TESTING/EIG/zbdt05.f(3)

Hey bestie 🫶 you're looking at TESTING/EIG/zbdt05.f(3) from the Library Functions Manual. This is the ZBDT05 page, and yes, we're gonna make it make sense. 💖

🌸 NAME 🌸

TESTING/EIG/zbdt05.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

       subroutine zbdt05 (m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)
           ZBDT05

💅 Function/Subroutine Documentation 💅

🎀 Signature 🎀

   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 🔥

Definition at line 123 of file zbdt05.f.

💖 Author 💖

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