CTPT02(3)

🎀 NAME 🎀

okay bestie, first things first: this page lives in the Library Functions Manual, and the header title is /home/abui...IN/ctpt02.f(3). The full NAME path is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ctpt02.f. That's the whole NAME section — it's literally just the file path. iconic.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

       subroutine CTPT02 (uplo, trans, diag, n, nrhs, ap, x, ldx, b, ldb, work,
           rwork, resid)

and the description is just CTPT02. no cap, that's the vibe.

💖 Function/Subroutine Documentation 💖

okay so the full subroutine signature is right here, and it's a whole mood:

   subroutine CTPT02 (character uplo, character trans, character diag, integer
       n, integer nrhs, complex, dimension( * ) ap, complex, dimension( ldx, *
       ) x, integer ldx, complex, dimension( ldb, * ) b, integer ldb, complex,
       dimension( * ) work, real, dimension( * ) rwork, real resid)

and the next line is literally just CTPT02. slay.

🌸 Purpose 🌸

CTPT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, when the triangular matrix A is stored in packed format. The test ratio is the maximum over

norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),

where op(A) = A, A**T, or A**H, b is the column of B, x is the solution vector, and EPS is the machine epsilon. 💅

bestie, this is the packed-format residual-checking subroutine. it's giving "I check the math so you don't have to." 🫶

💅 Parameters 💅

• UPLO — UPLO is CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — TRANS is CHARACTER*1. Specifies the operation applied to A.
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose)
• DIAG — DIAG is CHARACTER*1. Specifies whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• AP — AP is COMPLEX array, dimension (N*(N+1)/2). The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
  • if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
• 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. LDX >= max(1,N).
• B — B is COMPLEX array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — WORK is COMPLEX array, dimension (N).
• RWORK — RWORK is REAL array, dimension (N).
• RESID — RESID is REAL. The maximum over the number of right hand sides of norm(op(A)*B - B) / ( norm(op(A)) * norm(X) * EPS ).

👑 Author 👑

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

Definition at line 145 of file ctpt02.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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made with 💖 by LAPACK, Version 3.12.0 — file /home/abui...IN/ctpt02.f(3). slay, bestie. ✨