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Use the shear model's eigenvectors in the multi-channel FDD example - #75
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The closed-form shapes used stories + 1 as the denominator; for a uniform fixed-base shear building it is stories + 0.5, so the second and third shapes had MAC 0.865 and 0.591 against the model. The example now takes the shapes from the stiffness and mass matrices and runs identify_fdd on the CSV round trip data.
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The closed-form mode shapes in examples/multichannel_fdd.py used stories + 1 = 4 as the denominator. For a uniform fixed-base shear building the shapes are sin((2k - 1) * pi * j / (2n + 1)), so the second and third shapes had MAC 0.865 and 0.591 against the eigenvectors of the model. The printed MAC 1.000 did not show this because the channels were synthesized from the same shapes.
The example now computes the shapes from the stiffness and mass matrices with numpy.linalg.eigh and scales each to a largest component of +1. identify_fdd runs on the data reloaded from the CSV, so the round trip is part of the check. All three modes are identified with MAC 1.000 against the model shapes.
python -m pytest passes (359 passed, 1 skipped); ruff check, ruff format --check and mypy pass.