TESTING/EIG/sbdt01.f(3)

💖 NAME

TESTING/EIG/sbdt01.f — okay bestie, this page lives in the Library Functions Manual under TESTING/EIG/sbdt01.f(3), and it’s all about the SBDT01 subroutine. She’s a testing routine, and she’s doing her little reconstruction vibe check. 🎀

✨ 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

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. Literally the glow-up from bidiagonal back to general, no cap. ✨

The test ratio that checks 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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mwah 💋 — source/version/date tea: this page is from LAPACK Version 3.12.0, the footer line is for TESTING/EIG/sbdt01.f(3), and there’s literally no date printed on that footer line. Periodt. 🌈