atoti.math package¶

Module contents¶

Measures can be combined with mathematical operators.

Several native Python operators are supported:

The classic +, - and * operators

>>> df = pd.DataFrame(
...     columns=["City", "A", "B", "C", "D"],
...     data=[
...         ("Berlin", 15.0, 10.0, 10.1, 1.0),
...         ("London", 24.0, 16.0, 20.5, 3.14),
...         ("New York", -27.0, 15.0, 30.7, 10.0),
...     ],
... )
>>> store = session.read_pandas(df, keys=["City"], store_name="Math")
>>> cube = session.create_cube(store)
>>> l, m = cube.levels, cube.measures
>>> m["Sum"] = m["A.SUM"] + m["B.SUM"]
>>> m["Substract"] = m["A.SUM"] - m["B.SUM"]
>>> m["Multiply"] = m["A.SUM"] * m["B.SUM"]
>>> cube.query(
...     m["A.SUM"],
...     m["B.SUM"],
...     m["Sum"],
...     m["Substract"],
...     m["Multiply"],
...     levels=l["City"],
... )
           A.SUM  B.SUM     Sum Substract Multiply
City
Berlin     15.00  10.00   25.00      5.00   150.00
London     24.00  16.00   40.00      8.00   384.00
New York  -27.00  15.00  -12.00    -42.00  -405.00

The float division / and integer division //

>>> m["Float division"] = m["A.SUM"] / m["B.SUM"]
>>> m["Int division"] = m["A.SUM"] // m["B.SUM"]
>>> cube.query(
...     m["A.SUM"],
...     m["B.SUM"],
...     m["Float division"],
...     m["Int division"],
...     levels=l["City"],
... )
           A.SUM  B.SUM Float division Int division
City
Berlin     15.00  10.00           1.50         1.00
London     24.00  16.00           1.50         1.00
New York  -27.00  15.00          -1.80        -2.00

The exponentiation **

>>> m["a²"] = m["A.SUM"] ** 2
>>> cube.query(m["A.SUM"], m["a²"], levels=l["City"])
           A.SUM      a²
City
Berlin     15.00  225.00
London     24.00  576.00
New York  -27.00  729.00

The modulo %

>>> m["Modulo"] = m["A.SUM"] % m["B.SUM"]
>>> cube.query(m["A.SUM"], m["B.SUM"], m["Modulo"], levels=l["City"])
           A.SUM  B.SUM Modulo
City
Berlin     15.00  10.00   5.00
London     24.00  16.00   8.00
New York  -27.00  15.00   3.00

atoti.math.abs(measure)¶

Return a measure equal to the absolute value of the passed measure.

Example

>>> m["|A|"] = tt.math.abs(m["A.SUM"])
>>> cube.query(m["A.SUM"], m["|A|"], levels=[l["City"]])
           A.SUM    |A|
City
Berlin     15.00  15.00
London     24.00  24.00
New York  -27.00  27.00

Return type: Measure

atoti.math.ceil(measure)¶

Return a measure equal to the smallest integer that is >= to the passed measure.

Example

>>> m["⌈C⌉"] = tt.math.ceil(m["C.SUM"])
>>> cube.query(m["C.SUM"], m["⌈C⌉"], levels=[l["City"]])
          C.SUM ⌈C⌉
City
Berlin    10.10  11
London    20.50  21
New York  30.70  31

Return type: Measure

atoti.math.cos(measure)¶

Return a measure equal to the cosine of the passed measure in radians.

Example

>>> m["cos(D)"] = tt.math.cos(m["D.SUM"])
>>> cube.query(m["D.SUM"], m["cos(D)"], levels=[l["City"]])
          D.SUM cos(D)
City
Berlin     1.00    .54
London     3.14  -1.00
New York  10.00   -.84

Return type: Measure

atoti.math.erf(measure)¶

Return the error function of the input measure.

This can be used to compute traditional statistical measures such as the cumulative standard normal distribution.

For more information read:

Python’s built-in math.erf()

scipy.special.erf

The Wikipedia page

Example

>>> m["erf"] = tt.math.erf(m["D.SUM"])
>>> m["erf"].formatter = "DOUBLE[#,##0.000000]"
>>> cube.query(m["D.SUM"], m["erf"], levels=[l["City"]])
          D.SUM       erf
City
Berlin     1.00  0.842701
London     3.14  0.999991
New York  10.00  1.000000

Return type: Measure

atoti.math.erfc(measure)¶

Return the complementary error function of the input measure.

This is the complementary of atoti.math.erf(). It is defined as 1.0 - erf. It can be used for large values of x where a subtraction from one would cause a loss of significance.

Example

>>> m["erfc"] = tt.math.erfc(m["D.SUM"])
>>> m["1-erf"] = 1 - tt.math.erf(m["D.SUM"])
>>> m["erfc"].formatter = "DOUBLE[#.00E]"
>>> m["1-erf"].formatter = "DOUBLE[#.00E]"
>>> cube.query(m["D.SUM"], m["erfc"], m["1-erf"], levels=[l["City"]])
          D.SUM                    erfc                1-erf
City
Berlin     1.00     0.15729920705028488  0.15729920705028488
London     3.14    8.969565553264981E-6   8.9695655532962E-6
New York  10.00  2.0884875837625685E-45                  0.0

Return type: Measure

atoti.math.exp(measure)¶

Return a measure equal to the exponential value of the passed measure.

Example

>>> m["exp(D)"] = tt.math.exp(m["D.SUM"])
>>> cube.query(m["D.SUM"], m["exp(D)"], levels=[l["City"]])
          D.SUM     exp(D)
City
Berlin     1.00       2.72
London     3.14      23.10
New York  10.00  22,026.47

Return type: Measure

atoti.math.floor(measure)¶

Return a measure equal to the largest integer <= to the passed measure.

Example

>>> m["⌊C⌋"] = tt.math.floor(m["C.SUM"])
>>> cube.query(m["C.SUM"], m["⌊C⌋"], levels=[l["City"]])
          C.SUM ⌊C⌋
City
Berlin    10.10  10
London    20.50  20
New York  30.70  30

Return type: Measure

atoti.math.log(measure)¶

Return a measure equal to the natural logarithm (base e) of the passed measure.

Example

>>> m["log(D)"] = tt.math.log(m["D.SUM"])
>>> cube.query(m["D.SUM"], m["log(D)"], levels=[l["City"]])
          D.SUM log(D)
City
Berlin     1.00    .00
London     3.14   1.14
New York  10.00   2.30

Return type: Measure

atoti.math.log10(measure)¶

Return a measure equal to the base 10 logarithm of the passed measure.

Example

>>> m["log10(D)"] = tt.math.log10(m["D.SUM"])
>>> cube.query(m["D.SUM"], m["log10(D)"], levels=[l["City"]])
          D.SUM log10(D)
City
Berlin     1.00      .00
London     3.14      .50
New York  10.00     1.00

Return type: Measure

atoti.math.max(*measures)¶

Return a measure equal to the maximum of the passed arguments.

Example

>>> m["max"] = tt.math.max(m["A.SUM"], m["B.SUM"])
>>> cube.query(m["A.SUM"], m["B.SUM"], m["max"], levels=[l["City"]])
           A.SUM  B.SUM    max
City
Berlin     15.00  10.00  15.00
London     24.00  16.00  24.00
New York  -27.00  15.00  15.00

Return type: Measure

atoti.math.min(*measures)¶

Return a measure equal to the minimum of the passed arguments.

Example

>>> m["min"] = tt.math.min(m["A.SUM"], m["B.SUM"])
>>> cube.query(m["A.SUM"], m["B.SUM"], m["min"], levels=[l["City"]])
           A.SUM  B.SUM     min
City
Berlin     15.00  10.00   10.00
London     24.00  16.00   16.00
New York  -27.00  15.00  -27.00

Return type: Measure

atoti.math.round(measure)¶

Return a measure equal to the closest integer to the passed measure.

Example

>>> m["round(C)"] = tt.math.round(m["C.SUM"])
>>> cube.query(m["C.SUM"], m["round(C)"], levels=[l["City"]])
          C.SUM round(C)
City
Berlin    10.10       10
London    20.50       21
New York  30.70       31

Return type: Measure

atoti.math.sin(measure)¶

Return a measure equal to the sine of the passed measure in radians.

Example

>>> m["sin(D)"] = tt.math.sin(m["D.SUM"])
>>> cube.query(m["D.SUM"], m["sin(D)"], levels=[l["City"]])
          D.SUM sin(D)
City
Berlin     1.00    .84
London     3.14    .00
New York  10.00   -.54

Return type: Measure

atoti.math.sqrt(measure)¶

Return a measure equal to the square root of the passed measure.

Example

>>> m["√B"] = tt.math.sqrt(m["B.SUM"])
>>> cube.query(m["B.SUM"], m["√B"], levels=[l["City"]])
          B.SUM    √B
City
Berlin    10.00  3.16
London    16.00  4.00
New York  15.00  3.87

Return type: Measure

atoti.math.tan(measure)¶

Return a measure equal to the tangent of the passed measure in radians.

Example

>>> m["tan(D)"] = tt.math.tan(m["D.SUM"])
>>> cube.query(m["D.SUM"], m["tan(D)"], levels=[l["City"]])
          D.SUM tan(D)
City
Berlin     1.00   1.56
London     3.14   -.00
New York  10.00    .65

Return type: Measure