Apolyton Math Question. bring your calculus hats

[KrazyHorse]

awesome. forgot to attach.

rename to opt.exe from opt.zip.

poly doesn't like exe attachments.

[KrazyHorse]

      IMPLICIT DOUBLE PRECISION(A, T, X-Z)
      IMPLICIT INTEGER(B-S, U-W)
      
      
      COMMON/PARAMS/SCOEFF(5),SMAX(5),X,Z
      SAVE/PARAMS/
      
      COMMON/VARS/S(5),W
      SAVE/VARS/
      
      SMAX(1)=8
      SMAX(2)=12
      SMAX(3)=16
      SMAX(4)=20
      SMAX(5)=24
      
      PRINT *, "Enter E1"
      READ *, SCOEFF(1)
      
      PRINT *, "Enter E2"
      READ *, SCOEFF(2)
      
      PRINT *, "Enter E3"
      READ *, SCOEFF(3)
      
      PRINT *, "Enter E4"
      READ *, SCOEFF(4)
      
      PRINT *, "Enter E5"
      READ *, SCOEFF(5)
      
      PRINT *, "Enter x"
      READ *, X
      
      PRINT *, "Enter Z"
      READ *, Z
      
      T = TMIN()
      
      PRINT *, S(1), S(2), S(3), S(4), S(5), W, T
      
      RETURN
      END
      
      DOUBLE PRECISION FUNCTION TMIN()
			
      IMPLICIT DOUBLE PRECISION(A, T, X-Z)
      IMPLICIT INTEGER(B-S, U-W)
      
      DIMENSION SMIN(5)
      
      COMMON/PARAMS/SCOEFF(5),SMAX(5),X,Z
      SAVE/PARAMS/
      
      COMMON/VARS/S(5),W
      SAVE/VARS/

      TMIN = 1.0D10
      
      DO 103 I1=0,1
      DO 113 I2=0,1
      DO 123 I3=0,1
      DO 133 I4=0,1
      DO 143 I5=0,1
      DO 153 W=1,9
	S(1)=I1*SMAX(1)
	S(2)=I2*SMAX(2)
	S(3)=I3*SMAX(3)
	S(4)=I4*SMAX(4)
	S(5)=I5*SMAX(5)
	T=TCALC()
	IF(T.LE.TMIN) THEN
		TMIN=T
		DO 173 J=1, 5
      		 SMIN(J)=S(J)
 173	     CONTINUE
		WMIN=W
	ENDIF
 153 CONTINUE
 143 CONTINUE
 133 CONTINUE
 123 CONTINUE
 113 CONTINUE
 103 CONTINUE
 
	DO 183 J=1, 5
      	 S(J)=SMIN(J)
 183  CONTINUE
	 W=WMIN
			
	 END
			
	DOUBLE PRECISION FUNCTION TCALC()
		
	IMPLICIT DOUBLE PRECISION(A, T, X-Z)
        IMPLICIT INTEGER(B-S, U-W)
      
        COMMON/PARAMS/SCOEFF(5),SMAX(5),X,Z
        SAVE/PARAMS/
      
        COMMON/VARS/S(5),W
        SAVE/VARS/
      
        TCALC = 1.0D10
        C = CCALC(W,Z)
        A = ACALC()
        H = HCALC()
        IF(H.LT.1) GOTO 104
        TCALC = C*A/H
      
 104	RETURN
         END
			
			
	INTEGER FUNCTION CCALC(W,Z)
	
        DOUBLE PRECISION Z
        INTEGER W
      
        CCALC = INT(9.0/(W*(1.0+Z))-0.00001)+1

         END
      
        INTEGER FUNCTION HCALC()
      
        IMPLICIT DOUBLE PRECISION(A, T, X-Z)
        IMPLICIT INTEGER(B-S, U-W)
      
        COMMON/PARAMS/SCOEFF(5),SMAX(5),X,Z
        SAVE/PARAMS/
      
        COMMON/VARS/S(5),W
        SAVE/VARS/
      
        HCALC = 0
        DO 105 I = 1, 5
      	  HCALC=HCALC+SCOEFF(I)*S(I)
 105 CONTINUE
 
	END
			
	DOUBLE PRECISION FUNCTION ACALC()
			
	IMPLICIT DOUBLE PRECISION(A, T, X-Z)
        IMPLICIT INTEGER(B-S, U-W)
      
        COMMON/PARAMS/SCOEFF(5),SMAX(5),X,Z
        SAVE/PARAMS/
      
        COMMON/VARS/S(5),W
        SAVE/VARS/
      
        ACALC = X
        DO 106 I = 1, 5
      	 ACALC=ACALC+120.0*W*S(I)
 106 CONTINUE
 
	END

[Kuciwalker]

Fortran

[KrazyHorse]

physics language

[MRT144]

You're awesome KH!
I made a spreadsheet and corresponding chart to show the solution. I made the spreadsheet a few hours before i downloaded the program and had to basically just had to guess and check the graph.

but thats awesome KH and essentially what I wanted to make without the ability to do so.

BTW, 45 minutes for me? I am flattered.

[MRT144]

graph!

[Lul Thyme]

Originally posted by KrazyHorse


I don't see why not. If you're in a domain with continuous partial derivatives and no zeroes in any of the partial derivatives anywhere then the absolute minimum (and maximum, of course) on your domain must be at one of the corners.

On the boundary in general, if the boundary isn't bounded by hyperplanes like in this case.

Also that's IF there is an extremum it has to be on the boundary. You need compactness to omit this part IIRC.

I guess I knew this, I never thought about what derivatives of quotients of multivariable linar functions would look like.

I guess all the S variable are integers each so all of this is moot since there's only a finite number of possibilities.
(Except for w)

[KrazyHorse]

Originally posted by Lul Thyme


On the boundary in general, if the boundary isn't bounded by hyperplanes like in this case.

Also that's IF there is an extremum it has to be on the boundary. You need compactness to omit this part IIRC.

I guess I knew this, I never thought about what derivatives of quotients of multivariable linar functions would look like.

I guess all the S variable are integers each so all of this is moot since there's only a finite number of possibilities.
(Except for w)

w is bounded above by 9

And we're on a closed, bounded subset of R^n so bolzano-weierstrass tells me what I need to know here...

[TheStinger]

Lets face it,

you could all be making this up and frankly you probably are.

[Lul Thyme]

Originally posted by KrazyHorse


w is bounded above by 9

And we're on a closed, bounded subset of R^n so bolzano-weierstrass tells me what I need to know here...

Sure.
In this specific problem, the domain can be taken to be a finite set so you don't even need Bol-Wei to know it's compact.

If you reread my comment you'll see that I wasn't denying your conclusion in this specific case, just nitpicking that the way you stated it in general was missing a few things.

[Krill]

Is this something to do with CIV?

[Lul Thyme]

Originally posted by Krill
Is this something to do with CIV?

That would be blasphemy on the off-topic boards no?

[Krill]

Probably.

Not that I care much though

[KrazyHorse]

Originally posted by Lul Thyme


Sure.
In this specific problem, the domain can be taken to be a finite set so you don't even need Bol-Wei to know it's compact.

If you reread my comment you'll see that I wasn't denying your conclusion in this specific case, just nitpicking that the way you stated it in general was missing a few things.

Okay. No problem.

It's just that in this specific case the conclusion seemed obvious to me.

I know that if we'd had curved boundaries etc. my conclusion would not be true. But given any specific problem my physics brain immediately draws a picture of it.

That's what makes me a good physicist and a bad mathematician. Some math problems just don't have any rational picture you can draw of them...

[Krill]

The unfortunate thing for MRT is that none of that work is actually applicable to CIV, if that is indeed what MRT is using it for.