Add trajectory gradient optimization functions

[paquiteau]

• Closes Faster prephasors with linear programming #286
• Requires Acquisition Configuration #285

Changes proposed in this pull request:

• Add gradient waveform optimization using either linear or quadratic programming (requires an extra package)
• Example to compare and explains how this work.

[chaithyagr]

Be careful on spending too much time on this, we might get projection step up soon when I'm back :P

[paquiteau]

I think this complements the projection step, here you try to find the shortest path between two k-space/gradient states. Projection is, well, about projecting an existing trajectory. So they can coexist, and it could also serve as a nice reference to compare with.

[chaithyagr]

Just doing some basic checks first, still not done, need to go for lunch :P

[chaithyagr]

Number of gradient samples ?
Time points doesnt make much sense to me/

[paquiteau]

it really is the length of the waveform to optimize

[chaithyagr]

delta_kx ?

[paquiteau]

it's all 1D stuff (as if we were only optimizing the x gradient only)

[Daval-G]

I think this complements the projection step, here you try to find the shortest path between two k-space/gradient states. Projection is, well, about projecting an existing trajectory. So they can coexist, and it could also serve as a nice reference to compare with.

I think even without completing each other it's a good addition to gather multiple methods from the literature, it allows researchers to compare them, raising the standards (aka dropping sub-optimal methods and creating consensus)

[Daval-G]

(And btw I started making an example in #236 to gather & compare all gradient manipulation methods, it would be nice to build on that)