Gradient descent: Difference between revisions
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(→{{header|ALGOL 68}}: Use the actual gradient.) |
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=={{header|ALGOL 68}}== |
=={{header|ALGOL 68}}== |
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{{works with|ALGOL 68G|Any - tested with release 2.8.3.win32}} |
{{works with|ALGOL 68G|Any - tested with release 2.8.3.win32}} |
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{{Trans|Go}} modified to use the actual gradient function - |
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There appear to be a range of answers produced by the various samples... the results calculated by this sample differ from the Go sample |
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THe results agree with the Fortran sample and the Julia sample to 6 places. |
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<lang algol68>PROC steepest descent = ( REF[]LONG REAL x, LONG REAL alphap, tolerance )VOID: |
<lang algol68>PROC steepest descent = ( REF[]LONG REAL x, LONG REAL alphap, tolerance )VOID: |
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BEGIN |
BEGIN |
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LONG REAL alpha := alphap; |
LONG REAL alpha := alphap; |
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LONG REAL h := tolerance; |
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LONG REAL g0 := g( x ); # Initial estimate of result. # |
LONG REAL g0 := g( x ); # Initial estimate of result. # |
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# Calculate initial gradient. # |
# Calculate initial gradient. # |
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[ LWB x : UPB x ]LONG REAL fi := grad g( x |
[ LWB x : UPB x ]LONG REAL fi := grad g( x ); |
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# Calculate initial norm. # |
# Calculate initial norm. # |
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LONG REAL del g := 0.0; |
LONG REAL del g := 0.0; |
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x[i] -:= b * fi[i] |
x[i] -:= b * fi[i] |
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OD; |
OD; |
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# Calculate next gradient. # |
# Calculate next gradient. # |
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fi := grad g( x |
fi := grad g( x ); |
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# Calculate next norm. # |
# Calculate next norm. # |
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del g := 0; |
del g := 0; |
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OD; |
OD; |
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del g := long sqrt( del g ); |
del g := long sqrt( del g ); |
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IF del g > 0 THEN |
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b := alpha / del g; |
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# Calculate next value. # |
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LONG REAL g1 := g( x ); |
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# Adjust parameter. # |
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IF g1 > g0 THEN |
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alpha /:= 2 |
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ELSE |
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g0 := g1 |
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FI |
FI |
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OD |
OD |
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END # steepest descent # ; |
END # steepest descent # ; |
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# calculates the gradient of g(p). # |
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# Provides a rough calculation of gradient g(x). # |
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# The derivitives wrt x and y are (as in the Fortran sample ): # |
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# g' wrt x = 2( x - 1 )e^( - ( y^2 ) ) - 4xe^( -2( x^2) )y( y + 2 ) # |
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# g' wrt y = ( -2( x-1 )^2ye^( - (y^2) )) + e^(-2( x^2 ) )( y + 2 ) + e^( -2( x^2 ) )y # |
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BEGIN |
BEGIN |
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[ LWB |
[ LWB p : UPB p ]LONG REAL z; |
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LONG REAL x = p[ 0 ]; |
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LONG REAL |
LONG REAL y = p[ 1 ]; |
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z[ 0 ] := 2 * ( x - 1 ) * long exp( - ( y * y ) ) |
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y |
- 4 * x * long exp( -2 * ( x * x ) ) * y * ( y + 2 ); |
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z[ 1 ] := ( -2 * ( x - 1 ) * ( x - 1 ) * y ) * long exp( - y * y ) |
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+ long exp( -2 * x * x ) * ( y + 2 ) |
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OD; |
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+ long exp( -2 * x * x ) * y; |
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z |
z |
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END # grad g # ; |
END # grad g # ; |
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# Function for which minimum is to be found. # |
# Function for which minimum is to be found. # |
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# g( x, y ) = ( ( x - 1 )^2 )e^( - ( x^2 ) ) + y( y + 2 )e^( - 2(x^2)) # |
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PROC g = ( []LONG REAL x )LONG REAL: |
PROC g = ( []LONG REAL x )LONG REAL: |
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( x[ 0 ] - 1 ) |
( x[ 0 ] - 1 ) |
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