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

svd.sm (59,92 KiB) descargado 1439 vez(es).
svd.pdf (142,85 KiB) descargado 928 vez(es).

Best regards.
Alvaro.

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

svd_nr.pdf (122,43 KiB) descargado 816 vez(es).
svd_nr.sm (95,26 KiB) descargado 1374 vez(es).

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) descargado 1414 vez(es).
Maths SVD.sm (228,82 KiB) descargado 1453 vez(es).

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) descargado 1466 vez(es).

Pseudo inverse, but not based in the previous SVD.

pinv.sm (91,35 KiB) descargado 1370 vez(es).
pinv.pdf (168,98 KiB) descargado 880 vez(es).

Best regards.
Alvaro.

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

pinv_svd.sm (161,03 KiB) descargado 1407 vez(es).
pinv_svd.pdf (153,64 KiB) descargado 845 vez(es).

Best regards.
Alvaro.