Implement missing matrix scaling

[weslleyspereira]

I want to open this topic so we do not lose the idea in #733 (comment)

@langou said:

The comment reads: BLAS_dge_diag_scale, yes, it would, be nice to have a subroutine that does this.

The *LASCL2 and *LARSCL2 suites would be MUCH better if we could do column scaling or row scaling. Right now this is limited to column scaling. Dang it. This is not good. (Or alternatively, not my preference, one could have a TRANSX flag TRANS or NOTRANS.)

I wonder whether we should have a routine (or a set of routines) that does all four: column scaling only (X := X * Dc or X := X * inv(Dc)), row scaling only (X := Dr * X or X := X * inv(Dc)), column and row scaling both at once (X := Dr * X * Dc), similarity-transformation scaling (X := D * X * inv(D) or X := inv(D) * X * D).

This is kind of already described in Chapter 2: Dense and Banded BLAS, page 72 through the functions: _DIAG_SCALE, _LRSCALE, _LRSCALE,

SUBROUTINE BLAS_xGE_DIAG_SCALE( SIDE, M, N, D, INCD, A, LDA )

SUBROUTINE BLAS_xGE_DIAG_LRSCALE( M, N, DL, INCDL, DR, INCDR, A, LDA )

SUBROUTINE BLAS_xSY_DIAG_LRSCALE( UPLO, N, D, INCD, A, LDA )

A coupe of things missing though: (1) the choice between multiplying or dividing by the scaling factor, and (2) similarity transformation scaling.