+
+ REDUCEDMODELINGTEST
+ ===================
+
+ This test allows to analyze the characteristics of the collection of
+ states from a reduction point of view. Using an SVD, it measures how
+ the information decreases with the number of singular values, either
+ as values or, with a statistical point of view, as remaining variance.
+
+===> Information before launching:
+ -----------------------------
+
+ Characteristics of input data:
+ State dimension................: 100
+ Number of snapshots to test....: 30
+
+===> Summary of the 5 first singular values:
+ ---------------------------------------
+
+ Singular values σ:
+ σ[1] = 1.03513e+01
+ σ[2] = 1.03509e+01
+ σ[3] = 1.03258e+01
+ σ[4] = 1.02436e+01
+ σ[5] = 1.02386e+01
+
+ Singular values σ divided by the first one σ[1]:
+ σ[1] / σ[1] = 1.00000e+00
+ σ[2] / σ[1] = 9.99962e-01
+ σ[3] / σ[1] = 9.97533e-01
+ σ[4] / σ[1] = 9.89589e-01
+ σ[5] / σ[1] = 9.89104e-01
+
+===> Ordered singular values and remaining variance:
+ -----------------------------------------------
+
+ -------------------------------------------------------------------------
+ i | Singular value σ | σ[i]/σ[1] | Variance: part, remaining
+ -------------------------------------------------------------------------
+ 00 | 1.03513e+01 | 1.00000e+00 | 7% , 92.8%
+ 01 | 1.03509e+01 | 9.99962e-01 | 7% , 85.6%
+ 02 | 1.03258e+01 | 9.97533e-01 | 7% , 78.5%
+ 03 | 1.02436e+01 | 9.89589e-01 | 7% , 71.5%
+ 04 | 1.02386e+01 | 9.89104e-01 | 7% , 64.4%
+ 05 | 1.01050e+01 | 9.76200e-01 | 6% , 57.6%
+ 06 | 9.99948e+00 | 9.66009e-01 | 6% , 50.9%
+ 07 | 9.99643e+00 | 9.65714e-01 | 6% , 44.2%
+ 08 | 9.98375e+00 | 9.64489e-01 | 6% , 37.5%
+ 09 | 9.90828e+00 | 9.57198e-01 | 6% , 31.0%
+ 10 | 9.90691e+00 | 9.57066e-01 | 6% , 24.4%
+ 11 | 9.64803e+00 | 9.32056e-01 | 6% , 18.1%
+ 12 | 9.62587e+00 | 9.29916e-01 | 6% , 11.9%
+ 13 | 9.62344e+00 | 9.29681e-01 | 6% , 5.7%
+ 14 | 9.25446e+00 | 8.94035e-01 | 5% , 0.0%
+ 15 | 2.41400e-15 | 2.33206e-16 | 0% , 0.0%
+ 16 | 1.94612e-15 | 1.88006e-16 | 0% , 0.0%
+ 17 | 1.61527e-15 | 1.56044e-16 | 0% , 0.0%
+ 18 | 1.54864e-15 | 1.49608e-16 | 0% , 0.0%
+ 19 | 1.35243e-15 | 1.30653e-16 | 0% , 0.0%
+ 20 | 1.11119e-15 | 1.07347e-16 | 0% , 0.0%
+ 21 | 1.05852e-15 | 1.02260e-16 | 0% , 0.0%
+ 22 | 9.68764e-16 | 9.35883e-17 | 0% , 0.0%
+ 23 | 8.82878e-16 | 8.52912e-17 | 0% , 0.0%
+ 24 | 6.53296e-16 | 6.31122e-17 | 0% , 0.0%
+ 25 | 5.21872e-16 | 5.04159e-17 | 0% , 0.0%
+ 26 | 4.98146e-16 | 4.81238e-17 | 0% , 0.0%
+ 27 | 3.74898e-16 | 3.62173e-17 | 0% , 0.0%
+ 28 | 2.79953e-16 | 2.70452e-17 | 0% , 0.0%
+ 29 | 1.99083e-16 | 1.92326e-17 | 0% , 0.0%
+ -------------------------------------------------------------------------
+
+===> Summary of variance cut-off:
+ ----------------------------
+ Representing more than 90% of variance requires at least 14 mode(s).
+ Representing more than 99% of variance requires at least 15 mode(s).
+ Representing more than 99.9% of variance requires at least 15 mode(s).
+ Representing more than 99.99% of variance requires at least 15 mode(s).
+
+ Plot and save results in a file named "simple_ReducedModelingTest1.png"
+
+ ---------------------------------------------------------------------------
+
+ End of the "REDUCEDMODELINGTEST" verification
+
+ ---------------------------------------------------------------------------
+