SBDT01(3)

💖 NAME 💖

okay bestie, welcome to SBDT01(3) from the Library Functions Manual. This page is for the file path below — yes, NAME is literally one long path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/sbdt01.f

Also the header/footer path is /home/abui...IG/sbdt01.f(3) — it’s abbreviated like that in the page, so I’m keeping it exactly.

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine SBDT01 (m, n, kd, a, lda, q, ldq, d, e, pt, ldpt, work, resid)

SBDT01

🦋 Function/Subroutine Documentation 🦋

🫶 subroutine SBDT01 (integer m, integer n, integer kd, real, dimension( lda, * ) a, integer lda, real, dimension( ldq, * ) q, integer ldq, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldpt, * ) pt, integer ldpt, real, dimension( * ) work, real resid) 🫶

SBDT01

💫 Purpose 💫

okay so SBDT01 reconstructs a general matrix A from its bidiagonal form:

A = Q * B * P**T

where Q (m by min(m,n)) and P**T (min(m,n) by n) are orthogonal matrices and B is bidiagonal. slay.

The test ratio used to test the reduction is:

RESID = norm(A - Q * B * P**T) / ( n * norm(A) * EPS )

where EPS is the machine precision.

🌈 Parameters 🌈

• M — M is INTEGER; the number of rows of the matrices A and Q.
• N — N is INTEGER; the number of columns of the matrices A and P**T.
• KD — KD is INTEGER. If KD = 0, B is diagonal and the array E is not referenced. If KD = 1, the reduction was performed by xGEBRD; B is upper bidiagonal if M >= N, and lower bidiagonal if M < N. If KD = -1, the reduction was performed by xGBBRD; B is always upper bidiagonal.
• 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).
• Q — Q is REAL array, dimension (LDQ,N); the m by min(m,n) orthogonal matrix Q in the reduction A = Q * B * P**T.
• LDQ — LDQ is INTEGER; the leading dimension of the array Q. LDQ >= max(1,M).
• D — D is REAL array, dimension (min(M,N)); the diagonal elements of the bidiagonal matrix B.
• E — E is REAL array, dimension (min(M,N)-1); the superdiagonal elements of the bidiagonal matrix B if m >= n, or the subdiagonal elements of B if m < n.
• PT — PT is REAL array, dimension (LDPT,N); the min(m,n) by n orthogonal matrix P**T in the reduction A = Q * B * P**T.
• LDPT — LDPT is INTEGER; the leading dimension of the array PT. LDPT >= max(1,min(M,N)).
• WORK — WORK is REAL array, dimension (M+N).
• RESID — RESID is REAL; the test ratio: norm(A - Q * B * P**T) / ( n * norm(A) * EPS ).

👑 Author 👑

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

Definition at line 139 of file sbdt01.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that’s the whole page 💖 signing off with the footer deets: LAPACK Version 3.12.0, source path /home/abui...IG/sbdt01.f(3). The footer doesn’t show a separate date, so I’m not inventing one — no cap. ✨