Hi. Very short code. Singular Value Decomposition using QR decomposition.

svd.sm (59.92 KiB) downloaded 1246 time(s).
svd.pdf (142.85 KiB) downloaded 780 time(s).

Best regards.
Alvaro.

Singular Value Decomposition based on Numerical Recipes book. Faster and robust.

svd_nr.pdf (122.43 KiB) downloaded 682 time(s).
svd_nr.sm (95.26 KiB) downloaded 1192 time(s).

Best regards.
Alvaro.

Wrote

Singular Value Decomposition based on Numerical Recipes book. Faster and robust.

Thanks Alvaro ... OK all red SS 6179
I have no applications for the rectangular matrix.
Ultimately, all that stuff aims at solving singular square matrix,
2 examples Chemical Balance all done well.
Smath SVD can be used as well to sanity Greville.
Both documents take no time calculation.

Maths Pseudo Greville.sm (87.79 KiB) downloaded 1233 time(s).
Maths SVD.sm (228.82 KiB) downloaded 1262 time(s).

Wrote

Singular Value Decomposition based on Numerical Recipes book. Faster and robust.

Complete sanity vs Smath built-in SVD ... hyper fast.
Thanks Alvaro for sharing your great programming skill.

Maths svd.nr.sm (94.98 KiB) downloaded 1276 time(s).

Pseudo inverse, but not based in the previous SVD.

pinv.sm (91.35 KiB) downloaded 1182 time(s).
pinv.pdf (168.98 KiB) downloaded 665 time(s).

Best regards.
Alvaro.

Pseudo inverse, based in the previous (improved) SVD.

pinv_svd.sm (161.03 KiB) downloaded 1214 time(s).
pinv_svd.pdf (153.64 KiB) downloaded 706 time(s).

Best regards.
Alvaro.