Numerical Patterns

Normalize Values

Scale by the Maximum

Normalization can convert raw values to ratios by dividing each value by a reference such as the maximum.

Program

Play the program to choose the maximum value used for scaling.

max_value
normalize_values.f90
Replay: real traced execution (multi-file project)
program normalize_values_demo
    implicit none
    real :: raw(3), scaled(3)
    real :: max_value

    raw = [2.0, 4.0, 8.0]
    max_value = 8.0
    scaled = raw / max_value
    print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)
end program normalize_values_demo

program normalize_values_demo
    implicit none
    real :: raw(3), scaled(3)
    real :: max_value

    raw = [2.0, 4.0, 8.0]
    max_value = 4.0
    scaled = raw / max_value
    print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)
end program normalize_values_demo

program normalize_values_demo
    implicit none
    real :: raw(3), scaled(3)
    real :: max_value

    raw = [2.0, 4.0, 8.0]
    max_value = 10.0
    scaled = raw / max_value
    print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)
end program normalize_values_demo

  1. raw ← [2.0, 4.0, 8.0]

    6raw = [2.0, 4.0, 8.0]7max_value = 8.0
    values this step[2.0, 4.0, 8.0]raw

  2. max_value ← 8.0

    6raw = [2.0, 4.0, 8.0]7max_value = 8.08scaled = raw / max_value
    values this step8.0max_value

  3. scaled ← [0.25, 0.50, 1.00]

    7max_value = 8.08scaled = raw / max_value9print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)
    values this step[0.25, 0.50, 1.00]scaled[2.0, 4.0, 8.0]raw8.0max_value

  4. print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)

    8    scaled = raw / max_value9    print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)10end program normalize_values_demo
    output0.25 0.50 1.00
    values this step[0.25, 0.50, 1.00]scaled

  1. raw ← [2.0, 4.0, 8.0]

    6raw = [2.0, 4.0, 8.0]7max_value = 4.0
    values this step[2.0, 4.0, 8.0]raw

  2. max_value ← 4.0

    6raw = [2.0, 4.0, 8.0]7max_value = 4.08scaled = raw / max_value
    values this step4.0max_value

  3. scaled ← [0.50, 1.00, 2.00]

    7max_value = 4.08scaled = raw / max_value9print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)
    values this step[0.50, 1.00, 2.00]scaled[2.0, 4.0, 8.0]raw4.0max_value

  4. print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)

    8    scaled = raw / max_value9    print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)10end program normalize_values_demo
    output0.50 1.00 2.00
    values this step[0.50, 1.00, 2.00]scaled

  1. raw ← [2.0, 4.0, 8.0]

    6raw = [2.0, 4.0, 8.0]7max_value = 10.0
    values this step[2.0, 4.0, 8.0]raw

  2. max_value ← 10.0

    6raw = [2.0, 4.0, 8.0]7max_value = 10.08scaled = raw / max_value
    values this step10.0max_value

  3. scaled ← [0.20, 0.40, 0.80]

    7max_value = 10.08scaled = raw / max_value9print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)
    values this step[0.20, 0.40, 0.80]scaled[2.0, 4.0, 8.0]raw10.0max_value

  4. print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)

    8    scaled = raw / max_value9    print '(F0.2, 1X, F0.2, 1X, F0.2)', scaled(1), scaled(2), scaled(3)10end program normalize_values_demo
    output0.20 0.40 0.80
    values this step[0.20, 0.40, 0.80]scaled
array division `raw / max_value` divides every element by the scalar.
normalization Scaling by a reference value makes magnitudes easier to compare.
formatting `F0.2` prints each ratio with two decimal places.