Re: Solving Two Equations using MATRIX

Posted by David Marso on Jul 20, 2015; 3:37am
URL: http://spssx-discussion.165.s1.nabble.com/Solving-Two-Equations-using-MATRIX-tp5730174p5730175.html

Hi Ryan,
Good to see you here!
Here is a simple MATRIX program.
Please verify that I haven't dropped a stitch.
Curious as to what this is calculating.
Could it be related to the Determinant of a matrix?
If so there is the DET operator .

MATRIX.
COMPUTE R={1.00, .20, .25, .85, .30, .15;
            .20,1.00, .10, .05, .70, .30;
            .25, .10,1.00, .35, .40, .80;
            .85, .05, .35,1.00, .50, .45;
            .30, .70, .40, .50,1.00, .55;
            .15, .30, .80, .45, .55, 1.00}.
COMPUTE W={0,0,0, 2,-1,-1;
           0,0,0,-1, 2,-1;
           0,0,0,-1,-1, 2;
           0,0,0, 0, 0, 0;
           0,0,0, 0, 0, 0;
           0,0,0, 0, 0, 0}.

COMPUTE X=MSUM(R&*W).
COMPUTE y=0.
LOOP j=1 TO 3.
LOOP k=4 TO 6.
LOOP h=1 TO 3.
LOOP m=4 TO 6.
COMPUTE y=y +w(j,k)*w(h,m) *
            (r(j,h)-r(j,k)*r(k,h))*(r(k,m)-r(k,h)*r(h,m)) +                    
            (r(j,m)-r(j,h)*r(h,m))*(r(k,h)-r(k,j)*r(j,h)) +                      
            (r(j,h)-r(j,m)*r(m,h))*(r(k,m)-r(k,j)*r(j,m)) +                    
            (r(j,m)-r(j,k)*r(k,m))*(r(k,h)-r(k,m)*r(m,h)) .
END LOOP.
END LOOP.
END LOOP.
END LOOP.
COMPUTE y=SQRT(.5/??? -1) * y.
END MATRIX.

Ryan Black wrote

Dear SPSS-L,

Suppose we have a 6X6 correlation matrix. I have two equations I need to
solve.

The following is GIVEN:

COMPUTE r11 = 1.
COMPUTE r12 = .20.
COMPUTE r13 = .25.
COMPUTE r14 = .85.
COMPUTE r15 = .30.
COMPUTE r16 = .15.
COMPUTE r21 = .20.
COMPUTE r22 = 1.
COMPUTE r23 = .10.
COMPUTE r24 = .05.
COMPUTE r25 = .70.
COMPUTE r26 = .30.
COMPUTE r31 = .25.
COMPUTE r32 = .10.
COMPUTE r33 = 1.
COMPUTE r34 = .35.
COMPUTE r35 = .40.
COMPUTE r36 = .80.
COMPUTE r41 = .85.
COMPUTE r42 = .05.
COMPUTE r43 = .35.
COMPUTE r44 = 1.
COMPUTE r45 = .50.
COMPUTE r46 = .45.
COMPUTE r51 = .30.
COMPUTE r52 = .70.
COMPUTE r53 = .40.
COMPUTE r54 = .50.
COMPUTE r55 = 1.
COMPUTE r56 = .55.
COMPUTE r61 = .15.
COMPUTE r62 = .30.
COMPUTE r63 = .80.
COMPUTE r64 = .45.
COMPUTE r65 = .55.
COMPUTE r66 = 1.

COMPUTE wjk14 =  2.
COMPUTE wjk15 = -1.
COMPUTE wjk16 = -1.
COMPUTE wjk24 = -1.
COMPUTE wjk25 =  2.
COMPUTE wjk26 = -1.
COMPUTE wjk34 = -1.
COMPUTE wjk35 = -1.
COMPUTE wjk36 =  2.

FIRST EQUATION:

Sum[{j=1,3},{k=4,6}: w[j,k]*r[j,k]]

COMPUTE x = wjk14*r14 + wjk15*r15 + wjk16*r16 +
            wjk24*r24 + wjk25*r25 + wjk26*r26 +
            wjk34*r34 + wjk35*r35 + wjk36*r36.

While x is easy to solve outside of MATRIX, I'm curious how x could be
solved more efficiently in MATRIX.

Suppose the following is GIVEN as well:

COMPUTE whm14 =  2.
COMPUTE whm15 = -1.
COMPUTE whm16 = -1.
COMPUTE whm24 = -1.
COMPUTE whm25 =  2.
COMPUTE whm26 = -1.
COMPUTE whm34 = -1.
COMPUTE whm35 = -1.
COMPUTE whm36 =  2.

SECOND EQUATION:

y = Sqrt[(.5/(N-1))*Sum[{j=1,3},{k=4,6},{h=1,3},{m=4,6}:
         w[j,k]*w[h,m]*(

         (r[j,h]-r[j,k]*r[k,h])*(r[k,m]-r[k,h]*r[h,m]) +

         (r[j,m]-r[j,h]*r[h,m])*(r[k,h]-r[k,j]*r[j,h]) +

         (r[j,h]-r[j,m]*r[m,h])*(r[k,m]-r[k,j]*r[j,m]) +

         (r[j,m]-r[j,k]*r[k,m])*(r[k,h]-r[k,m]*r[m,h]))]]

As you can see, y is far more tedious to solve outside of MATRIX. The first
of 81 "Sum[{..." terms could be solved using COMPUTE as follows:

COMPUTE jk14_hm14 =
wjk14*whm14*((r11-r14*r41)*(r44-r41*r14)+(r14-r11*r14)*(r41-r41*r11)+(r11-r14*r41)*(r44-r41*r14)+(r14-r14*r44)*(r41-r44*r41)).

but then I'd have to work it out for the following 80 terms:

compute jk15_hm14 = .
compute jk16_hm14 = .
compute jk24_hm14 = .
compute jk25_hm14 = .
compute jk26_hm14 = .
compute jk34_hm14 = .
compute jk35_hm14 = .
compute jk36_hm14 = .

compute jk14_hm24 = .
compute jk15_hm24 = .
compute jk16_hm24 = .
compute jk24_hm24 = .
compute jk25_hm24 = .
compute jk26_hm24 = .
compute jk34_hm24 = .
compute jk35_hm24 = .
compute jk36_hm24 = .

compute jk14_hm34 = .
compute jk15_hm34 = .
compute jk16_hm34 = .
compute jk24_hm34 = .
compute jk25_hm34 = .
compute jk26_hm34 = .
compute jk34_hm34 = .
compute jk35_hm34 = .
compute jk36_hm34 = .

compute jk14_hm15 = .
compute jk15_hm15 = .
compute jk16_hm15 = .
compute jk24_hm15 = .
compute jk25_hm15 = .
compute jk26_hm15 = .
compute jk34_hm15 = .
compute jk35_hm15 = .
compute jk36_hm15 = .

compute jk14_hm16 = .
compute jk15_hm16 = .
compute jk16_hm16 = .
compute jk24_hm16 = .
compute jk25_hm16 = .
compute jk26_hm16 = .
compute jk34_hm16 = .
compute jk35_hm16 = .
compute jk36_hm16 = .

compute jk14_hm25 = .
compute jk15_hm25 = .
compute jk16_hm25 = .
compute jk24_hm25 = .
compute jk25_hm25 = .
compute jk26_hm25 = .
compute jk34_hm25 = .
compute jk35_hm25 = .
compute jk36_hm25 = .

compute jk14_hm26 = .
compute jk15_hm26 = .
compute jk16_hm26 = .
compute jk24_hm26 = .
compute jk25_hm26 = .
compute jk26_hm26 = .
compute jk34_hm26 = .
compute jk35_hm26 = .
compute jk36_hm26 = .

compute jk14_hm35 = .
compute jk15_hm35 = .
compute jk16_hm35 = .
compute jk24_hm35 = .
compute jk25_hm35 = .
compute jk26_hm35 = .
compute jk34_hm35 = .
compute jk35_hm35 = .
compute jk36_hm35 = .

compute jk14_hm36 = .
compute jk15_hm36 = .
compute jk16_hm36 = .
compute jk24_hm36 = .
compute jk25_hm36 = .
compute jk26_hm36 = .
compute jk34_hm36 = .
compute jk35_hm36 = .
compute jk36_hm36 = .

and then sum the 81 terms and multiply by Sqrt[(.5/(N-1)).

Any tips would be most appreciated.

Thanks,

Ryan

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD