Constrained Estimate. The method computes $\vB(r)$ using (\[eq:bdef\]) from a three dimensional $\vv(\vx)$ defined everywhere in a large region of space and constrained to match the TF data. For the analysis below, we use the SFI++ survey of spiral galaxies with I-band Tully-Fisher distances, [@mas06; @spring07], which builds on the original Spiral Field I-band Survey [@gio94; @gio95; @hg99] and Spiral Cluster I-band Survey [@gio97a; @gio97b]. We use the published SFI++ magnitudes and velocity widths, and derive our own peculiar velocities, rather than taking the published distances as given. We shall use the [*inverse*]{} of the Tully-Fisher (ITF) relationship. The main advantages of ITF methods is that samples selected by magnitude, as most are, will be minimally plagued by Malmquist bias effects when analyzed in the inverse direction [@schechter; @a82]. We assume that the circular velocity parameter, $\eta \equiv {\rm log} (line\; width)$, of a galaxy is, up to a random scatter, related to its absolute magnitude, $M$, by means of a linear [*inverse*]{} Tully-Fisher (ITF) relation, i.e., $$\label{eq:ITF}
\eta=s M + \eta_0 .$$ The preparation of the data is done following [@DN10]. We include all field, group, and cluster galaxies. Galaxies in groups and clusters are treated as individual objects, 