Algorithm 358: singular value decomposition of a complex matrix [F1, 4, 5]

✍ Scribed by Businger, Peter A.; Golub, Gene H.

• Book ID: 118027647
• Publisher: Association for Computing Machinery
• Year: 1969
• Tongue: English
• Weight: 656 KB
• Volume: 12
• Category: Article
• ISSN: 0001-0782
• DOI: 10.1145/363235.363249

✦ Synopsis

Ising generates n-sequences ($1, "", S,) of zeros and ones where x = ~i~ S~ and t = ~,-~1 I S~+I -S~ I are given. The main idea is to interleave compositions of x and n --x objects and resort to a lexicographic generation of compositions. We call these sequences Ising configurations since we believe they first appeared in the study of the so-called Ising problem (See Hill [1], Ising [2]). The number R(n, x, t) of distinct configurations with fixed n, x, t is well known [1, 2]:

Now define a block of l's (or zeros) in the sequence as a set of a maximum number of consecutive l's (or zeros) eventually consisting of a single element. For given n, x, t, the number p of blocks of l's may easily be deduced from t, as well as the number q of blocks of zeros. In fact, a block of l's