SBDT05(3)

🎀 SBDT05(3) — Library Functions Manual 🎀

🌸 NAME 🌸

Okay bestie, this page is about this file, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/sbdt05.f

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✨ SYNOPSIS ✨

💫 Functions/Subroutines 💫

Here's the synopsis, literally:

subroutine SBDT05 (m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)
    SBDT05

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🦋 Function/Subroutine Documentation 🦋

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

💡 Purpose 💡

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. Slay.

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. Periodt.

🎀 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (M,N).
• RESID — RESID is 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.

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🌈 Author 🌈

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xoxo, this iconic page is from LAPACK Version 3.12.0, file /home/abui...IG/sbdt05.f(3) 💖🫶✨