Deep copy warning -- efficient coding?

[Charles_Driver]

If I am constructing a symmetric matrix S, typically I have done something like
S[i,j] = complex operation
s[j,i] = s[i,j]

with stan 2.18 this approach generates a lot of warnings. What is the preferred way to approach this?

[bgoodri]

I think s[j,i] = s[i,j] does not actually trigger a warning, but other things do. The most common way to avoid them is to use foo += bar; rather than foo = foo + bar;. Unfortunately, the Info does not print out the filename or line number, but you can probably figure out where they are.

DIAGNOSTIC(S) FROM PARSER:
Info: left-hand side variable (name=o) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=o) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=o) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=o) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=l) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=DRDI) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=cz1) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=cz0) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=out) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=out) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=covm) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=l) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=l) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=counter) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=counter) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=sDIFFUSION) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=sMANIFESTVAR) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=sT0VAR) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=discreteDIFFUSION) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=discreteDIFFUSION) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=eta) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=etacov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=etacov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=etacov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=eta) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=etacov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=etacov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=discreteDIFFUSION) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=eta) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=state) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=state) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ypredcov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ypredcov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ukfmeasures) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=merrorstates) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ukfmeasures) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ukfmeasures) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ukfstates) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=sDIFFUSION) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=sMANIFESTVAR) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=sT0VAR) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=discreteDIFFUSION) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=discreteDIFFUSION) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=eta) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=etacov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=etacov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=etacov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=eta) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=etacov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=etacov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=discreteDIFFUSION) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=eta) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=state) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=state) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ypredcov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ypredcov) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ukfmeasures) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=merrorstates) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ukfmeasures) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ukfmeasures) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=ukfstates) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=pop_DIFFUSION) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=pop_MANIFESTVAR) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=pop_T0VAR) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
Info: left-hand side variable (name=popsd) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.

[Charles_Driver]

Thanks, I’m aware of the += and am happy to be able to use that in more cases with 2.18, but still this function generates 4 warnings:

sm <- '
functions{
matrix covsqrt2corsqrt(matrix mat, int invert){ 
        matrix[rows(mat),cols(mat)] o;
        vector[rows(mat)] s;
        o=mat;
      
        for(i in 1:rows(o)){ //set upper tri to lower
          for(j in min(i+1,rows(mat)):rows(mat)){
            o[j,i] = inv_logit(o[j,i])*2-1; 
            o[i,j] = o[j,i];
          }
          o[i,i]=1;
        }
      
        if(invert==1) o = inverse(o);
      
        for(i in 1:rows(o)){
          s[i] = inv_sqrt(o[i,] * o[,i]);
          if(is_inf(s[i])) s[i]=0;
        }
        o= diag_pre_multiply(s,o);
        return o;
}
}
model{
}'

s <- stan_model(model_code = sm)

[bgoodri]

I think that comes from if(invert==1) o = inverse(o); and o= diag_pre_multiply(s,o); rather than o[i,j] = o[j,i];

[Charles_Driver]

That would only generate two warnings by my count, but regardless, the general question still stands – is an operation like:

o = inverse(o)

actually inefficient, and if so, how should one handle this situation?

[bgoodri]

I think all of the ways to handle that would also involve a copy, although some might avoid the message. You could do something like

if (invert) {
  matrix[rows(o), cols(o)] o_inv = inverse(o);
  ... 
}

[Charles_Driver]

Ok. It’s nice that such information is available, but it’s not so nice when it generates a page of spurious warnings that (I think?) can’t be disabled. Also, o[i,j] = o[j,i]; does generate the warning.

[bgoodri]

They can’t be disabled but they can be avoided. In the loop, maybe try

real tmp = whatever;
o[i,j] = tmp;
o[j,i] = tmp;

[Charles_Driver]

Ok, and that should be of equal or greater efficiency? Seems like an extra operation to my naive thinking.

[bgoodri]

Same efficiency, less warnings about the lack of efficiency.

[mitzimorris]

this is parser bug - https://github.com/stan-dev/stan/issues/2677