TESTING/EIG/sbdt05.f(3)

📦
version 3.12.1 · 2 versions
, in arch rolling

🌸 NAME 🌸

okay so this is the page for TESTING/EIG/sbdt05.f, bestie — it lives in the Library Functions Manual and it’s all about the LAPACK test routine sbdt05 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine sbdt05 (m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)

and that’s the whole synopsis, no cap ✨

💅 Function/Subroutine Documentation 💅

the actual documented signature is:

subroutine sbdt05 (integer m, integer n, real, dimension( lda, * ) a,
     integer lda, real, dimension( * ) s, integer ns, real, dimension( ldu, *
     ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real,
     dimension( * ) work, real resid)

SBDT05 — yes bestie, that’s the name on the label 💖

🎯 Purpose 🎯

okay so SBDT05 reconstructs a bidiagonal matrix B from its (partial) SVD:

S = U' * B * V

where U and V are orthogonal matrices and S is diagonal.

the test ratio to test the singular value decomposition is:

RESID = norm( S - U' * B * V ) / ( n * norm(B) * EPS )

where VT = V' and EPS is the machine precision. that’s the whole purpose, periodt 💖

🧾 Parameters 🧾

  • M — INTEGER. the number of rows of the matrices A and U.
  • N — INTEGER. the number of columns of the matrices A and VT.
  • A — REAL array, dimension (LDA,N). the m by n matrix A.
  • LDA — INTEGER. the leading dimension of the array A. constraint: LDA >= max(1,M).
  • S — REAL array, dimension (NS). the singular values from the (partial) SVD of B, sorted in decreasing order.
  • NS — INTEGER. the number of singular values/vectors from the (partial) SVD of B.
  • U — REAL array, dimension (LDU,NS). the n by ns orthogonal matrix U in S = U' * B * V.
  • LDU — INTEGER. the leading dimension of the array U. constraint: LDU >= max(1,N).
  • VT — REAL array, dimension (LDVT,N). the n by ns orthogonal matrix V in S = U' * B * V.
  • LDVT — INTEGER. the leading dimension of the array VT.
  • WORK — REAL array, dimension (M,N).
  • RESID — REAL. the test ratio: norm(S - U' * A * V) / ( n * norm(A) * EPS ).

👑 Author 👑

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

Definition at line 125 of file sbdt05.f.

🪄 Author (the auto-generated one) 🪄

Generated automatically by Doxygen for LAPACK from the source code.

🌈 that’s a wrap, bestie — this is TESTING/EIG/sbdt05.f(3) from LAPACK Version 3.12.0. bye! 💖

📦 where this page comes from