TESTING/LIN/cqrt16.f(3)

💖 NAME 💖

TESTING/LIN/cqrt16.f — that’s the file, bestie, and this is its Library Functions Manual page. CQRT16 is the subroutine inside, and it’s lowkey giving “linear algebra residual check” main character energy. ✨

✨ SYNOPSIS ✨

Under Functions/Subroutines, you’ve got this:

subroutine cqrt16 (trans, m, n, nrhs, a, lda, x, ldx, b, ldb, rwork,
    resid)
    CQRT16

🌸 Function/Subroutine Documentation 🌸

Here’s the full signature, no cap:

subroutine cqrt16 (character trans, integer m, integer n, integer nrhs,
       complex, dimension( lda, * ) a, integer lda, complex, dimension( ldx, *
       ) x, integer ldx, complex, dimension( ldb, * ) b, integer ldb, real,
       dimension( * ) rwork, real resid)
       CQRT16

🎯 Purpose 🎯

CQRT16 computes the residual for a solution of a system of linear equations A*x = b or A'*x = b:

RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),

where EPS is the machine epsilon. 💅

🧾 Parameters 🧾

• TRANS — TRANS is CHARACTER*1. It specifies the form of the system of equations:
  • = 'N': A *x = b
  • = 'T': A^T*x = b, where A^T is the transpose of A
  • = 'C': A^H*x = b, where A^H is the conjugate transpose of A
• M — M is INTEGER. The number of rows of the matrix A. M >= 0.
• N — N is INTEGER. The number of columns of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of columns of B, the matrix of right hand sides. NRHS >= 0.
• A — A is COMPLEX array, dimension (LDA,N). The original M x N matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• X — X is COMPLEX array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — LDX is INTEGER. The leading dimension of the array X. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
• B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.
• LDB — LDB is INTEGER. The leading dimension of the array B. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
• RWORK — RWORK is REAL array, dimension (M).
• RESID — RESID is REAL. The maximum over the number of right hand sides of norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).

👑 Author 👑

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

Definition at line 131 of file cqrt16.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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Sign-off time, bestie: this page is from LAPACK Version 3.12.0, file TESTING/LIN/cqrt16.f(3). The footer didn’t show a date, so I’m not inventing one — just vibes and version numbers. 💖✨