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 Built-in Scalar FunctionsWindow (Analytical) Functions 

COUNT Examples

SELECT
  dept_no,
  COUNT(*) AS cnt,
  COUNT(DISTINCT name) AS cnt_name
FROM employee
GROUP BY dept_no
See also

SELECT.

LIST()

Concatenates values into a string list

Result type

BLOB

Syntax
LIST ([ALL | DISTINCT] <expr> [, separator ])
Table 1. LIST Function Parameters
Parameter Description

expr

Expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF that returns the string data type or a BLOB.Fields of numeric and date/time types are converted to strings.Aggregate functions are not allowed as expressions.

separator

Optional alternative separator, a string expression.Comma is the default separator

LIST returns a string consisting of the non-NULL argument values in the group, separated either by a comma or by a user-supplied separator.If there are no non-NULL values (this includes the case where the group is empty), NULL is returned.

  • ALL (the default) results in all non-NULL values being listed.With DISTINCT, duplicates are removed, except if expr is a BLOB.

  • The optional separator argument may be any string expression.This makes it possible to specify e.g. ascii_char(13) as a separator.

  • The expr and separator arguments support BLOBs of any size and character set.

  • Datetime and numeric arguments are implicitly converted to strings before concatenation.

  • The result is a text BLOB, except when expr is a BLOB of another subtype.

  • The ordering of the list values is undefined — the order in which the strings are concatenated is determined by read order from the source set which, in tables, is not generally defined.If ordering is important, the source data can be pre-sorted using a derived table or similar.

    Caution

    This is a trick/workaround, and it depends on implementation details of the optimizer/execution order.This trick doesn’t always work, and it is not guaranteed to work across versions.

    Some reports indicate this no longer works in Firebird 5.0, or only in more limited circumstances than in previous versions.

LIST Examples

  1. Retrieving the list, order undefined:

    SELECT LIST (display_name, '; ') FROM GR_WORK;

  2. Retrieving the list in alphabetical order, using a derived table:

    SELECT LIST (display_name, '; ')
FROM (SELECT display_name
      FROM GR_WORK
      ORDER BY display_name);
See also

SELECT

MAX()

Maximum

Result type

Returns a result of the same data type the input expression.

Syntax
MAX ([ALL | DISTINCT] <expr>)
Table 1. MAX Function Parameters
Parameter Description

expr

Expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

MAX returns the maximum non-NULL element in the result set.

  • If the group is empty or contains only NULLs, the result is NULL.

  • If the input argument is a string, the function will return the value that will be sorted last if COLLATE is used.

  • This function fully supports text BLOBs of any size and character set.

Note

The DISTINCT parameter makes no sense if used with MAX() as it doesn’t change the result;it is implemented only for compliance with the standard.

MAX Examples

SELECT
  dept_no,
  MAX(salary)
FROM employee
GROUP BY dept_no
See also

[fblangref50-aggfuncs-min], SELECT

MIN()

Minimum

Result type

Returns a result of the same data type the input expression.

Syntax
MIN ([ALL | DISTINCT] <expr>)
Table 1. MIN Function Parameters
Parameter Description

expr

Expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

MIN returns the minimum non-NULL element in the result set.

  • If the group is empty or contains only NULLs, the result is NULL.

  • If the input argument is a string, the function will return the value that will be sorted first if COLLATE is used.

  • This function fully supports text BLOBs of any size and character set.

Note

The DISTINCT parameter makes no sense if used with MIN() as it doesn’t change the result;it is implemented only for compliance with the standard.

MIN Examples

SELECT
  dept_no,
  MIN(salary)
FROM employee
GROUP BY dept_no
See also

[fblangref50-aggfuncs-max], SELECT

SUM()

Sum

Result type

Depends on the input type

Syntax
SUM ([ALL | DISTINCT] <expr>)
Table 1. SUM Function Parameters
Parameter Description

expr

Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

SUM calculates and returns the sum of non-NULL values in the group.

  • If the group is empty or contains only NULLs, the result is NULL.

  • ALL is the default option — all values in the set that are not NULL are processed.If DISTINCT is specified, duplicates are removed from the set and the SUM evaluation is done afterwards.

The result type of SUM depends on the input type:

FLOAT, DOUBLE PRECISION

DOUBLE PRECISION

SMALLINT, INTEGER

BIGINT

BIGINT, INT128

INT128

DECIMAL/NUMERIC(p, n) with p < 10

DECIMAL/NUMERIC(18, n)

DECIMAL/NUMERIC(p, n) with p >= 10

DECIMAL/NUMERIC(38, n)

DECFLOAT(16), DECFLOAT(34)

DECFLOAT(34)

SUM Examples

SELECT
  dept_no,
  SUM (salary),
FROM employee
GROUP BY dept_no
See also

SELECT

Statistical Aggregate Functions

CORR()

Correlation coefficient

Result type

DOUBLE PRECISION

Syntax
CORR ( <expr1>, <expr2> )
Table 1. CORR Function Parameters
Parameter Description

exprN

Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The CORR function return the correlation coefficient for a pair of numerical expressions.

The function CORR(<expr1>, <expr2>) is equivalent to

COVAR_POP(<expr1>, <expr2>) / (STDDEV_POP(<expr2>) * STDDEV_POP(<expr1>))

This is also known as the Pearson correlation coefficient.

In a statistical sense, correlation is the degree to which a pair of variables are linearly related.A linear relation between variables means that the value of one variable can to a certain extent predict the value of the other.The correlation coefficient represents the degree of correlation as a number ranging from -1 (high inverse correlation) to 1 (high correlation).A value of 0 corresponds to no correlation.

If the group or window is empty, or contains only NULL values, the result will be NULL.

CORR Examples

select
  corr(alength, aheight) AS c_corr
from measure
See also

[fblangref50-aggfuncs-covar-pop], [fblangref50-aggfuncs-stddev-pop]

COVAR_POP()

Population covariance

Result type

DOUBLE PRECISION

Syntax
COVAR_POP ( <expr1>, <expr2> )
Table 1. COVAR_POP Function Parameters
Parameter Description

exprN

Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function COVAR_POP returns the population covariance for a pair of numerical expressions.

The function COVAR_POP(<expr1>, <expr2>) is equivalent to

(SUM(<expr1> * <expr2>) - SUM(<expr1>) * SUM(<expr2>) / COUNT(*)) / COUNT(*)

If the group or window is empty, or contains only NULL values, the result will be NULL.

COVAR_POP Examples

select
  covar_pop(alength, aheight) AS c_covar_pop
from measure
See also

[fblangref50-aggfuncs-covar-samp], [fblangref50-aggfuncs-sum], [fblangref50-aggfuncs-count]

COVAR_SAMP()

Sample covariance

Result type

DOUBLE PRECISION

Syntax
COVAR_SAMP ( <expr1>, <expr2> )
Table 1. COVAR_SAMP Function Parameters
Parameter Description

exprN

Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function COVAR_SAMP returns the sample covariance for a pair of numerical expressions.

The function COVAR_SAMP(<expr1>, <expr2>) is equivalent to

(SUM(<expr1> * <expr2>) - SUM(<expr1>) * SUM(<expr2>) / COUNT(*)) / (COUNT(*) - 1)

If the group or window is empty, contains only 1 row, or contains only NULL values, the result will be NULL.

COVAR_SAMP Examples

select
  covar_samp(alength, aheight) AS c_covar_samp
from measure
See also

[fblangref50-aggfuncs-covar-pop], [fblangref50-aggfuncs-sum], [fblangref50-aggfuncs-count]

STDDEV_POP()

Population standard deviation

Result type

DOUBLE PRECISION or NUMERIC depending on the type of expr

Syntax
STDDEV_POP ( <expr> )
Table 1. STDDEV_POP Function Parameters
Parameter Description

expr

Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function STDDEV_POP returns the population standard deviation for a group or window.NULL values are skipped.

The function STDDEV_POP(<expr>) is equivalent to

SQRT(VAR_POP(<expr>))

If the group or window is empty, or contains only NULL values, the result will be NULL.

STDDEV_POP Examples

select
  dept_no
  stddev_pop(salary)
from employee
group by dept_no
See also

[fblangref50-aggfuncs-stddev-samp], [fblangref50-aggfuncs-var-pop], SQRT

STDDEV_SAMP()

Sample standard deviation

Result type

DOUBLE PRECISION or NUMERIC depending on the type of expr

Syntax
STDDEV_POP ( <expr> )
Table 1. STDDEV_SAMP Function Parameters
Parameter Description

expr

Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function STDDEV_SAMP returns the sample standard deviation for a group or window.NULL values are skipped.

The function STDDEV_SAMP(<expr>) is equivalent to

SQRT(VAR_SAMP(<expr>))

If the group or window is empty, contains only 1 row, or contains only NULL values, the result will be NULL.

STDDEV_SAMP Examples

select
  dept_no
  stddev_samp(salary)
from employee
group by dept_no
See also

[fblangref50-aggfuncs-stddev-pop], [fblangref50-aggfuncs-var-samp], SQRT

VAR_POP()

Population variance

Result type

DOUBLE PRECISION or NUMERIC depending on the type of expr

Syntax
VAR_POP ( <expr> )
Table 1. VAR_POP Function Parameters
Parameter Description

expr

Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function VAR_POP returns the population variance for a group or window.NULL values are skipped.

The function VAR_POP(<expr>) is equivalent to

(SUM(<expr> * <expr>) - SUM (<expr>) * SUM (<expr>) / COUNT(<expr>))
  / COUNT (<expr>)

If the group or window is empty, or contains only NULL values, the result will be NULL.

VAR_POP Examples

select
  dept_no
  var_pop(salary)
from employee
group by dept_no
See also

[fblangref50-aggfuncs-var-samp], [fblangref50-aggfuncs-sum], [fblangref50-aggfuncs-count]

VAR_SAMP()

Sample variance

Result type

DOUBLE PRECISION or NUMERIC depending on the type of expr

Syntax
VAR_SAMP ( <expr> )
Table 1. VAR_SAMP Function Parameters
Parameter Description

expr

Numeric expression.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function VAR_POP returns the sample variance for a group or window.NULL values are skipped.

The function VAR_SAMP(<expr>) is equivalent to

(SUM(<expr> * <expr>) - SUM(<expr>) * SUM (<expr>) / COUNT (<expr>))
  / (COUNT(<expr>) - 1)

If the group or window is empty, contains only 1 row, or contains only NULL values, the result will be NULL.

VAR_SAMP Examples

select
  dept_no
  var_samp(salary)
from employee
group by dept_no
See also

[fblangref50-aggfuncs-var-pop], [fblangref50-aggfuncs-sum], [fblangref50-aggfuncs-count]

Linear Regression Aggregate Functions

Linear regression functions are useful for trend line continuation.The trend or regression line is usually a pattern followed by a set of values.Linear regression is useful to predict future values.To continue the regression line, you need to know the slope and the point of intersection with the y-axis.As set of linear functions can be used for calculating these values.

In the function syntax, y is interpreted as an x-dependent variable.

The linear regression aggregate functions take a pair of arguments, the dependent variable expression (y) and the independent variable expression (x), which are both numeric value expressions.Any row in which either argument evaluates to NULL is removed from the rows that qualify.If there are no rows that qualify, then the result of REGR_COUNT is 0 (zero), and the other linear regression aggregate functions result in NULL.

REGR_AVGX()

Average of the independent variable of the regression line

Result type

DOUBLE PRECISION

Syntax
REGR_AVGX ( <y>, <x> )
Table 1. REGR_AVGX Function Parameters
Parameter Description

y

Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

x

Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_AVGX calculates the average of the independent variable (x) of the regression line.

The function REGR_AVGX(<y>, <x>) is equivalent to

SUM(<exprX>) / REGR_COUNT(<y>, <x>)

<exprX> :==
  CASE WHEN <x> IS NOT NULL AND <y> IS NOT NULL THEN <x> END
See also

[fblangref50-aggfuncs-regr-avgy], [fblangref50-aggfuncs-regr-count], [fblangref50-aggfuncs-sum]

REGR_AVGY()

Average of the dependent variable of the regression line

Result type

DOUBLE PRECISION

Syntax
REGR_AVGY ( <y>, <x> )
Table 1. REGR_AVGY Function Parameters
Parameter Description

y

Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

x

Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_AVGY calculates the average of the dependent variable (y) of the regression line.

The function REGR_AVGY(<y>, <x>) is equivalent to

SUM(<exprY>) / REGR_COUNT(<y>, <x>)

<exprY> :==
  CASE WHEN <x> IS NOT NULL AND <y> IS NOT NULL THEN <y> END
See also

[fblangref50-aggfuncs-regr-avgx], [fblangref50-aggfuncs-regr-count], [fblangref50-aggfuncs-sum]

REGR_COUNT()

Number of non-empty pairs of the regression line

Result type

DOUBLE PRECISION

Syntax
REGR_COUNT ( <y>, <x> )
Table 1. REGR_COUNT Function Parameters
Parameter Description

y

Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

x

Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_COUNT counts the number of non-empty pairs of the regression line.

The function REGR_COUNT(<y>, <x>) is equivalent to

COUNT(*) FILTER (WHERE <x> IS NOT NULL AND <y> IS NOT NULL)
See also

[fblangref50-aggfuncs-count]

REGR_INTERCEPT()

Point of intersection of the regression line with the y-axis

Result type

DOUBLE PRECISION

Syntax
REGR_INTERCEPT ( <y>, <x> )
Table 1. REGR_INTERCEPT Function Parameters
Parameter Description

y

Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

x

Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_INTERCEPT calculates the point of intersection of the regression line with the y-axis.

The function REGR_INTERCEPT(<y>, <x>) is equivalent to

REGR_AVGY(<y>, <x>) - REGR_SLOPE(<y>, <x>) * REGR_AVGX(<y>, <x>)

REGR_INTERCEPT Examples

Forecasting sales volume

with recursive years (byyear) as (
  select 1991
  from rdb$database
  union all
  select byyear + 1
  from years
  where byyear < 2020
),
s as (
  select
    extract(year from order_date) as byyear,
    sum(total_value) as total_value
  from sales
  group by 1
),
regr as (
  select
    regr_intercept(total_value, byyear) as intercept,
    regr_slope(total_value, byyear) as slope
  from s
)
select
  years.byyear as byyear,
  intercept + (slope * years.byyear) as total_value
from years
cross join regr
BYYEAR TOTAL_VALUE
------ ------------
  1991    118377.35
  1992    414557.62
  1993    710737.89
  1994   1006918.16
  1995   1303098.43
  1996   1599278.69
  1997   1895458.96
  1998   2191639.23
  1999   2487819.50
  2000   2783999.77
...
See also

[fblangref50-aggfuncs-regr-avgx], [fblangref50-aggfuncs-regr-avgy], [fblangref50-aggfuncs-regr-slope]

REGR_R2()

Coefficient of determination of the regression line

Result type

DOUBLE PRECISION

Syntax
REGR_R2 ( <y>, <x> )
Table 1. REGR_R2 Function Parameters
Parameter Description

y

Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

x

Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The REGR_R2 function calculates the coefficient of determination, or R-squared, of the regression line.

The function REGR_R2(<y>, <x>) is equivalent to

POWER(CORR(<y>, <x>), 2)
See also

[fblangref50-aggfuncs-corr], POWER

REGR_SLOPE()

Slope of the regression line

Result type

DOUBLE PRECISION

Syntax
REGR_SLOPE ( <y>, <x> )
Table 1. REGR_SLOPE Function Parameters
Parameter Description

y

Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

x

Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_SLOPE calculates the slope of the regression line.

The function REGR_SLOPE(<y>, <x>) is equivalent to

COVAR_POP(<y>, <x>) / VAR_POP(<exprX>)

<exprX> :==
  CASE WHEN <x> IS NOT NULL AND <y> IS NOT NULL THEN <x> END
See also

[fblangref50-aggfuncs-covar-pop], [fblangref50-aggfuncs-var-pop]

REGR_SXX()

Sum of squares of the independent variable

Result type

DOUBLE PRECISION

Syntax
REGR_SXX ( <y>, <x> )
Table 1. REGR_SXX Function Parameters
Parameter Description

y

Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

x

Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_SXX calculates the sum of squares of the independent expression variable (x).

The function REGR_SXX(<y>, <x>) is equivalent to

REGR_COUNT(<y>, <x>) * VAR_POP(<exprX>)

<exprX> :==
  CASE WHEN <x> IS NOT NULL AND <y> IS NOT NULL THEN <x> END
See also

[fblangref50-aggfuncs-regr-count], [fblangref50-aggfuncs-var-pop]

REGR_SXY()

Sum of products of the independent variable and the dependent variable

Result type

DOUBLE PRECISION

Syntax
REGR_SXY ( <y>, <x> )
Table 1. REGR_SXY Function Parameters
Parameter Description

y

Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

x

Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_SXY calculates the sum of products of independent variable expression (x) times dependent variable expression (y).

The function REGR_SXY(<y>, <x>) is equivalent to

REGR_COUNT(<y>, <x>) * COVAR_POP(<y>, <x>)
See also

[fblangref50-aggfuncs-covar-pop], [fblangref50-aggfuncs-regr-count]

REGR_SYY()

Sum of squares of the dependent variable

Result type

DOUBLE PRECISION

Syntax
REGR_SYY ( <y>, <x> )
Table 1. REGR_SYY Function Parameters
Parameter Description

y

Dependent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

x

Independent variable of the regression line.It may contain a table column, a constant, a variable, an expression, a non-aggregate function or a UDF.Aggregate functions are not allowed as expressions.

The function REGR_SYY calculates the sum of squares of the dependent variable (y).

The function REGR_SYY(<y>, <x>) is equivalent to

REGR_COUNT(<y>, <x>) * VAR_POP(<exprY>)

<exprY> :==
  CASE WHEN <x> IS NOT NULL AND <y> IS NOT NULL THEN <y> END
See also

[fblangref50-aggfuncs-regr-count], [fblangref50-aggfuncs-var-pop]