[Related: Documentation] dgesvdx IL IU parameters

[lecarrera-tec]

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For the range case of dgesvdx, the documentation for IL and IU says:

1 <= IL <= IU <= min(M,N)

but the correct order is: 1 <= IU <= IL <= min(M,N) as the greater singular values pop up first.

Also, in the documentation for LWORK says:

LWORK >= MAX(1,MIN(M,N)*(MIN(M,N)+4)) for the paths (comments inside the code): - PATH 1 (M much larger than N) - PATH 1t (N much larger than M) LWORK >= MAX(1,MIN(M,N)*2+MAX(M,N)) for the other paths.

But for PATH 1: minwrk = n*(n*3+20) for PATH 1t: minwrk = m*(m*3+20) for PATH 2: minwrk = max(n*(n*2+19),4*n+m) and for PATH 2t: minwrk = max(m*(m*2+19),4*m+n)

So, the documentation should say: LWORK >= MAX(1,MIN(M,N)(3MIN(M,N)+20)) for the paths (comments inside the code): - PATH 1 (M much larger than N) - PATH 1t (N much larger than M) LWORK >= MAX(1, MIN(M,N)* (2 * MIN(M,N)+19), 4*MIN(M,N) + MAX(M,N)) for the other paths.

[weslleyspereira]

Thanks @lecarrera-tec !

[edited] I agree with your correction for the LWORK. In fact, IL and IU are input parameters for the case RANGE='I' and refer to the singular values in ascending order. Note that IU.LT.IL provokes an error:

https://github.com/Reference-LAPACK/lapack/blob/2dafa3d2756a7825c23a8c8456781561e36668ae/SRC/dgesvdx.f#L354-L358

Thanks to @langou for noticing that!

* Do you plan to submit a pull request? If not, I can do it. Just to mention, the same problems exist in the other three gesvdx methods.

[weslleyspereira]

Test for Lapack DGESVDX with RANGE=I : https://gist.github.com/weslleyspereira/0587d103761e3aee36163e00d753de49