ZBDT05(3)

💅 ZBDT05(3) — Library Functions Manual energy ✨

Okay bestie, this page is from the Library Functions Manual, and it's all about ZBDT05(3). Buckle up.

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🎀 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zbdt05.f — that's the file, no cap.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

subroutine ZBDT05 (m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)
           ZBDT05

🌸 Function/Subroutine Documentation 🌸

subroutine ZBDT05 (integer m, integer n, complex*16, dimension( lda, * ) a,
       integer lda, double precision, dimension( * ) s, integer ns, complex*16,
       dimension( * ) u, integer ldu, complex*16, dimension( ldvt, * ) vt,
       integer ldvt, complex*16, dimension( * ) work, double precision resid)
       ZBDT05

🦋 Purpose

Okay so ZBDT05 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. Slay.

💖 Parameters

• M — M is INTEGER; the number of rows of the matrices A and U.
• N — N is INTEGER; the number of columns of the matrices A and VT.
• A — A is COMPLEX*16 array, dimension (LDA,N); the m by n matrix A.
• LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M).
• S — S is DOUBLE PRECISION array, dimension (NS); the singular values from the (partial) SVD of B, sorted in decreasing order.
• NS — NS is INTEGER; the number of singular values/vectors from the (partial) SVD of B.
• U — U is COMPLEX*16 array, dimension (LDU,NS); the n by ns orthogonal matrix U in S = U' * B * V.
• LDU — LDU is INTEGER; the leading dimension of the array U. LDU >= max(1,N).
• VT — VT is COMPLEX*16 array, dimension (LDVT,N); the n by ns orthogonal matrix V in S = U' * B * V.
• LDVT — LDVT is INTEGER; the leading dimension of the array VT.
• WORK — WORK is COMPLEX*16 array, dimension (M,N).
• RESID — RESID is DOUBLE PRECISION; 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 123 of file zbdt05.f.

🦋 Author (generated edition)

Generated automatically by Doxygen for LAPACK from the source code.

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⭐ Source/version sign-off: LAPACK, Version 3.12.0, with the page path /home/abui...IG/zbdt05.f(3). There's no date in this footer, so we're not inventing one — keeping it 100, bestie. 💜