TESTING/EIG/dsvdch.f(3)

🌸 NAME

TESTING/EIG/dsvdch.f — bestie, this is the Library Functions Manual page for TESTING/EIG/dsvdch.f(3), and it’s all about the DSVDCH routine. Slay ✨

🦋 SYNOPSIS

✨ Functions/Subroutines

• subroutine dsvdch (n, s, e, svd, tol, info) — DSVDCH

💅 Function/Subroutine Documentation

🎀 subroutine dsvdch

subroutine dsvdch (integer n, double precision, dimension( * ) s, double precision, dimension( * ) e, double precision, dimension( * ) svd, double precision tol, integer info)

DSVDCH

🌟 Purpose

okay so DSVDCH checks to see if SVD(1) ,..., SVD(N) are accurate singular values of the bidiagonal matrix B with diagonal entries S(1) ,..., S(N) and superdiagonal entries E(1) ,..., E(N-1)). It does this by expanding each SVD(I) into an interval [SVD(I) * (1-EPS) , SVD(I) * (1+EPS)], merging overlapping intervals if any, and using Sturm sequences to count and verify whether each resulting interval has the correct number of singular values (using DSVDCT). Here EPS=TOL*MAX(N/10,1)*MAZHEP, where MACHEP is the machine precision. The routine assumes the singular values are sorted with SVD(1) the largest and SVD(N) smallest. If each interval contains the correct number of singular values, INFO = 0 is returned, otherwise INFO is the index of the first singular value in the first bad interval.

💜 Parameters

• N — N is INTEGER; the dimension of the bidiagonal matrix B.
• S — S is DOUBLE PRECISION array, dimension (N); the diagonal entries of the bidiagonal matrix B.
• E — E is DOUBLE PRECISION array, dimension (N-1); the superdiagonal entries of the bidiagonal matrix B.
• SVD — SVD is DOUBLE PRECISION array, dimension (N); the computed singular values to be checked.
• TOL — TOL is DOUBLE PRECISION; error tolerance for checking, a multiplier of the machine precision.
• INFO — INFO is INTEGER
  • =0 if the singular values are all correct (to within 1 +- TOL*MAZHEPS)
  • >0 if the interval containing the INFO-th singular value contains the incorrect number of singular values.

🫶 Author

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

Definition at line 96 of file dsvdch.f.

🧚 Author

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