def determine_model_type():
"""Determine the global model type.
@return: The name of the model type, which will be one of 'all', 'diff', 'mf', or 'local_tm'. If all parameters are fixed (and no spins selected), None is returned.
@rtype: str or None
"""
# Test if sequence data is loaded.
if not exists_mol_res_spin_data():
raise RelaxNoSequenceError
# If there is a local tm, fail if not all residues have a local tm parameter.
local_tm = False
for spin in spin_loop():
# Skip deselected spins.
if not spin.select:
continue
# No params.
if not hasattr(spin, 'params') or not spin.params:
continue
# Local tm.
if not local_tm and 'local_tm' in spin.params:
local_tm = True
# Inconsistencies.
elif local_tm and not 'local_tm' in spin.params:
raise RelaxError("All spins must either have a local tm parameter or not.")
# Check if any model-free parameters are allowed to vary.
mf_all_fixed = True
mf_all_deselected = True
for spin in spin_loop():
# Skip deselected spins.
if not spin.select:
continue
# At least one spin is selected.
mf_all_deselected = False
# Test the fixed flag.
if not hasattr(spin, 'fixed'):
mf_all_fixed = False
break
if not spin.fixed:
mf_all_fixed = False
break
# No spins selected?!?
if mf_all_deselected:
# All parameters fixed!
if not hasattr(cdp, 'diff_tensor') or cdp.diff_tensor.fixed:
return None
return 'diff'
# Local tm.
if local_tm:
return 'local_tm'
# Test if the diffusion tensor data is loaded.
if not diffusion_tensor.diff_data_exists():
# Catch when the local tm value is set but not in the parameter list.
for spin in spin_loop():
if hasattr(spin, 'local_tm') and spin.local_tm != None and not 'local_tm' in spin.params:
raise RelaxError("The local tm value is set but not located in the model parameter list.")
# Normal error.
raise RelaxNoTensorError('diffusion')
# 'diff' model type.
if mf_all_fixed:
# All parameters fixed!
if cdp.diff_tensor.fixed:
return None
return 'diff'
# 'mf' model type.
if cdp.diff_tensor.fixed:
return 'mf'
# 'all' model type.
else:
return 'all'
def determine_model_type():
"""Determine the global model type.
@return: The name of the model type, which will be one of 'all', 'diff', 'mf', or 'local_tm'. If all parameters are fixed (and no spins selected), None is returned.
@rtype: str or None
"""
# Test if sequence data is loaded.
if not exists_mol_res_spin_data():
raise RelaxNoSequenceError
# If there is a local tm, fail if not all residues have a local tm parameter.
local_tm = False
for spin in spin_loop():
# Skip deselected spins.
if not spin.select:
continue
# No params.
if not hasattr(spin, 'params') or not spin.params:
continue
# Local tm.
if not local_tm and 'local_tm' in spin.params:
local_tm = True
# Inconsistencies.
elif local_tm and not 'local_tm' in spin.params:
raise RelaxError(
"All spins must either have a local tm parameter or not.")
# Check if any model-free parameters are allowed to vary.
mf_all_fixed = True
mf_all_deselected = True
for spin in spin_loop():
# Skip deselected spins.
if not spin.select:
continue
# At least one spin is selected.
mf_all_deselected = False
# Test the fixed flag.
if not hasattr(spin, 'fixed'):
mf_all_fixed = False
break
if not spin.fixed:
mf_all_fixed = False
break
# No spins selected?!?
if mf_all_deselected:
# All parameters fixed!
if not hasattr(cdp, 'diff_tensor') or cdp.diff_tensor.fixed:
return None
return 'diff'
# Local tm.
if local_tm:
return 'local_tm'
# Test if the diffusion tensor data is loaded.
if not diffusion_tensor.diff_data_exists():
# Catch when the local tm value is set but not in the parameter list.
for spin in spin_loop():
if hasattr(
spin, 'local_tm'
) and spin.local_tm != None and not 'local_tm' in spin.params:
raise RelaxError(
"The local tm value is set but not located in the model parameter list."
)
# Normal error.
raise RelaxNoTensorError('diffusion')
# 'diff' model type.
if mf_all_fixed:
# All parameters fixed!
if cdp.diff_tensor.fixed:
return None
return 'diff'
# 'mf' model type.
if cdp.diff_tensor.fixed:
return 'mf'
# 'all' model type.
else:
return 'all'
def linear_constraints(num_params,
model_type=None,
spin=None,
spin_id=None,
scaling_matrix=None):
"""Set up the model-free linear constraint matrices A and b.
Standard notation
=================
The order parameter constraints are::
0 <= S2 <= 1
0 <= S2f <= 1
0 <= S2s <= 1
By substituting the formula S2 = S2f.S2s into the above inequalities, the additional two
inequalities can be derived::
S2 <= S2f
S2 <= S2s
Correlation time constraints are::
te >= 0
tf >= 0
ts >= 0
tf <= ts
te, tf, ts <= 2 * tm
Additional constraints used include::
Rex >= 0
0.9e-10 <= r <= 2e-10
-300e-6 <= CSA <= 0
Rearranged notation
===================
The above inequality constraints can be rearranged into::
S2 >= 0
-S2 >= -1
S2f >= 0
-S2f >= -1
S2s >= 0
-S2s >= -1
S2f - S2 >= 0
S2s - S2 >= 0
te >= 0
tf >= 0
ts >= 0
ts - tf >= 0
Rex >= 0
r >= 0.9e-10
-r >= -2e-10
CSA >= -300e-6
-CSA >= 0
Matrix notation
===============
In the notation A.x >= b, where A is an matrix of coefficients, x is an array of parameter
values, and b is a vector of scalars, these inequality constraints are::
| 1 0 0 0 0 0 0 0 0 | | 0 |
| | | |
|-1 0 0 0 0 0 0 0 0 | | -1 |
| | | |
| 0 1 0 0 0 0 0 0 0 | | 0 |
| | | |
| 0 -1 0 0 0 0 0 0 0 | | -1 |
| | | |
| 0 0 1 0 0 0 0 0 0 | | S2 | | 0 |
| | | | | |
| 0 0 -1 0 0 0 0 0 0 | | S2f | | -1 |
| | | | | |
|-1 1 0 0 0 0 0 0 0 | | S2s | | 0 |
| | | | | |
|-1 0 1 0 0 0 0 0 0 | | te | | 0 |
| | | | | |
| 0 0 0 1 0 0 0 0 0 | . | tf | >= | 0 |
| | | | | |
| 0 0 0 0 1 0 0 0 0 | | ts | | 0 |
| | | | | |
| 0 0 0 0 0 1 0 0 0 | | Rex | | 0 |
| | | | | |
| 0 0 0 0 -1 1 0 0 0 | | r | | 0 |
| | | | | |
| 0 0 0 0 0 0 1 0 0 | | CSA | | 0 |
| | | |
| 0 0 0 0 0 0 0 1 0 | | 0.9e-10 |
| | | |
| 0 0 0 0 0 0 0 -1 0 | | -2e-10 |
| | | |
| 0 0 0 0 0 0 0 0 1 | | -300e-6 |
| | | |
| 0 0 0 0 0 0 0 0 -1 | | 0 |
@param num_params: The number of parameters in the model.
@type num_params: int
@keyword model_type: The model type, one of 'all', 'diff', 'mf', or 'local_tm'.
@type model_type: str
@keyword spin: The spin data container. If this argument is supplied, then the
spin_id argument will be ignored.
@type spin: SpinContainer instance
@keyword spin_id: The spin identification string.
@type spin_id: str
@keyword scaling_matrix: The diagonal, square scaling matrix.
@type scaling_matrix: numpy diagonal matrix
"""
# Upper limit flag for correlation times.
upper_time_limit = 1
# Initialisation (0..j..m).
A = []
b = []
zero_array = zeros(num_params, float64)
i = 0
j = 0
# Diffusion tensor parameters.
if model_type != 'mf' and diffusion_tensor.diff_data_exists():
# Spherical diffusion.
if cdp.diff_tensor.type == 'sphere':
# 0 <= tm <= 200 ns.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-200.0 * 1e-9 / scaling_matrix[i, i])
i = i + 1
j = j + 2
# Spheroidal diffusion.
elif cdp.diff_tensor.type == 'spheroid':
# 0 <= tm <= 200 ns.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-200.0 * 1e-9 / scaling_matrix[i, i])
i = i + 1
j = j + 2
# Prolate diffusion, Da >= 0.
if cdp.diff_tensor.spheroid_type == 'prolate':
A.append(zero_array * 0.0)
A[j][i] = 1.0
b.append(0.0 / scaling_matrix[i, i])
i = i + 1
j = j + 1
# Add two to i for the theta and phi parameters.
i = i + 2
# Oblate diffusion, Da <= 0.
elif cdp.diff_tensor.spheroid_type == 'oblate':
A.append(zero_array * 0.0)
A[j][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
i = i + 1
j = j + 1
# Add two to i for the theta and phi parameters.
i = i + 2
else:
# Add three to i for the Da, theta and phi parameters.
i = i + 3
# Ellipsoidal diffusion.
elif cdp.diff_tensor.type == 'ellipsoid':
# 0 <= tm <= 200 ns.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-200.0 * 1e-9 / scaling_matrix[i, i])
i = i + 1
j = j + 2
# Da >= 0.
A.append(zero_array * 0.0)
A[j][i] = 1.0
b.append(0.0 / scaling_matrix[i, i])
i = i + 1
j = j + 1
# 0 <= Dr <= 1.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-1.0 / scaling_matrix[i, i])
i = i + 1
j = j + 2
# Add three to i for the alpha, beta, and gamma parameters.
i = i + 3
# Model-free parameters.
if model_type != 'diff':
# The loop.
if spin:
loop = [spin]
else:
loop = spin_loop(spin_id)
# Loop over the spins.
for spin in loop:
# Skip deselected spins.
if not spin.select:
continue
# Save current value of i.
old_i = i
# Loop over the model-free parameters.
for l in range(len(spin.params)):
# Local tm.
if spin.params[l] == 'local_tm':
if upper_time_limit:
# 0 <= tm <= 200 ns.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-200.0 * 1e-9 / scaling_matrix[i, i])
j = j + 2
else:
# 0 <= tm.
A.append(zero_array * 0.0)
A[j][i] = 1.0
b.append(0.0 / scaling_matrix[i, i])
j = j + 1
# Order parameters {S2, S2f, S2s}.
elif match('s2', spin.params[l]):
# 0 <= S2 <= 1.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-1.0 / scaling_matrix[i, i])
j = j + 2
# S2 <= S2f and S2 <= S2s.
if spin.params[l] == 's2':
for m in range(len(spin.params)):
if spin.params[m] == 's2f' or spin.params[
m] == 's2s':
A.append(zero_array * 0.0)
A[j][i] = -1.0
A[j][old_i + m] = 1.0
b.append(0.0)
j = j + 1
# Correlation times {te, tf, ts}.
elif match('t[efs]', spin.params[l]):
# te, tf, ts >= 0.
A.append(zero_array * 0.0)
A[j][i] = 1.0
b.append(0.0 / scaling_matrix[i, i])
j = j + 1
# tf <= ts.
if spin.params[l] == 'ts':
for m in range(len(spin.params)):
if spin.params[m] == 'tf':
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j][old_i + m] = -1.0
b.append(0.0)
j = j + 1
# te, tf, ts <= 2 * tm. (tf not needed because tf <= ts).
if upper_time_limit:
if not spin.params[l] == 'tf':
if model_type == 'mf':
A.append(zero_array * 0.0)
A[j][i] = -1.0
b.append(-2.0 * cdp.diff_tensor.tm /
scaling_matrix[i, i])
else:
A.append(zero_array * 0.0)
A[j][0] = 2.0
A[j][i] = -1.0
b.append(0.0)
j = j + 1
# Rex.
elif spin.params[l] == 'rex':
A.append(zero_array * 0.0)
A[j][i] = 1.0
b.append(0.0 / scaling_matrix[i, i])
j = j + 1
# Bond length.
elif spin.params[l] == 'r':
# 0.9e-10 <= r <= 2e-10.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.9e-10 / scaling_matrix[i, i])
b.append(-2e-10 / scaling_matrix[i, i])
j = j + 2
# CSA.
elif spin.params[l] == 'csa':
# -300e-6 <= CSA <= 0.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(-300e-6 / scaling_matrix[i, i])
b.append(0.0 / scaling_matrix[i, i])
j = j + 2
# Increment i.
i = i + 1
# Convert to numpy data structures.
A = array(A, int8)
b = array(b, float64)
return A, b
def linear_constraints(num_params, model_type=None, spin=None, spin_id=None, scaling_matrix=None):
"""Set up the model-free linear constraint matrices A and b.
Standard notation
=================
The order parameter constraints are::
0 <= S2 <= 1
0 <= S2f <= 1
0 <= S2s <= 1
By substituting the formula S2 = S2f.S2s into the above inequalities, the additional two
inequalities can be derived::
S2 <= S2f
S2 <= S2s
Correlation time constraints are::
te >= 0
tf >= 0
ts >= 0
tf <= ts
te, tf, ts <= 2 * tm
Additional constraints used include::
Rex >= 0
0.9e-10 <= r <= 2e-10
-300e-6 <= CSA <= 0
Rearranged notation
===================
The above inequality constraints can be rearranged into::
S2 >= 0
-S2 >= -1
S2f >= 0
-S2f >= -1
S2s >= 0
-S2s >= -1
S2f - S2 >= 0
S2s - S2 >= 0
te >= 0
tf >= 0
ts >= 0
ts - tf >= 0
Rex >= 0
r >= 0.9e-10
-r >= -2e-10
CSA >= -300e-6
-CSA >= 0
Matrix notation
===============
In the notation A.x >= b, where A is an matrix of coefficients, x is an array of parameter
values, and b is a vector of scalars, these inequality constraints are::
| 1 0 0 0 0 0 0 0 0 | | 0 |
| | | |
|-1 0 0 0 0 0 0 0 0 | | -1 |
| | | |
| 0 1 0 0 0 0 0 0 0 | | 0 |
| | | |
| 0 -1 0 0 0 0 0 0 0 | | -1 |
| | | |
| 0 0 1 0 0 0 0 0 0 | | S2 | | 0 |
| | | | | |
| 0 0 -1 0 0 0 0 0 0 | | S2f | | -1 |
| | | | | |
|-1 1 0 0 0 0 0 0 0 | | S2s | | 0 |
| | | | | |
|-1 0 1 0 0 0 0 0 0 | | te | | 0 |
| | | | | |
| 0 0 0 1 0 0 0 0 0 | . | tf | >= | 0 |
| | | | | |
| 0 0 0 0 1 0 0 0 0 | | ts | | 0 |
| | | | | |
| 0 0 0 0 0 1 0 0 0 | | Rex | | 0 |
| | | | | |
| 0 0 0 0 -1 1 0 0 0 | | r | | 0 |
| | | | | |
| 0 0 0 0 0 0 1 0 0 | | CSA | | 0 |
| | | |
| 0 0 0 0 0 0 0 1 0 | | 0.9e-10 |
| | | |
| 0 0 0 0 0 0 0 -1 0 | | -2e-10 |
| | | |
| 0 0 0 0 0 0 0 0 1 | | -300e-6 |
| | | |
| 0 0 0 0 0 0 0 0 -1 | | 0 |
@param num_params: The number of parameters in the model.
@type num_params: int
@keyword model_type: The model type, one of 'all', 'diff', 'mf', or 'local_tm'.
@type model_type: str
@keyword spin: The spin data container. If this argument is supplied, then the
spin_id argument will be ignored.
@type spin: SpinContainer instance
@keyword spin_id: The spin identification string.
@type spin_id: str
@keyword scaling_matrix: The diagonal, square scaling matrix.
@type scaling_matrix: numpy diagonal matrix
"""
# Upper limit flag for correlation times.
upper_time_limit = 1
# Initialisation (0..j..m).
A = []
b = []
zero_array = zeros(num_params, float64)
i = 0
j = 0
# Diffusion tensor parameters.
if model_type != "mf" and diffusion_tensor.diff_data_exists():
# Spherical diffusion.
if cdp.diff_tensor.type == "sphere":
# 0 <= tm <= 200 ns.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-200.0 * 1e-9 / scaling_matrix[i, i])
i = i + 1
j = j + 2
# Spheroidal diffusion.
elif cdp.diff_tensor.type == "spheroid":
# 0 <= tm <= 200 ns.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-200.0 * 1e-9 / scaling_matrix[i, i])
i = i + 1
j = j + 2
# Prolate diffusion, Da >= 0.
if cdp.diff_tensor.spheroid_type == "prolate":
A.append(zero_array * 0.0)
A[j][i] = 1.0
b.append(0.0 / scaling_matrix[i, i])
i = i + 1
j = j + 1
# Add two to i for the theta and phi parameters.
i = i + 2
# Oblate diffusion, Da <= 0.
elif cdp.diff_tensor.spheroid_type == "oblate":
A.append(zero_array * 0.0)
A[j][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
i = i + 1
j = j + 1
# Add two to i for the theta and phi parameters.
i = i + 2
else:
# Add three to i for the Da, theta and phi parameters.
i = i + 3
# Ellipsoidal diffusion.
elif cdp.diff_tensor.type == "ellipsoid":
# 0 <= tm <= 200 ns.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-200.0 * 1e-9 / scaling_matrix[i, i])
i = i + 1
j = j + 2
# Da >= 0.
A.append(zero_array * 0.0)
A[j][i] = 1.0
b.append(0.0 / scaling_matrix[i, i])
i = i + 1
j = j + 1
# 0 <= Dr <= 1.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-1.0 / scaling_matrix[i, i])
i = i + 1
j = j + 2
# Add three to i for the alpha, beta, and gamma parameters.
i = i + 3
# Model-free parameters.
if model_type != "diff":
# The loop.
if spin:
loop = [spin]
else:
loop = spin_loop(spin_id)
# Loop over the spins.
for spin in loop:
# Skip deselected spins.
if not spin.select:
continue
# Save current value of i.
old_i = i
# Loop over the model-free parameters.
for l in range(len(spin.params)):
# Local tm.
if spin.params[l] == "local_tm":
if upper_time_limit:
# 0 <= tm <= 200 ns.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-200.0 * 1e-9 / scaling_matrix[i, i])
j = j + 2
else:
# 0 <= tm.
A.append(zero_array * 0.0)
A[j][i] = 1.0
b.append(0.0 / scaling_matrix[i, i])
j = j + 1
# Order parameters {S2, S2f, S2s}.
elif match("s2", spin.params[l]):
# 0 <= S2 <= 1.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.0 / scaling_matrix[i, i])
b.append(-1.0 / scaling_matrix[i, i])
j = j + 2
# S2 <= S2f and S2 <= S2s.
if spin.params[l] == "s2":
for m in range(len(spin.params)):
if spin.params[m] == "s2f" or spin.params[m] == "s2s":
A.append(zero_array * 0.0)
A[j][i] = -1.0
A[j][old_i + m] = 1.0
b.append(0.0)
j = j + 1
# Correlation times {te, tf, ts}.
elif match("t[efs]", spin.params[l]):
# te, tf, ts >= 0.
A.append(zero_array * 0.0)
A[j][i] = 1.0
b.append(0.0 / scaling_matrix[i, i])
j = j + 1
# tf <= ts.
if spin.params[l] == "ts":
for m in range(len(spin.params)):
if spin.params[m] == "tf":
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j][old_i + m] = -1.0
b.append(0.0)
j = j + 1
# te, tf, ts <= 2 * tm. (tf not needed because tf <= ts).
if upper_time_limit:
if not spin.params[l] == "tf":
if model_type == "mf":
A.append(zero_array * 0.0)
A[j][i] = -1.0
b.append(-2.0 * cdp.diff_tensor.tm / scaling_matrix[i, i])
else:
A.append(zero_array * 0.0)
A[j][0] = 2.0
A[j][i] = -1.0
b.append(0.0)
j = j + 1
# Rex.
elif spin.params[l] == "rex":
A.append(zero_array * 0.0)
A[j][i] = 1.0
b.append(0.0 / scaling_matrix[i, i])
j = j + 1
# Bond length.
elif spin.params[l] == "r":
# 0.9e-10 <= r <= 2e-10.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(0.9e-10 / scaling_matrix[i, i])
b.append(-2e-10 / scaling_matrix[i, i])
j = j + 2
# CSA.
elif spin.params[l] == "csa":
# -300e-6 <= CSA <= 0.
A.append(zero_array * 0.0)
A.append(zero_array * 0.0)
A[j][i] = 1.0
A[j + 1][i] = -1.0
b.append(-300e-6 / scaling_matrix[i, i])
b.append(0.0 / scaling_matrix[i, i])
j = j + 2
# Increment i.
i = i + 1
# Convert to numpy data structures.
A = array(A, int8)
b = array(b, float64)
return A, b
