75 lines
3.9 KiB
Fortran
75 lines
3.9 KiB
Fortran
REAL FUNCTION STDDEV(X) !Standard deviation for successive values.
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REAL X !The latest value.
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REAL V !Scratchpad.
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INTEGER N !Ongoing: count of the values.
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REAL EX,EX2 !Ongoing: sum of X and X**2.
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SAVE N,EX,EX2 !Retain values from one invocation to the next.
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DATA N,EX,EX2/0,0.0,0.0/ !Initial values.
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N = N + 1 !Another value arrives.
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EX = X + EX !Augment the total.
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EX2 = X**2 + EX2 !Augment the sum of squares.
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V = EX2/N - (EX/N)**2 !The variance, but, it might come out negative!
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STDDEV = SIGN(SQRT(ABS(V)),V) !Protect the SQRT, but produce a negative result if so.
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END FUNCTION STDDEV !For the sequence of received X values.
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REAL FUNCTION STDDEVP(X) !Standard deviation for successive values.
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REAL X !The latest value.
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INTEGER N !Ongoing: count of the values.
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REAL A,V !Ongoing: average, and sum of squared deviations.
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SAVE N,A,V !Retain values from one invocation to the next.
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DATA N,A,V/0,0.0,0.0/ !Initial values.
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N = N + 1 !Another value arrives.
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V = (N - 1)*(X - A)**2 /N + V !First, as it requires the existing average.
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A = (X - A)/N + A != [x + (n - 1).A)]/n: recover the total from the average.
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STDDEVP = SQRT(V/N) !V can never be negative, even with limited precision.
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END FUNCTION STDDEVP !For the sequence of received X values.
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REAL FUNCTION STDDEVW(X) !Standard deviation for successive values.
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REAL X !The latest value.
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REAL V,D !Scratchpads.
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INTEGER N !Ongoing: count of the values.
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REAL EX,EX2 !Ongoing: sum of X and X**2.
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REAL W !Ongoing: working mean.
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SAVE N,EX,EX2,W !Retain values from one invocation to the next.
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DATA N,EX,EX2/0,0.0,0.0/ !Initial values.
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IF (N.LE.0) W = X !Take the first value as the working mean.
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N = N + 1 !Another value arrives.
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D = X - W !Its deviation from the working mean.
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EX = D + EX !Augment the total.
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EX2 = D**2 + EX2 !Augment the sum of squares.
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V = EX2/N - (EX/N)**2 !The variance, but, it might come out negative!
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STDDEVW = SIGN(SQRT(ABS(V)),V) !Protect the SQRT, but produce a negative result if so.
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END FUNCTION STDDEVW !For the sequence of received X values.
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REAL FUNCTION STDDEVPW(X) !Standard deviation for successive values.
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REAL X !The latest value.
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INTEGER N !Ongoing: count of the values.
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REAL A,V !Ongoing: average, and sum of squared deviations.
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REAL W !Ongoing: working mean.
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SAVE N,A,V,W !Retain values from one invocation to the next.
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DATA N,A,V/0,0.0,0.0/ !Initial values.
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IF (N.LE.0) W = X !Oh for self-modifying code!
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N = N + 1 !Another value arrives.
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D = X - W !Its deviation from the working mean.
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V = (N - 1)*(D - A)**2 /N + V !First, as it requires the existing average.
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A = (D - A)/N + A != [x + (n - 1).A)]/n: recover the total from the average.
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STDDEVPW = SQRT(V/N) !V can never be negative, even with limited precision.
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END FUNCTION STDDEVPW !For the sequence of received X values.
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PROGRAM TEST
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INTEGER I !A stepper.
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REAL A(8) !The example data.
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DATA A/2.0,3*4.0,2*5.0,7.0,9.0/ !Alas, another opportunity to use @ passed over.
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REAL B !An offsetting base.
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WRITE (6,1)
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1 FORMAT ("Progressive calculation of the standard deviation."/
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1 " I",7X,"A(I) EX EX2 Av V*N Ed Ed2 wAv V*N")
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B = 1000000 !Provoke truncation error.
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DO I = 1,8 !Step along the data series,
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WRITE (6,2) I,INT(A(I) + B), !No fractional part, so I don't want F11.0.
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1 STDDEV(A(I) + B),STDDEVP(A(I) + B), !Showing progressive values.
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2 STDDEVW(A(I) + B),STDDEVPW(A(I) + B) !These with a working mean.
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2 FORMAT (I2,I11,1X,4F12.6) !Should do for the example.
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END DO !On to the next value.
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END
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