CBDT03(3)

💅 CBDT03(3) — Library Functions Manual

okay so bestie, this page is from the Library Functions Manual, and the source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/cbdt03.f — yes, the whole path, and it's serving full main-character energy. 🫶

NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/cbdt03.f — that's the name on this page, and it's giving "my identity is my file path" in the most iconic way. 💅

SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine CBDT03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
    CBDT03

Function/Subroutine Documentation 💖

subroutine CBDT03 (character uplo, integer n, integer kd, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldu, * ) u, integer ldu, real, dimension( * ) s, complex, dimension( ldvt, * ) vt, integer ldvt, complex, dimension( * ) work, real resid)
    CBDT03

Purpose 🔥

It's literally this, no cap:

!>
!> CBDT03 reconstructs a bidiagonal matrix B from its 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( B - U * S * VT ) / ( n * norm(B) * EPS )
!> where VT = V' and EPS is the machine precision.
!>

Group-chat translation: it reconstructs the bidiagonal matrix B from its SVD and checks the decomposition with the RESID ratio above. ✨

Parameters 🎀

• UPLO — CHARACTER*1. Specifies whether the matrix B is upper or lower bidiagonal. = 'U': upper bidiagonal. = 'L': lower bidiagonal.
• N — INTEGER. The order of the matrix B.
• KD — INTEGER. The bandwidth of the bidiagonal matrix B. If KD = 1, the matrix B is bidiagonal. If KD = 0, B is diagonal and E is not referenced. If KD is greater than 1, it is assumed to be 1; if KD is less than 0, it is assumed to be 0.
• D — REAL array, dimension (N). The n diagonal elements of the bidiagonal matrix B.
• E — REAL array, dimension (N-1). The (n-1) superdiagonal elements of B if UPLO = 'U', or the (n-1) subdiagonal elements of B if UPLO = 'L'.
• U — COMPLEX array, dimension (LDU,N). The n by n orthogonal matrix U in the reduction B = U'*A*P.
• LDU — INTEGER. The leading dimension of the array U. LDU >= max(1,N).
• S — REAL array, dimension (N). The singular values from the SVD of B, sorted in decreasing order.
• VT — COMPLEX array, dimension (LDVT,N). The n by n orthogonal matrix V' in the reduction B = U * S * V'.
• LDVT — INTEGER. The leading dimension of the array VT.
• WORK — COMPLEX array, dimension (2*N).
• RESID — REAL. The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS ).

Author 🫶

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

Definition at line 133 of file cbdt03.f. ⭐

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Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie — this one is LAPACK Version 3.12.0, from /home/abui...IG/cbdt03.f(3). The footer didn't give a date, so we're leaving it mysterious. 💜✨