith(java.lang.String, int)
public static boolean endsWithIgnoreCase(@Nullable String str, @Nullable String suffix)
String
ends with the specified suffix,
ignoring upper/lower case.str
- the String
to checksuffix
- the suffix to look forString.endsWith(java.lang.String)
public static boolean substringMatch(CharSequence str, int index, CharSequence substring)
str
- the original string (or StringBuilder)index
- the index in the original string to start matching againstsubstring
- the substring to match at the given indexpublic static int countOccurrencesOf(String str, String sub)
sub
in string str
.str
- string to search insub
- string to search forpublic static String replace(String inString, String oldPattern, @Nullable String newPattern)
inString
- String
to examineoldPattern
- String
to replacenewPattern
- String
to insertString
with the replacementspublic static String delete(String inString, String pattern)
inString
- the original String
pattern
- the pattern to delete all occurrences ofString
public static String deleteAny(String inString, @Nullable String charsToDelete)
String
.inString
- the original String
charsToDelete
- a set of characters to delete.
E.g. "az\n" will delete 'a's, 'z's and new lines.String
@Nullable public static String quote(@Nullable String str)
String
with single quotes.str
- the input String
(e.g. "myString")String
(e.g. "'myString'"),
or null
if the input was null
@Nullable public static Object quoteIfString(@Nullable Object obj)
String
with single quotes
if it is a String
; keeping the Object as-is else.obj
- the input Object (e.g. "myString")String
(e.g. "'myString'"),
or the input object as-is if not a String
public static String unqualify(String qualifiedName)
qualifiedName
- the qualified namepublic static String unqualify(String qualifiedName, char separator)
qualifiedName
- the qualified nameseparator
- the separatorpublic static String capitalize(String str)
String
, changing the first letter to
upper case as per Character.toUpperCase(char)
.
No other letters are changed.str
- the String
to capitalizeString
public static String uncapitalize(String str)
String
, changing the first letter to
lower case as per Character.toLowerCase(char)
.
No other letters are changed.str
- the String
to uncapitalizeString
@Nullable public static String getFilename(@Nullable String path)
"mypath/myfile.txt" → "myfile.txt"
.path
- the file path (may be null
)null
if none@Nullable public static String getFilenameExtension(@Nullable String path)
path
- the file path (may be null
)null
if nonepublic static String stripFilenameExtension(String path)
path
- the file pathpublic static String applyRelativePath(String path, String relativePath)
path
- the path to start from (usually a full file path)relativePath
- the relative path to apply
(relative to the full file path above)public static String cleanPath(String path)
The result is convenient for path comparison. For other uses, notice that Windows separators ("\") are replaced by simple slashes.
NOTE that cleanPath
should not be depended
upon in a security context. Other mechanisms should be used to prevent
path-traversal issues.
path
- the original pathpublic static boolean pathEquals(String path1, String path2)
path1
- first path for comparisonpath2
- second path for comparisonpublic static String uriDecode(String source, Charset charset)
"a"
through "z"
, "A"
through "Z"
,
and "0"
through "9"
stay the same."-"
, "_"
, "."
, and "*"
stay the same.%<i>xy</i>
" is interpreted as a hexadecimal representation of the character.source
- the encoded Stringcharset
- the character setIllegalArgumentException
- when the given source contains invalid encoded sequencesURLDecoder.decode(String, String)
@Nullable public static Locale parseLocale(String localeValue)
String
value into a Locale
, accepting
the Locale.toString()
format as well as BCP 47 language tags as
specified by Locale.forLanguageTag(java.lang.String)
.localeValue
- the locale value: following either Locale's
toString()
format ("en", "en_UK", etc), also accepting spaces as
separators (as an alternative to underscores), or BCP 47 (e.g. "en-UK")Locale
instance, or null
if noneIllegalArgumentException
- in case of an invalid locale specificationparseLocaleString(java.lang.String)
,
Locale.forLanguageTag(java.lang.String)
@Nullable public static Locale parseLocaleString(String localeString)
String
representation into a Locale
.
For many parsing scenarios, this is an inverse operation of
Locale's toString
, in a lenient sense.
This method does not aim for strict Locale
design compliance;
it is rather specifically tailored for typical Spring parsing needs.
Note: This delegate does not accept the BCP 47 language tag format.
Please use parseLocale(java.lang.String)
for lenient parsing of both formats.
localeString
- the locale String
: following Locale's
toString()
format ("en", "en_UK", etc), also accepting spaces as
separators (as an alternative to underscores)Locale
instance, or null
if noneIllegalArgumentException
- in case of an invalid locale specification@Deprecated public static String toLanguageTag(Locale locale)
Locale.toLanguageTag()
locale
- the Locale to transform to a language tagString
public static TimeZone parseTimeZoneString(String timeZoneString)
timeZoneString
value into a TimeZone
.timeZoneString
- the time zone String
, following TimeZone.getTimeZone(String)
but throwing IllegalArgumentException
in case of an invalid time zone specificationTimeZone
instanceIllegalArgumentException
- in case of an invalid time zone specificationpublic static String[] toStringArray(@Nullable Collection<String> collection)
collection
- the Collection
to copy
(potentially null
or empty)String
arraypublic static String[] toStringArray(@Nullable Enumeration<String> enumeration)
enumeration
- the Enumeration
to copy
(potentially null
or empty)String
arraypublic static String[] addStringToArray(@Nullable String[] array, String str)
String
to the given String
array,
returning a new array consisting of the input array contents plus
the given String
.array
- the array to append to (can be null
)str
- the String
to appendnull
)@Nullable public static String[] concatenateStringArrays(@Nullable String[] array1, @Nullable String[] array2)
String
arrays into one,
with overlapping array elements included twice.
The order of elements in the original arrays is preserved.
array1
- the first array (can be null
)array2
- the second array (can be null
)null
if both given arrays were null
)@Deprecated @Nullable public static String[] mergeStringArrays(@Nullable String[] array1, @Nullable String[] array2)
LinkedHashSet
(with every entry included at most once, even entries within the first array)String
arrays into one, with overlapping
array elements only included once.
The order of elements in the original arrays is preserved (with the exception of overlapping elements, which are only included on their first occurrence).
array1
- the first array (can be null
)array2
- the second array (can be null
)null
if both given arrays were null
)public static String[] sortStringArray(String[] array)
String
array if necessary.array
- the original array (potentially empty)null
)public static String[] trimArrayElements(String[] array)
String
array, calling
String.trim()
on each non-null element.array
- the original String
array (potentially empty)public static String[] removeDuplicateStrings(String[] array)
As of 4.2, it preserves the original order, as it uses a LinkedHashSet
.
array
- the String
array (potentially empty)@Nullable public static String[] split(@Nullable String toSplit, @Nullable String delimiter)
String
at the first occurrence of the delimiter.
Does not include the delimiter in the result.toSplit
- the string to split (potentially null
or empty)delimiter
- to split the string up with (potentially null
or empty)null
if the delimiter wasn't found in the given input String
@Nullable public static Properties splitArrayElementsIntoProperties(String[] array, String delimiter)
Properties
instance is then generated, with the left of the delimiter
providing the key, and the right of the delimiter providing the value.
Will trim both the key and value before adding them to the Properties
.
array
- the array to processdelimiter
- to split each element using (typically the equals symbol)Properties
instance representing the array contents,
or null
if the array to process was null
or empty@Nullable public static Properties splitArrayElementsIntoProperties(String[] array, String delimiter, @Nullable String charsToDelete)
Properties
instance is then generated, with the left of the
delimiter providing the key, and the right of the delimiter providing the value.
Will trim both the key and value before adding them to the
Properties
instance.
array
- the array to processdelimiter
- to split each element using (typically the equals symbol)charsToDelete
- one or more characters to remove from each element
prior to attempting the split operation (typically the quotation mark
symbol), or null
if no removal should occurProperties
instance representing the array contents,
or null
if the array to process was null
or emptypublic static String[] tokenizeToStringArray(@Nullable String str, String delimiters)
String
into a String
array via a
StringTokenizer
.
Trims tokens and omits empty tokens.
The given delimiters
string can consist of any number of
delimiter characters. Each of those characters can be used to separate
tokens. A delimiter is always a single character; for multi-character
delimiters, consider using delimitedListToStringArray(java.lang.String, java.lang.String)
.
str
- the String
to tokenize (potentially null
or empty)delimiters
- the delimiter characters, assembled as a String
(each of the characters is individually considered as a delimiter)StringTokenizer
,
String.trim()
,
delimitedListToStringArray(java.lang.String, java.lang.String)
public static String[] tokenizeToStringArray(@Nullable String str, String delimiters, boolean trimTokens, boolean ignoreEmptyTokens)
String
into a String
array via a
StringTokenizer
.
The given delimiters
string can consist of any number of
delimiter characters. Each of those characters can be used to separate
tokens. A delimiter is always a single character; for multi-character
delimiters, consider using delimitedListToStringArray(java.lang.String, java.lang.String)
.
str
- the String
to tokenize (potentially null
or empty)delimiters
- the delimiter characters, assembled as a String
(each of the characters is individually considered as a delimiter)trimTokens
- trim the tokens via String.trim()
ignoreEmptyTokens
- omit empty tokens from the result array
(only applies to tokens that are empty after trimming; StringTokenizer
will not consider subsequent delimiters as token in the first place).StringTokenizer
,
String.trim()
,
delimitedListToStringArray(java.lang.String, java.lang.String)
public static String[] delimitedListToStringArray(@Nullable String str, @Nullable String delimiter)
String
that is a delimited list and convert it into a
String
array.
A single delimiter
may consist of more than one character,
but it will still be considered as a single delimiter string, rather
than as a bunch of potential delimiter characters, in contrast to
tokenizeToStringArray(java.lang.String, java.lang.String)
.
str
- the input String
(potentially null
or empty)delimiter
- the delimiter between elements (this is a single delimiter,
rather than a bunch individual delimiter characters)tokenizeToStringArray(java.lang.String, java.lang.String)
public static String[] delimitedListToStringArray(@Nullable String str, @Nullable String delimiter, @Nullable String charsToDelete)
String
that is a delimited list and convert it into
a String
array.
A single delimiter
may consist of more than one character,
but it will still be considered as a single delimiter string, rather
than as a bunch of potential delimiter characters, in contrast to
tokenizeToStringArray(java.lang.String, java.lang.String)
.
str
- the input String
(potentially null
or empty)delimiter
- the delimiter between elements (this is a single delimiter,
rather than a bunch individual delimiter characters)charsToDelete
- a set of characters to delete; useful for deleting unwanted
line breaks: e.g. "\r\n\f" will delete all new lines and line feeds in a String
tokenizeToStringArray(java.lang.String, java.lang.String)
public static String[] commaDelimitedListToStringArray(@Nullable String str)
str
- the input String
(potentially null
or empty)public static Set<String> commaDelimitedListToSet(@Nullable String str)
Note that this will suppress duplicates, and as of 4.2, the elements in
the returned set will preserve the original order in a LinkedHashSet
.
str
- the input String
(potentially null
or empty)String
entries in the listremoveDuplicateStrings(String[])
public static String collectionToDelimitedString(@Nullable Collection<?> coll, String delim, String prefix, String suffix)
coll
- the Collection
to convert (potentially null
or empty)delim
- the delimiter to use (typically a ",")prefix
- the String
to start each element withsuffix
- the String
to end each element withString
public static String collectionToDelimitedString(@Nullable Collection<?> coll, String delim)
Collection
into a delimited String
(e.g. CSV).
Useful for toString()
implementations.
coll
- the Collection
to convert (potentially null
or empty)delim
- the delimiter to use (typically a ",")String
public static String collectionToCommaDelimitedString(@Nullable Collection<?> coll)
Collection
into a delimited String
(e.g., CSV).
Useful for toString()
implementations.
coll
- the Collection
to convert (potentially null
or empty)String
public static String arrayToDelimitedString(@Nullable Object[] arr, String delim)
String
array into a delimited String
(e.g. CSV).
Useful for toString()
implementations.
arr
- the array to display (potentially null
or empty)delim
- the delimiter to use (typically a ",")String
public static String arrayToCommaDelimitedString(@Nullable Object[] arr)
String
array into a comma delimited String
(i.e., CSV).
Useful for toString()
implementations.
arr
- the array to display (potentially null
or empty)String
public static String truncate(CharSequence charSequence)
CharSequence
.
Delegates to truncate(CharSequence, int)
, supplying 100
as the threshold.
charSequence
- the CharSequence
to truncateCharSequence
if its length does not exceed the thresholdpublic static String truncate(CharSequence charSequence, int threshold)
CharSequence
.
If the length of the CharSequence
is greater than the threshold,
this method returns a subsequence of the CharSequence
(up to the threshold) appended
with the suffix " (truncated)..."
. Otherwise, this method returns
charSequence.toString()
.
charSequence
- the CharSequence
to truncatethreshold
- the maximum length after which to truncate; must be a
positive numberCharSequence
if its length does not exceed the threshold