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

svd.sm (59,92 KiB) scaricato 1443 volta(e).
svd.pdf (142,85 KiB) scaricato 938 volta(e).

Best regards.
Alvaro.

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

svd_nr.pdf (122,43 KiB) scaricato 819 volta(e).
svd_nr.sm (95,26 KiB) scaricato 1381 volta(e).

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) scaricato 1419 volta(e).
Maths SVD.sm (228,82 KiB) scaricato 1458 volta(e).

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) scaricato 1474 volta(e).

Pseudo inverse, but not based in the previous SVD.

pinv.sm (91,35 KiB) scaricato 1373 volta(e).
pinv.pdf (168,98 KiB) scaricato 885 volta(e).

Best regards.
Alvaro.

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

pinv_svd.sm (161,03 KiB) scaricato 1414 volta(e).
pinv_svd.pdf (153,64 KiB) scaricato 850 volta(e).

Best regards.
Alvaro.