TESTING/LIN/ddrvrfp.f(3)

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version 3.12.1 · 2 versions
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🎀 TESTING/LIN/ddrvrfp.f(3) 🎀

okay so this page lives in the Library Functions Manual, and it is literally all about the DDRVRFP routine, bestie. 💖

🌸 NAME 🌸

TESTING/LIN/ddrvrfp.f — yes queen, that's the page. It documents DDRVRFP in the Library Functions Manual.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine ddrvrfp (nout, nn, nval, nns, nsval, nnt, ntval, thresh, a, asav, afac, ainv, b, bsav, xact, x, arf, arfinv, d_work_dlatms, d_work_dpot01, d_temp_dpot02, d_temp_dpot03, d_work_dlansy, d_work_dpot02, d_work_dpot03)
    DDRVRFP

🌈 Function/Subroutine Documentation 🌈

subroutine ddrvrfp (integer nout, integer nn, integer, dimension( nn ) nval, integer nns, integer, dimension( nns ) nsval, integer nnt, integer, dimension( nnt ) ntval, double precision thresh, double precision, dimension( * ) a, double precision, dimension( * ) asav, double precision, dimension( * ) afac, double precision, dimension( * ) ainv, double precision, dimension( * ) b, double precision, dimension( * ) bsav, double precision, dimension( * ) xact, double precision, dimension( * ) x, double precision, dimension( * ) arf, double precision, dimension( * ) arfinv, double precision, dimension( * ) d_work_dlatms, double precision, dimension( * ) d_work_dpot01, double precision, dimension( * ) d_temp_dpot02, double precision, dimension( * ) d_temp_dpot03, double precision, dimension( * ) d_work_dlansy, double precision, dimension( * ) d_work_dpot02, double precision, dimension( * ) d_work_dpot03)
    DDRVRFP

💜 Purpose 💜

DDRVRFP tests the LAPACK RFP routines: DPFTRF, DPFTRS, and DPFTRI.

This testing routine follows the same tests as DDRVPO (the test for the full format Symmetric Positive Definite solver).

The tests happen in Full Format, and conversion back and forth from full format to RFP format is performed using the routines DTRTTF and DTFTTR.

First, a specific matrix A of size N is created. There are nine types of different matrixes possible:

  1. Diagonal
  2. Random, CNDNUM = 2
  3. * First row and column zero
  4. * Last row and column zero
  5. * Middle row and column zero
  6. Random, CNDNUM = sqrt(0.1/EPS)
  7. Random, CNDNUM = 0.1/EPS
  8. Scaled near underflow
  9. Scaled near overflow
(* - tests error exits from DPFTRF, no test ratios are computed)

A solution XACT of size N-by-NRHS is created and the associated right hand side B as well. Then DPFTRF 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. This gives X. Then L (or U) is used to compute the inverse of A, AINV. The following four tests are then 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). Errors occur when the INFO parameter is not as expected. Failures occur when a test ratio is greater than THRES.

🎀 Parameters 🎀

  • NOUT — NOUT is INTEGER. The unit number for output.
  • 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.
  • A — A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
  • ASAV — ASAV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
  • AFAC — AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
  • AINV — AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
  • B — B is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
  • BSAV — BSAV is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
  • XACT — XACT is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
  • X — X is DOUBLE PRECISION array, dimension (NMAX*MAXRHS)
  • ARF — ARF is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2)
  • ARFINV — ARFINV is DOUBLE PRECISION array, dimension ((NMAX*(NMAX+1))/2)
  • D_WORK_DLATMS — D_WORK_DLATMS is DOUBLE PRECISION array, dimension ( 3*NMAX )
  • D_WORK_DPOT01 — D_WORK_DPOT01 is DOUBLE PRECISION array, dimension ( NMAX )
  • D_TEMP_DPOT02 — D_TEMP_DPOT02 is DOUBLE PRECISION array, dimension ( NMAX*MAXRHS )
  • D_TEMP_DPOT03 — D_TEMP_DPOT03 is DOUBLE PRECISION array, dimension ( NMAX*NMAX )
  • D_WORK_DLANSY — D_WORK_DLANSY is DOUBLE PRECISION array, dimension ( NMAX )
  • D_WORK_DPOT02 — D_WORK_DPOT02 is DOUBLE PRECISION array, dimension ( NMAX )
  • D_WORK_DPOT03 — D_WORK_DPOT03 is DOUBLE PRECISION array, dimension ( NMAX )

👑 Author 👑

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

Definition at line 232 of file ddrvrfp.f.

🫶 Author 🫶

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💖 That's the whole page, bestie. Signing off from LAPACK, Version 3.12.0, on TESTING/LIN/ddrvrfp.f(3) — go slay your RFP tests. 💅✨
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