Grad sandw.m - Revision history

Kuprov: Update function See also links and function index membership

2026-06-06T18:37:07Z

Update function See also links and function index membership

Kuprov: Rename Arguments section heading to Parameters

2026-06-05T17:49:13Z

Rename Arguments section heading to Parameters

Kuprov: Spot-edit Spinach function page first-line NOTOC and template fields

2026-06-05T17:28:01Z

Spot-edit Spinach function page first-line NOTOC and template fields

Kuprov: Normalise sequential blank lines

2026-04-25T11:25:36Z

Normalise sequential blank lines

Kuprov: /* Notes */

2019-08-25T08:56:24Z

‎Notes

Admin: /* See also */

2018-08-15T13:26:51Z

‎See also

Admin: /* Examples */

2018-08-15T13:26:38Z

‎Examples

Admin at 13:26, 15 August 2018

2018-08-15T13:26:05Z

Kuprov: Created page with "Computes the effect of a gradient sandwich on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gra..."

2015-09-07T12:02:58Z

Created page with "Computes the effect of a gradient sandwich on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gra..."

New page

Computes the effect of a gradient sandwich on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gradients are linear, and that they are antisymmetric about the middle of the sample. Syntax:

rho=grad_sandw(spin_system,L,rho,P,g_amps,s_len,g_durs,s_facs)

Arguments:

rho - spin system state vector

L - system Liouvillian

P - total propagator for all events happening
between the two gradients

g_amps - row vector containing the amplitudes of
the two gradients, Gauss/cm

s_len - sample length, cm

g_durs - row vector containing the durations of
the two gradients, seconds

s_facs - shape factors of the two gradients, use
[1 1] for square gradient pulses

Note: the function integrates over sample coordinates - subsequent gradient pulses would not refocus the magnetization that it has left defocused. More information on the subject is available in Luke's paper (http://dx.doi.org/10.1016/j.jmr.2014.01.011).

@@ Line 39: / Line 39: @@
 ==See also==
-[[grad_pulse.m]], [[imaging.m]]
+[[grad_pulse.m]], [[imaging.m]], [[bruker_write.m]], [[cartesian2polar.m]], [[chirp_pulse.m]], [[pmlg5.m]], [[polar2cartesian.m]], [[pulse_shape.m]], [[read_wave.m]], [[restrans.m]], [[rseq_compiler.m]], [[rsequence.m]], [[sawtooth.m]], [[sech_pulse.m]], [[shaped_pulse_af.m]], [[shaped_pulse_xy.m]], [[spinal.m]], [[triwave.m]], [[vg_pulse.m]], [[wave_basis.m]], [[Kernel_functions]]
 ''Version 2.2, authors: [[Luke Edwards]], [[Ilya Kuprov]]''

@@ Line 6: / Line 6: @@
       rho=grad_sandw(spin_system,L,rho,P,g_amps,s_len,g_durs,s_facs)
-==Arguments==
+==Parameters==
                rho   - spin system state vector

← Older revision		Revision as of 17:28, 5 June 2026
Line 1:		Line 1:
−	{{DISPLAYTITLE:grad_sandw.m}}	+	{{DISPLAYTITLE:grad_sandw.m}} __NOTOC__
	Emulates the effect of a gradient sandwich on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gradients are linear, and that they are antisymmetric about the middle of the sample.		Emulates the effect of a gradient sandwich on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gradients are linear, and that they are antisymmetric about the middle of the sample.

@@ Line 40: / Line 40: @@
 ==See also==
 [[grad_pulse.m]], [[imaging.m]]
 ''Version 2.2, authors: [[Luke Edwards]], [[Ilya Kuprov]]''

@@ Line 35: / Line 35: @@
 ==Notes==
-# The function integrates over sample coordinates - subsequent gradient pulses would not refocus the magnetization that it has defocused. To simulate a gradient sandwich, use grad_sandw.m function. More information on the subject is available in Luke's paper (http://dx.doi.org/10.1016/j.jmr.2014.01.011).
+# '''WARNING''' This function integrates over the spatial coordinate after the gradient pulses are completed - subsequent gradient pulses would not refocus the magnetisation that this function removed because it is removed mathematically. If your experiment has multiple gradient pulses, you must model the spatially distributed spin dynamics explicitly using [[imaging.m]] context.
-#This function is OK for standalone gradient pairs; for more sophisticated gradient work, use the imaging context.
+# More information on the subject is available in Luke's paper (http://dx.doi.org/10.1016/j.jmr.2014.01.011).
 ==See also==

@@ Line 32: / Line 32: @@
 ==Examples==
-See examples/fundamentals/gradient_test_1.m file for an example of using this function.
+See examples/fundamentals/gradient_test_2.m file for an example of using this function.
 ==Notes==

@@ Line 1: / Line 1: @@
-Computes the effect of a gradient sandwich on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gradients are linear, and that they are antisymmetric about the middle of the sample. Syntax:
+{{DISPLAYTITLE:grad_sandw.m}}
       rho=grad_sandw(spin_system,L,rho,P,g_amps,s_len,g_durs,s_facs)
-Arguments:
+==Arguments==
-−
                rho   - spin system state vector
-−
                  L   - system Liouvillian
-−
                  P   - total propagator for all events happening
                        between the two gradients
-−
             g_amps   - row vector containing the amplitudes of
                        the two gradients, Gauss/cm
-−
              s_len   - sample length, cm
-−
             g_durs   - row vector containing the durations of
                        the two gradients, seconds
-−
             s_facs   - shape factors of the two gradients, use
                        [1 1] for square gradient pulses
-Note: the function integrates over sample coordinates - subsequent gradient pulses would not refocus the magnetization that it has left defocused. More information on the subject is available in Luke's paper (http://dx.doi.org/10.1016/j.jmr.2014.01.011).
+==Outputs==