Module ns_cpmg_2site_star
source code
The numerical fit of 2-site Bloch-McConnell equations for CPMG-type
experiments, the NS CPMG 2-site star and NS CPMG 2-site star full models.
Description
The function uses an explicit matrix that contains relaxation,
exchange and chemical shift terms. It does the 180deg pulses in the
CPMG train with conjugate complex matrices. The approach of
Bloch-McConnell can be found in chapter 3.1 of Palmer, A. G. 2004
Chem. Rev., 104, 3623-3640. This function was written,
initially in MATLAB, in 2010.
Code origin
The code was submitted at http://thread.gmane.org/gmane.science.nmr.relax.devel/4132
by Paul Schanda.
Links
More information on the NS CPMG 2-site star model can be found in
the:
More information on the NS CPMG 2-site star full model can be found
in the:
numpy float array of rank [NE][NS][NM][NO][ND][2][2]
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rcpmg_star_rankN(R2A=None,
R2B=None,
dw=None,
k_AB=None,
k_BA=None,
tcp=None)
Definition of the exchange matrix, for rank
[NE][NS][NM][NO][ND][2][2]. |
source code
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r2eff_ns_cpmg_2site_star(M0=None,
r20a=None,
r20b=None,
pA=None,
dw=None,
dw_orig=None,
kex=None,
inv_tcpmg=None,
tcp=None,
back_calc=None,
num_points=None,
power=None)
The 2-site numerical solution to the Bloch-McConnell equation using
complex conjugate matrices. |
source code
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m_r20a = array([[-1., 0...
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m_r20b = array([[ 0., 0...
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m_k_AB = array([[-1., 0...
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m_k_BA = array([[ 0., 1...
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m_dw = array([[ 0., 0...
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__package__ = ' lib.dispersion '
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Imports:
add,
array,
conj,
dot,
einsum,
fabs,
float64,
isfinite,
log,
min,
multiply,
sum,
fix_invalid,
masked_where,
matrix_power,
isNaN,
matrix_exponential
rcpmg_star_rankN(R2A=None,
R2B=None,
dw=None,
k_AB=None,
k_BA=None,
tcp=None)
| source code
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Definition of the exchange matrix, for rank
[NE][NS][NM][NO][ND][2][2].
- Parameters:
R2A (numpy float array of rank [NE][NS][NM][NO][ND]) - The transverse, spin-spin relaxation rate for state A.
R2B (numpy float array of rank [NE][NS][NM][NO][ND]) - The transverse, spin-spin relaxation rate for state B.
dw (numpy float array of rank [NE][NS][NM][NO][ND]) - 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.
tcp (numpy float array of rank [NE][NS][NM][NO][ND]) - The tau_CPMG times (1 / 4.nu1).
- Returns: numpy float array of rank [NE][NS][NM][NO][ND][2][2]
- The relaxation matrix R and complex conjugate cR2.
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r2eff_ns_cpmg_2site_star(M0=None,
r20a=None,
r20b=None,
pA=None,
dw=None,
dw_orig=None,
kex=None,
inv_tcpmg=None,
tcp=None,
back_calc=None,
num_points=None,
power=None)
| source code
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The 2-site numerical solution to the Bloch-McConnell equation using
complex conjugate matrices.
This function calculates and stores the R2eff values.
- Parameters:
M0 (numpy float64, rank-1, 2D array) - This is a vector that contains the initial magnetizations
corresponding to the A and B state transverse magnetizations.
r20a (numpy float array of rank [NE][NS][NM][NO][ND]) - The R2 value for state A in the absence of exchange.
r20b (numpy float array of rank [NE][NS][NM][NO][ND]) - The R2 value for state B in the absence of exchange.
pA (float) - The population of state A.
dw (numpy float array of rank [NE][NS][NM][NO][ND]) - The chemical exchange difference between states A and B in rad/s.
dw_orig (numpy float array of rank-1) - The chemical exchange difference between states A and B in ppm.
This is only for faster checking of zero value, which result in
no exchange.
kex (float) - The kex parameter value (the exchange rate in rad/s).
inv_tcpmg (numpy float array of rank [NE][NS][NM][NO][ND]) - The inverse of the total duration of the CPMG element (in inverse
seconds).
tcp (numpy float array of rank [NE][NS][NM][NO][ND]) - The tau_CPMG times (1 / 4.nu1).
back_calc (numpy float array of rank [NE][NS][NM][NO][ND]) - The array for holding the back calculated R2eff values. Each
element corresponds to one of the CPMG nu1 frequencies.
num_points (numpy int array of rank [NE][NS][NM][NO]) - The number of points on the dispersion curve, equal to the length
of the tcp and back_calc arguments.
power (numpy int array of rank [NE][NS][NM][NO][ND]) - The matrix exponential power array.
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m_r20a
- Value:
array([[-1., 0.],
[ 0., 0.]])
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m_r20b
- Value:
array([[ 0., 0.],
[ 0., -1.]])
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m_k_AB
- Value:
array([[-1., 0.],
[ 1., 0.]])
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m_k_BA
- Value:
array([[ 0., 1.],
[ 0., -1.]])
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m_dw
- Value:
array([[ 0., 0.],
[ 0., 1.]])
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