TESTING/EIG/cbdt03.f(3)

🌸 TESTING/EIG/cbdt03.f(3) 🌸

Bestie, this is the TESTING/EIG/cbdt03.f(3) page from the Library Functions Manual — and yes, we're about to make Fortran bidiagonal SVD testing sound cute. 💅

💖 NAME 💖

TESTING/EIG/cbdt03.f — that's literally the whole name, no cap.

✨ 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 is the main character here. 👑

🌟 Purpose

Okay so CBDT03 reconstructs a bidiagonal matrix B from its SVD:

S = U' * B * V

where U and V are orthogonal matrices and S is diagonal. Slay.

The test ratio used 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. Math but make it fashion. ✨

🎀 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, and if KD = 0, B is diagonal and E is not referenced. If KD is greater than 1, it is assumed to be 1, and 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 the bidiagonal matrix 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.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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