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

svd.sm (59,92 KiB) descargado 1438 vez(es).
svd.pdf (142,85 KiB) descargado 927 vez(es).

Best regards.
Alvaro.

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

svd_nr.pdf (122,43 KiB) descargado 815 vez(es).
svd_nr.sm (95,26 KiB) descargado 1373 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 1452 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 1369 vez(es).
pinv.pdf (168,98 KiB) descargado 879 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 844 vez(es).

Best regards.
Alvaro.