TESTING/LIN/ctpt02.f(3)

✨ NAME ✨

ctpt02.f — the absolute icon of a test routine for packed triangular systems, no cap 💅

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🎀 SYNOPSIS 🎀

subroutine ctpt02 (uplo, trans, diag, n, nrhs, ap, x, ldx, b, ldb, work,
    rwork, resid)

CTPT02 — the baddie that computes residuals and we're obsessed 🫶

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🌸 DESCRIPTION 🌸

Okay bestie, so here's the tea: 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. It's literally serving main character energy for accuracy checks ✨.

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. So it's basically asking "how good is your solution, really?" and the answer better be slay 💯.

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👑 PARAMETERS 👑

• UPLO — is a CHARACTER*1. It specifies whether the matrix A is upper or lower triangular, periodt.
  • = 'U': Upper triangular 💖
  • = 'L': Lower triangular 💜
• TRANS — is a CHARACTER*1. It specifies the operation applied to A. The way this works is lowkey iconic.
  • = 'N': A * X = B (No transpose) 🙅‍♀️
  • = 'T': A**T * X = B (Transpose) 🔄
  • = 'C': A**H * X = B (Conjugate transpose) 🌈
• DIAG — is a CHARACTER*1. It specifies whether or not the matrix A is unit triangular. No cap, this matters.
  • = 'N': Non-unit triangular 😤
  • = 'U': Unit triangular 👑
• N — is INTEGER. The order of the matrix A. So like, N >= 0. Must be, okay? 💀
• NRHS — is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0. Giving us all the X and B energy fr fr.
• AP — is COMPLEX array, dimension (N*(N+1)/2). This is 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.

It's giving packed storage realness 💅

• X — is COMPLEX array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations. So proud of you, X 🥲
• LDX — is INTEGER. The leading dimension of the array X. LDX >= max(1,N). Don't play with this, bestie.
• B — is COMPLEX array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations. We <3 B for holding it down 💖
• LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N). It's literal math, no shortcuts 🔥
• WORK — is COMPLEX array, dimension (N). Just doing its job, lowkey iconic 💼
• RWORK — is REAL array, dimension (N). Real ones know 🌸
• RESID — is REAL. The maximum over the number of right hand sides of

norm(op(A)*B - B) / ( norm(op(A)) * norm(X) * EPS ).

This is the final boss of the residual check. The whole point. The moment. Periodt. 👑

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🦋 AUTHOR 🦋

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

Definition at line 145 of file ctpt02.f. So go check it out if you want the full source 💫

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🌈 SIGN-OFF 🌈

Brought to you with love by the absolute legends at LAPACK, Version 3.12.0, straight from TESTING/LIN/ctpt02.f — generated automatically by Doxygen for LAPACK from the source code. Stay slay, bestie, and remember: residuals are just vibes with numbers 💖✨👑