TESTING/LIN/zdrvrfp.f(3)

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💅 TESTING/LIN/zdrvrfp.f(3) — from the Library Functions Manual 🎀

okay so bestie, buckle up, because this one is a big one — zdrvrfp is the LAPACK testing driver for the RFP (rectangular full packed) routines, and she does NOT do things halfway. ✨

🌸 SYNOPSIS 🌸

Functions/Subroutines:

subroutine zdrvrfp (nout, nn, nval, nns, nsval, nnt, ntval, thresh, a,
    asav, afac, ainv, b, bsav, xact, x, arf, arfinv, z_work_zlatms,
    z_work_zpot02, z_work_zpot03, d_work_zlatms, d_work_zlanhe,
    d_work_zpot01, d_work_zpot02, d_work_zpot03)

ZDRVRFP — that's her, that's the icon. 👑

✨ Function/Subroutine Documentation ✨

subroutine zdrvrfp (integer nout, integer nn, integer, dimension( nn ) nval,
    integer nns, integer, dimension( nns ) nsval, integer nnt, integer,
    dimension( nnt ) ntval, double precision thresh, complex*16, dimension(
    * ) a, complex*16, dimension( * ) asav, complex*16, dimension( * ) afac,
    complex*16, dimension( * ) ainv, complex*16, dimension( * ) b,
    complex*16, dimension( * ) bsav, complex*16, dimension( * ) xact,
    complex*16, dimension( * ) x, complex*16, dimension( * ) arf,
    complex*16, dimension( * ) arfinv, complex*16, dimension( * )
    z_work_zlatms, complex*16, dimension( * ) z_work_zpot02, complex*16,
    dimension( * ) z_work_zpot03, double precision, dimension( * )
    d_work_zlatms, double precision, dimension( * ) d_work_zlanhe, double
    precision, dimension( * ) d_work_zpot01, double precision, dimension( *
    ) d_work_zpot02, double precision, dimension( * ) d_work_zpot03)

ZDRVRFP 💖

🦋 Purpose 🦋

okay so what does she actually do? ZDRVRFP tests the LAPACK RFP routines:

  • ZPFTRF
  • ZPFTRS
  • ZPFTRI

She's running the exact same tests as ZDRVPO (which is the test for the full format Symmetric Positive Definite solver) — no cap, same energy, different format.

Here's the twist that makes it make sense: the tests themselves are performed in Full Format, and conversion back and forth from full format to RFP format is handled by ZTRTTF and ZTFTTR. So basically she dresses full-format in RFP clothes and back again, slay. 💅

First up, a specific matrix A of size N is created. There are nine types of different matrixes possible, and yes, all nine are iconic in their own way:

  1. Diagonal
  2. Random, CNDNUM = 2
  3. First row and column zero *
  4. Last row and column zero *
  5. Middle row and column zero *

and on the other side:

  1. Random, CNDNUM = sqrt(0.1/EPS)
  2. Random, CNDNUM = 0.1/EPS
  3. Scaled near underflow
  4. Scaled near overflow
(* — these ones test error exits from ZPFTRF, and no test ratios are computed for them. They're the chaos gremlins of the group. 🙈)

A solution XACT of size N-by-NRHS is created and the associated right hand side B as well. Then ZPFTRF is called to compute L (or U), the Cholesky factor of A. Then L (or U) is used to solve the linear system of equations AX = B. That gives you X. Then L (or U) is used to compute the inverse of A, AINV. And then — drumroll — the following four tests are performed:

  1. norm( L*L' - A ) / ( N * norm(A) * EPS ) or norm( U'*U - A ) / ( N * norm(A) * EPS )
  2. norm(B - A*X) / ( norm(A) * norm(X) * EPS )
  3. norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS )
  4. ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )

where EPS is the machine precision, RCOND the condition number of A, and norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4). 💀 the way that's so precise.

Errors occur when the INFO parameter is not as expected. Failures occur when a test ratio is greater than THRES. periodt.

🧚 Parameters 🧚

  • NOUT — NOUT is INTEGER. The unit number for output. your output goes here bestie 🫶
  • NN — NN is INTEGER. The number of values of N contained in the vector NVAL.
  • NVAL — NVAL is INTEGER array, dimension (NN). The values of the matrix dimension N.
  • NNS — NNS is INTEGER. The number of values of NRHS contained in the vector NSVAL.
  • NSVAL — NSVAL is INTEGER array, dimension (NNS). The values of the number of right-hand sides NRHS.
  • NNT — NNT is INTEGER. The number of values of MATRIX TYPE contained in the vector NTVAL.
  • NTVAL — NTVAL is INTEGER array, dimension (NNT). The values of matrix type (between 0 and 9 for PO/PP/PF matrices).
  • THRESH — THRESH is DOUBLE PRECISION. The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0. (yes, zero, all of them, no filter, main character energy 🌈)
  • A — A is COMPLEX*16 array, dimension (NMAX*NMAX)
  • ASAV — ASAV is COMPLEX*16 array, dimension (NMAX*NMAX)
  • AFAC — AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)
  • AINV — AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
  • B — B is COMPLEX*16 array, dimension (NMAX*MAXRHS)
  • BSAV — BSAV is COMPLEX*16 array, dimension (NMAX*MAXRHS)
  • XACT — XACT is COMPLEX*16 array, dimension (NMAX*MAXRHS)
  • X — X is COMPLEX*16 array, dimension (NMAX*MAXRHS)
  • ARF — ARF is COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2)
  • ARFINV — ARFINV is COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2)
  • Z_WORK_ZLATMS — Z_WORK_ZLATMS is COMPLEX*16 array, dimension ( 3*NMAX )
  • Z_WORK_ZPOT02 — Z_WORK_ZPOT02 is COMPLEX*16 array, dimension ( NMAX*MAXRHS )
  • Z_WORK_ZPOT03 — Z_WORK_ZPOT03 is COMPLEX*16 array, dimension ( NMAX*NMAX )
  • D_WORK_ZLATMS — D_WORK_ZLATMS is DOUBLE PRECISION array, dimension ( NMAX )
  • D_WORK_ZLANHE — D_WORK_ZLANHE is DOUBLE PRECISION array, dimension ( NMAX )
  • D_WORK_ZPOT01 — D_WORK_ZPOT01 is DOUBLE PRECISION array, dimension ( NMAX )
  • D_WORK_ZPOT02 — D_WORK_ZPOT02 is DOUBLE PRECISION array, dimension ( NMAX )
  • D_WORK_ZPOT03 — D_WORK_ZPOT03 is DOUBLE PRECISION array, dimension ( NMAX )

like, that's a LOT of workspace arrays and honestly? respect. 🍓

👑 Author 👑

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

Definition at line 238 of file zdrvrfp.f.

⭐ Author (the meta one) ⭐

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