2022-01-13 14:05:24 +08:00
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/* Copyright (c) 2022, NVIDIA CORPORATION. All rights reserved.
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2021-10-21 19:04:49 +08:00
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* * Neither the name of NVIDIA CORPORATION nor the names of its
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* contributors may be used to endorse or promote products derived
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* from this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
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* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/* Computation of Gerschgorin interval for symmetric, tridiagonal matrix */
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#include <cstdio>
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#include <cstdlib>
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#include <cmath>
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#include <cfloat>
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#include "util.h"
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#include "gerschgorin.h"
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////////////////////////////////////////////////////////////////////////////////
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//! Compute Gerschgorin interval for symmetric, tridiagonal matrix
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//! @param d diagonal elements
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//! @param s superdiagonal elements
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//! @param n size of matrix
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//! @param lg lower limit of Gerschgorin interval
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//! @param ug upper limit of Gerschgorin interval
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////////////////////////////////////////////////////////////////////////////////
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void computeGerschgorin(float *d, float *s, unsigned int n, float &lg,
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float &ug) {
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lg = FLT_MAX;
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ug = -FLT_MAX;
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// compute bounds
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for (unsigned int i = 1; i < (n - 1); ++i) {
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// sum over the absolute values of all elements of row i
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float sum_abs_ni = fabsf(s[i - 1]) + fabsf(s[i]);
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lg = min(lg, d[i] - sum_abs_ni);
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ug = max(ug, d[i] + sum_abs_ni);
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}
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// first and last row, only one superdiagonal element
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// first row
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lg = min(lg, d[0] - fabsf(s[0]));
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ug = max(ug, d[0] + fabsf(s[0]));
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// last row
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lg = min(lg, d[n - 1] - fabsf(s[n - 2]));
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ug = max(ug, d[n - 1] + fabsf(s[n - 2]));
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// increase interval to avoid side effects of fp arithmetic
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float bnorm = max(fabsf(ug), fabsf(lg));
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// these values depend on the implementation of floating count that is
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// employed in the following
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float psi_0 = 11 * FLT_EPSILON * bnorm;
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float psi_n = 11 * FLT_EPSILON * bnorm;
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lg = lg - bnorm * 2 * n * FLT_EPSILON - psi_0;
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ug = ug + bnorm * 2 * n * FLT_EPSILON + psi_n;
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ug = max(lg, ug);
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}
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