Wed Oct  8 08:24:59 2025

llsq_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test llsq().

llsq_test01():
  llsq() computes the formula for a line of the form
    y = A * x + B
  which minimizes the RMS error to a set of N data values.

  Estimated relationship is y = 62.148 * x + -40.5076
  Expected value is         y = 61.272 * x - 39.062

     I      X       Y        B+A*X      |error|

     0  1.470000  52.210000  50.849933  -1.360067
     1  1.500000  54.120000  52.714372  -1.405628
     2  1.520000  54.480000  53.957332  -0.522668
     3  1.550000  55.840000  55.821771  -0.018229
     4  1.570000  56.200000  57.064730  0.864730
     5  1.600000  56.570000  58.929169  2.359169
     6  1.630000  59.930000  60.793609  0.863609
     7  1.650000  61.290000  62.036568  0.746568
     8  1.680000  63.110000  63.901007  0.791007
     9  1.700000  66.470000  65.143967  -1.326033
    10  1.730000  66.280000  67.008406  0.728406
    11  1.750000  67.100000  68.251365  1.151365
    12  1.780000  70.920000  70.115804  -0.804196
    13  1.800000  72.190000  71.358764  -0.831236
    14  1.830000  74.460000  73.223203  -1.236797

  RMS error =                           1.12022
  Graphics saved as "llsq_data.png"
  Graphics saved as "llsq_approx.png"

  Repeat calculation, using np.linalg.lstsq():
  Estimated relationship is y = 62.148 * x + -40.5076

llsq_test02():
  llsq0() computes the formula for a line of the form
    y = A * x 
  which minimizes the RMS error to a set of N data values.

  Estimated relationship is y = 0.641657 * x

     I      X       Y          A*X      |error|

     0  0.000000  0.000000  0.000000  0.000000
     1  0.100000  0.086500  0.064166  -0.022334
     2  0.150000  0.101500  0.096249  -0.005251
     3  0.200000  0.110600  0.128331  0.017731
     4  0.250000  0.127900  0.160414  0.032514
     5  0.300000  0.189200  0.192497  0.003297
     6  0.350000  0.269500  0.224580  -0.044920
     7  0.400000  0.288800  0.256663  -0.032137
     8  0.450000  0.242500  0.288746  0.046246
     9  0.500000  0.346500  0.320828  -0.025672
    10  0.550000  0.322500  0.352911  0.030411
    11  0.600000  0.376400  0.384994  0.008594
    12  0.650000  0.426300  0.417077  -0.009223
    13  0.700000  0.456200  0.449160  -0.007040

  RMS error =                           0.0251999
  Graphics saved as "llsq_test02.png"

llsq_test()
  Normal end of execution.
Wed Oct  8 08:25:00 2025