Module ns_matrices

A collection of functions for generating the relaxation matrices for the numerical solutions.

These are for the numerical solutions to the Bloch-McConnell equations for relaxation dispersion.

Functions

numpy rank-2, 4D array r180x_2d(flip=3.14159265359)
The 2D rotation matrix for an imperfect X-axis pi-pulse.

numpy rank-2, 7D array r180x_3d(flip=3.14159265359)
The 3D rotation matrix for an imperfect X-axis pi-pulse.

numpy rank-2, 4D array rcpmg_2d(R2A=None, R2B=None, dw=None, k_AB=None, k_BA=None)
Definition of the 2D exchange matrix.

numpy rank-2, 7D array rcpmg_3d(R1A=None, R1B=None, R2A=None, R2B=None, pA=None, pB=None, dw=None, k_AB=None, k_BA=None)
Definition of the 3D exchange matrix.

rr1rho_3d_3site(matrix=None, R1=None, r1rho_prime=None, pA=None, pB=None, pC=None, wA=None, wB=None, wC=None, w1=None, k_AB=None, k_BA=None, k_BC=None, k_CB=None, k_AC=None, k_CA=None)
Definition of the 3D exchange matrix.

rr1rho_3d(matrix=None, R1=None, r1rho_prime=None, pA=None, pB=None, wA=None, wB=None, w1=None, k_AB=None, k_BA=None)
Definition of the 3D exchange matrix.

Variables

__package__ = 'lib.dispersion'

Imports: cos, sin, pi, array, float64, matrix

Function Details

r180x_2d(flip=3.14159265359)

The 2D rotation matrix for an imperfect X-axis pi-pulse.

Parameters:

• flip (float) - The X-axis pi-pulse flip angle (in rad). This is currently unused, hence perfect pi-pulses are assumed.

Returns: numpy rank-2, 4D array

The 2D rotational matrix.

r180x_3d(flip=3.14159265359)

The 3D rotation matrix for an imperfect X-axis pi-pulse.

Parameters:

• flip (float) - The X-axis pi-pulse flip angle (in rad).

Returns: numpy rank-2, 7D array

The 3D rotational matrix.

rcpmg_2d(R2A=None, R2B=None, dw=None, k_AB=None, k_BA=None)

Definition of the 2D exchange matrix.

Parameters:

• R2A (float) - The transverse, spin-spin relaxation rate for state A.
• R2B (float) - The transverse, spin-spin relaxation rate for state B.
• dw (float) - The chemical exchange difference between states A and B in rad/s.
• k_AB (float) - The forward exchange rate from state A to state B.
• k_BA (float) - The reverse exchange rate from state B to state A.

Returns: numpy rank-2, 4D array

The relaxation matrix.

rcpmg_3d(R1A=None, R1B=None, R2A=None, R2B=None, pA=None, pB=None, dw=None, k_AB=None, k_BA=None)

Definition of the 3D exchange matrix.

Parameters:

• R1A (float) - The longitudinal, spin-lattice relaxation rate for state A.
• R1B (float) - The longitudinal, spin-lattice relaxation rate for state B.
• R2A (float) - The transverse, spin-spin relaxation rate for state A.
• R2B (float) - The transverse, spin-spin relaxation rate for state B.
• pA (float) - The population of state A.
• pB (float) - The population of state B.
• dw (float) - The chemical exchange difference between states A and B in rad/s.
• k_AB (float) - The forward exchange rate from state A to state B.
• k_BA (float) - The reverse exchange rate from state B to state A.

Returns: numpy rank-2, 7D array

The relaxation matrix.

rr1rho_3d_3site(matrix=None, R1=None, r1rho_prime=None, pA=None, pB=None, pC=None, wA=None, wB=None, wC=None, w1=None, k_AB=None, k_BA=None, k_BC=None, k_CB=None, k_AC=None, k_CA=None)

Definition of the 3D exchange matrix.

Parameters:

• matrix (numpy rank-2 9D array) - The matrix to fill.
• R1 (float) - The longitudinal, spin-lattice relaxation rate.
• r1rho_prime (float) - The R1rho transverse, spin-spin relaxation rate in the absence of exchange.
• pA (float) - The population of state A.
• pB (float) - The population of state B.
• pC (float) - The population of state C.
• wA (float) - The chemical shift offset of state A from the spin-lock.
• wB (float) - The chemical shift offset of state B from the spin-lock.
• wC (float) - The chemical shift offset of state C from the spin-lock.
• w1 (float) - The spin-lock field strength in rad/s.
• k_AB (float) - The forward exchange rate from state A to state B.
• k_BA (float) - The reverse exchange rate from state B to state A.
• k_BC (float) - The forward exchange rate from state B to state C.
• k_CB (float) - The reverse exchange rate from state C to state B.
• k_AC (float) - The forward exchange rate from state A to state C.
• k_CA (float) - The reverse exchange rate from state C to state A.

rr1rho_3d(matrix=None, R1=None, r1rho_prime=None, pA=None, pB=None, wA=None, wB=None, w1=None, k_AB=None, k_BA=None)

Definition of the 3D exchange matrix.

This code originates from the funNumrho.m file from the Skrynikov & Tollinger code (the sim_all.tar file https://web.archive.org/web/https://gna.org/support/download.php?file_id=18404 attached to https://web.archive.org/web/https://gna.org/task/?7712#comment5).

Parameters:

• matrix (numpy rank-2 6D array) - The matrix to fill.
• R1 (float) - The longitudinal, spin-lattice relaxation rate.
• r1rho_prime (float) - The R1rho transverse, spin-spin relaxation rate in the absence of exchange.
• pA (float) - The population of state A.
• pB (float) - The population of state B.
• wA (float) - The chemical shift offset of state A from the spin-lock.
• wB (float) - The chemical shift offset of state A from the spin-lock.
• w1 (float) - The spin-lock field strength in rad/s.
• k_AB (float) - The forward exchange rate from state A to state B.
• k_BA (float) - The reverse exchange rate from state B to state A.