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bugfix for R_sq output to ensure it is always an array #13

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jnschmid merged 1 commit into from
Jan 5, 2026
Merged

bugfix for R_sq output to ensure it is always an array #13

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88 changes: 44 additions & 44 deletions uqpce/pce/stats/statistics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -23,9 +23,9 @@ def calc_R_sq(var_basis, matrix_coeffs, responses):
Inputs: var_basis- evaluated variable basis
matrix_coeffs- matrix coefficients
responses- vector of responses

Calculates the R squared statistic for the given system.

Design and Analysis of Experiments (8th) by Douglas Montgomery (pg. 464)
"""
thresh = 1e-8
Expand All @@ -39,14 +39,14 @@ def calc_R_sq(var_basis, matrix_coeffs, responses):

R_sq = 1 - (err_sum_sq / tot_sum_sq) # equation for R^2

if R_sq > 1:
if R_sq > 1 + thresh:
if (R_sq > 1).any():
if (R_sq > 1 + thresh).any():
warn(
f'R squared value was {R_sq}. Check the variable basis and '
'responses.'
)

R_sq = 1.0
R_sq[(R_sq > 1.0) and (R_sq > 1 + thresh)] = 1.0

return R_sq

Expand All @@ -56,9 +56,9 @@ def calc_R_sq_adj(var_basis, matrix_coeffs, responses):
Inputs: var_basis- evaluated variable basis
matrix_coeffs- matrix coefficients
responses- vector of responses

Calculates the adjusted R squared statistic for the given system.

Design and Analysis of Experiments (8th) by Douglas Montgomery (pg. 464)
"""
act_model_size, min_model_size = var_basis.shape
Expand All @@ -78,7 +78,7 @@ def calc_PRESS_res(var_basis, responses):
"""
Inputs: var_basis- evaluated variable basis
responses- the responses

Calculate the PRESS residual for a given model.
"""
resp_count = len(responses)
Expand Down Expand Up @@ -124,11 +124,11 @@ def calc_pred_conf_int(var_basis, matrix_coeffs, responses, signif, var_basis_ve
matrix_coeffs- the matrix coefficients
responses- the responses
signif- significance of the model (i.e. 95% conf int has signif=0.05)
var_basis_ver- the variable basis whose mean confidence interval
var_basis_ver- the variable basis whose mean confidence interval
will be evaluated against the model variable basis

Calcualtes the prediction confidence interval for a given point.

Design and Analysis of Experiments (8th) by Douglas Montgomery (pg. 469)
"""
const = 1
Expand Down Expand Up @@ -163,11 +163,11 @@ def calc_mean_conf_int(var_basis, matrix_coeffs, responses, signif, var_basis_ve
matrix_coeffs- the matrix coefficients
responses- the responses
signif- significance of the model (i.e. 95% conf int has signif=0.05)
var_basis_ver- the variable basis whose mean confidence interval
var_basis_ver- the variable basis whose mean confidence interval
will be evaluated against the model variable basis

Calculates the confidence interval on the mean response.

Design and Analysis of Experiments (8th) by Douglas Montgomery (pg. 468)
"""
var_basis_ver = np.atleast_2d(var_basis_ver)
Expand Down Expand Up @@ -234,7 +234,7 @@ def calc_coeff_conf_int(var_basis, matrix_coeffs, responses, signif):
matrix_coeffs- the matrix coefficients
responses- the responses
signif- significance of the model (i.e. 95% conf int has signif=0.05)

Design and Analysis of Experiments (8th) by Douglas Montgomery (pg. 467)
"""
resp_count, term_count = var_basis.shape
Expand Down Expand Up @@ -262,13 +262,13 @@ def calc_var_conf_int(matrix_coeffs, coeff_uncert, norm_sq):
Inputs: matrix_coeffs- an array of the matrix coefficients
coeff_uncert- the uncertainty of each coefficient
norm_sq- the norm squared of the model
Calculates the bounds on the variance from the calculated bounds on the
matrix coefficients. This equation was created by replacing the matrix
coefficients in the variance equation with the lower and upper bounds on the

Calculates the bounds on the variance from the calculated bounds on the
matrix coefficients. This equation was created by replacing the matrix
coefficients in the variance equation with the lower and upper bounds on the
matrix coefficients.
Equation derived from method of calculating variance and the matrix

Equation derived from method of calculating variance and the matrix
coefficient uncertainties.
"""
coeff_mag = np.abs(matrix_coeffs).reshape(-1,)
Expand Down Expand Up @@ -317,10 +317,10 @@ def get_sobol_bounds(matrix_coeffs, sobols, coeff_uncert, norm_sq):
sobols- sobol sensitivities
coeff_uncert- uncertainties of the coefficients
norm_sq- the norm squared

Calculates the bounds on the sobols from the coefficient uncertainty.
Equation derived from method of calculating sobols and the matrix

Equation derived from method of calculating sobols and the matrix
coefficient uncertainties.
"""
threshold = 1e-4 # sobol significance level
Expand Down Expand Up @@ -419,9 +419,9 @@ def calc_error_variance(var_basis, matrix_coeffs, responses):
Inputs: var_basis- evaluated variable basis
matrix_coeffs- the matrix coefficients
responses- the responses

Calculates the unbiased estimator of the error variance.

Design and Analysis of Experiments (8th) by Douglas Montgomery (pg. 453)
"""
# sigma squared eq (Design and Analysis of Experiments, pg 453)
Expand Down Expand Up @@ -459,9 +459,9 @@ def calc_error_sum_of_sq(var_basis, matrix_coeffs, responses):
Inputs: var_basis- the variable basis
matrix_coeffs- the matrix coefficients
responses- the responses

Calculates the error sum of squares.

Design and Analysis of Experiments (8th) by Douglas Montgomery (pg. 453)
"""
resp_mat = np.matmul(responses.T, responses)
Expand All @@ -473,10 +473,10 @@ def calc_error_sum_of_sq(var_basis, matrix_coeffs, responses):
def calc_total_sum_of_sq(var_basis, responses):
"""
Inputs: var_basis- the variable basis
responses- the responses
responses- the responses

Calculates the total sum of squares.

Design and Analysis of Experiments (8th) by Douglas Montgomery (pg. 463)
"""
act_model_size = var_basis.shape[0]
Expand All @@ -490,9 +490,9 @@ def calc_sum_sq_regr(matrix_coeffs, responses, var_basis):
Inputs: matrix_coeffs- the matrix coefficients
responses- the responses
var_basis- the variable basis

Calculates the regression sum of squares.

Design and Analysis of Experiments (8th) by Douglas Montgomery (pg. 463)
"""
resp_cnt = len(responses)
Expand All @@ -508,12 +508,12 @@ def calc_sum_sq_regr(matrix_coeffs, responses, var_basis):
def calc_mean_sq_err(responses, matrix_coeffs, var_basis):
"""
Inputs: responses- the actual responses from the analysis tool
matrix_coeffs - the coefficients for the terms from the
matrix_coeffs - the coefficients for the terms from the
MatrixSystem
var_basis- the varible basis with values plugged in

Calculates the mean squared error for the given matrices.

Equation from original UQPCE version.
"""
mean_sq_err_thresh = 1e-15
Expand Down Expand Up @@ -555,17 +555,17 @@ def calc_mean_sq_err(responses, matrix_coeffs, var_basis):

def calc_partial_F(regr_sum_sq_all, regr_sum_sq, mean_sq_err_all, deg_free):
"""
Inputs: regr_sum_sq_all- the regression sum of squares value for the model
Inputs: regr_sum_sq_all- the regression sum of squares value for the model
with the larger number of terms
regr_sum_sq- the regression sum of squares value for the model
regr_sum_sq- the regression sum of squares value for the model
with the smaller number of terms
mean_sq_err_all- the mean squared error for the model with the
mean_sq_err_all- the mean squared error for the model with the
larger number of terms
deg_free- the number of degrees of freedom

Calculates the partial F statistic used in stepwise regression.
"Applied Statistics and Probablity for Engineers" (4th) by Douglas

"Applied Statistics and Probablity for Engineers" (4th) by Douglas
Montgomery (pg. 486)
"""
partial_F = ((regr_sum_sq_all - regr_sum_sq) / deg_free) / mean_sq_err_all
Expand Down Expand Up @@ -608,7 +608,7 @@ def calc_term_count(order, var_count):
"""
Inputs: order- the order of the model
var_count- the number of variables in the model

Calculates the number of terms in a model.
"""
term_count = int(
Expand All @@ -623,7 +623,7 @@ def calc_min_responses(order, var_count):
"""
Inputs: order- the order of the model
var_count- the number of variables in the model

Calculates the minimum responses required for a model.
"""
return calc_term_count(order, var_count) + 1