TESTING/EIG/dsvdct.f(3)

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💖 NAME 💖

Bestie, welcome to TESTING/EIG/dsvdct.f(3) — it's a Library Functions Manual page, and the name on the cover is literally TESTING/EIG/dsvdct.f. ✨

✨ SYNOPSIS ✨

🛠️ Functions/Subroutines 🛠️

subroutine dsvdct (n, s, e, shift, num)
    DSVDCT

🎀 Function/Subroutine Documentation 🎀

The full signature is:

subroutine dsvdct (integer n, double precision, dimension( * ) s, double precision, dimension( * ) e, double precision shift, integer num)

and the routine's whole name is DSVDCT. 💅

🌸 Purpose 🌸

Okay so DSVDCT counts the number NUM of eigenvalues of a 2*N by 2*N tridiagonal matrix T which are less than or equal to SHIFT. T is formed by putting zeros on the diagonal and making the off-diagonals equal to S(1), E(1), S(2), E(2), ... , E(N-1), S(N). If SHIFT is positive, NUM is equal to N plus the number of singular values of a bidiagonal matrix B less than or equal to SHIFT. Here B has diagonal entries S(1), ..., S(N) and superdiagonal entries E(1), ... E(N-1). If SHIFT is negative, NUM is equal to the number of singular values of B greater than or equal to -SHIFT.

See W. Kahan , Report CS41, Computer Science Dept., Stanford University, July 21, 1966.

🦋 Parameters 🦋

  • N — N is INTEGER; this is the dimension of the bidiagonal matrix B. 💖
  • S — S is DOUBLE PRECISION array, dimension (N); these are the diagonal entries of the bidiagonal matrix B. ✨
  • E — E is DOUBLE PRECISION array of dimension (N-1); these are the superdiagonal entries of the bidiagonal matrix B. 🦋
  • SHIFT — SHIFT is DOUBLE PRECISION; the shift, used as described under Purpose. 🎀
  • NUM — NUM is INTEGER; the number of eigenvalues of T less than or equal to SHIFT. 👑

👑 Author 👑

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 86 of file dsvdct.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

Cute sign-off, bestie: the footer vibes are LAPACK, Version 3.12.0, and TESTING/EIG/dsvdct.f(3) — no separate date line is listed there, so we're not making one up. 💅🫶

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