TESTING/EIG/cbdt05.f(3)

💅 TESTING/EIG/cbdt05.f 💅

okay so bestie, this is the TESTING/EIG/cbdt05.f(3) page from the Library Functions Manual — yes, the cbdt05 subroutine is the main character here and she's here to reconstruct a bidiagonal matrix and check an SVD. No cap. 🦋

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🌸 NAME 🌸

TESTING/EIG/cbdt05.f

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✨ SYNOPSIS ✨

   Functions/Subroutines
       subroutine cbdt05 (m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)
           CBDT05

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🦋 Function/Subroutine Documentation 🦋

   subroutine cbdt05 (integer m, integer n, complex, dimension( lda, * ) a,
       integer lda, real, dimension( * ) s, integer ns, complex, dimension( * )
       u, integer ldu, complex, dimension( ldvt, * ) vt, integer ldvt, complex,
       dimension( * ) work, real resid)
       CBDT05

✨ Purpose ✨

CBDT05 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. periodt 💅

lowkey important: that RESID formula up there uses B, but the RESID parameter description below uses A — yes, both are in the original, so we're keeping both exactly. 👀

🎀 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 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 COMPLEX 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 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 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 123 of file cbdt05.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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