Difference between revisions of "V2fplanck.m"
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{{DISPLAYTITLE:v2fplanck.m}} __NOTOC__ | {{DISPLAYTITLE:v2fplanck.m}} __NOTOC__ | ||
| − | + | Translates a stationary 3D velocity field and diffusion-tensor field into a Fokker-Planck evolution generator; see IK's review (http://dx.doi.org/10.1016/j.jmr.2016.07.005) for the construction of the generator, and this function builds the M matrix in Equation 7. | |
| − | Translates a stationary 3D velocity field and | ||
==Syntax== | ==Syntax== | ||
| − | F=v2fplanck(spin_system,parameters) | + | F=v2fplanck(spin_system,parameters) |
| − | == | + | ==Parameters== |
| − | parameters.u - X components of the velocity vectors | + | parameters.u - X components of the velocity vectors |
for each voxel in the sample, m/s | for each voxel in the sample, m/s | ||
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==Outputs== | ==Outputs== | ||
| − | F - spatial dynamics generator | + | F - spatial dynamics generator |
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==Examples== | ==Examples== | ||
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See examples/imaging and examples/nmr_diffusion directories in the example set. | See examples/imaging and examples/nmr_diffusion directories in the example set. | ||
==Notes== | ==Notes== | ||
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The direct product order is Z(x)Y(x)X(x)Spin, this corresponds to a column-wise vectorization of a 3D array with dimensions ordered as [X Y Z]. | The direct product order is Z(x)Y(x)X(x)Spin, this corresponds to a column-wise vectorization of a 3D array with dimensions ordered as [X Y Z]. | ||
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==See also== | ==See also== | ||
| − | + | [[imaging.m]], [[hydrodynamics.m]], [[fourdif.m]], [[fdmat.m]], [[polyadic.m]], [[polyadic/inflate.m]], [[g2fplanck.m]], [[mri_2d_plot.m]], [[ngridpts.m]], [[phantoms.m]], [[Imaging_module]] | |
| − | [[imaging.m]], [[hydrodynamics.m]], [[fourdif.m]], [[fdmat.m]], [[polyadic.m]] | ||
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''Version 2.1, authors: [[Ilya Kuprov]], [[Ahmed Allami]]'' | ''Version 2.1, authors: [[Ilya Kuprov]], [[Ahmed Allami]]'' | ||
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Latest revision as of 19:43, 6 June 2026
Translates a stationary 3D velocity field and diffusion-tensor field into a Fokker-Planck evolution generator; see IK's review (http://dx.doi.org/10.1016/j.jmr.2016.07.005) for the construction of the generator, and this function builds the M matrix in Equation 7.
Syntax
F=v2fplanck(spin_system,parameters)
Parameters
parameters.u - X components of the velocity vectors
for each voxel in the sample, m/s
parameters.v - Y components of the velocity vectors
for each voxel in the sample, m/s
parameters.w - Z components of the velocity vectors
for each voxel in the sample, m/s
parameters.diff - diffusion coefficient or 3x3 tensor, m^2/s
for situations when this parameter is the
same in every voxel
parameters.dxx - Cartesian components of the diffusion
parameters.dxy tensor for each voxel of the sample
...
parameters.dzz
parameters.dims - dimensions of the 3D box, meters
parameters.npts - number of points in each dimension
of the 3D box
parameters.deriv - {'fourier'} uses Fourier diffe-
rentiation matrices; {'period',n}
requests n-point central finite-
difference matrices with periodic
boundary conditions
Outputs
F - spatial dynamics generator
Examples
See examples/imaging and examples/nmr_diffusion directories in the example set.
Notes
The direct product order is Z(x)Y(x)X(x)Spin, this corresponds to a column-wise vectorization of a 3D array with dimensions ordered as [X Y Z].
Polyadic objects are returned, use polyadic/inflate.m to get the corresponding sparse matrix.
See also
imaging.m, hydrodynamics.m, fourdif.m, fdmat.m, polyadic.m, polyadic/inflate.m, g2fplanck.m, mri_2d_plot.m, ngridpts.m, phantoms.m, Imaging_module
Version 2.1, authors: Ilya Kuprov, Ahmed Allami
