private static void Main()
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for LINPACK_BENCH.
//
// Discussion:
//
// LINPACK_BENCH drives the double precision LINPACK benchmark program.
//
// Modified:
//
// 30 November 2006
//
// Parameters:
//
// N is the problem size.
//
{
const int N = 1000;
const int LDA = N + 1;
const double cray = 0.056;
int i;
int j;
double[] time = new double[6];
Console.WriteLine("");
Console.WriteLine("LINPACK_BENCH");
Console.WriteLine("");
Console.WriteLine(" The LINPACK benchmark.");
Console.WriteLine(" Datatype: Double precision");
Console.WriteLine(" Matrix order N = " + N + "");
Console.WriteLine(" Leading matrix dimension LDA = " + LDA + "");
double ops = 2 * N * N * N / 3.0 + 2.0 * (N * N);
//
// Allocate space for arrays.
//
double[] a = typeMethods.r8mat_gen(LDA, N);
double[] b = new double[N];
int[] ipvt = new int[N];
double[] resid = new double[N];
double[] rhs = new double[N];
double[] x = new double[N];
double a_max = 0.0;
for (j = 0; j < N; j++)
{
for (i = 0; i < N; i++)
{
a_max = Math.Max(a_max, a[i + j * LDA]);
}
}
for (i = 0; i < N; i++)
{
x[i] = 1.0;
}
for (i = 0; i < N; i++)
{
b[i] = 0.0;
for (j = 0; j < N; j++)
{
b[i] += a[i + j * LDA] * x[j];
}
}
DateTime t1 = DateTime.Now;
int info = DGEFA.dgefa(ref a, LDA, N, ref ipvt);
if (info != 0)
{
Console.WriteLine("");
Console.WriteLine("LINPACK_BENCH - Fatal error!");
Console.WriteLine(" The matrix A is apparently singular.");
Console.WriteLine(" Abnormal end of execution.");
return;
}
DateTime t2 = DateTime.Now;
time[0] = (t2 - t1).TotalSeconds;
t1 = DateTime.Now;
int job = 0;
DGESL.dgesl(a, LDA, N, ipvt, ref b, job);
t2 = DateTime.Now;
time[1] = (t2 - t1).TotalSeconds;
double total = time[0] + time[1];
//
// Compute a residual to verify results.
//
a = typeMethods.r8mat_gen(LDA, N);
for (i = 0; i < N; i++)
{
x[i] = 1.0;
}
for (i = 0; i < N; i++)
{
rhs[i] = 0.0;
for (j = 0; j < N; j++)
{
rhs[i] += a[i + j * LDA] * x[j];
}
}
for (i = 0; i < N; i++)
{
resid[i] = -rhs[i];
for (j = 0; j < N; j++)
{
resid[i] += a[i + j * LDA] * b[j];
}
}
double resid_max = 0.0;
for (i = 0; i < N; i++)
{
resid_max = Math.Max(resid_max, Math.Abs(resid[i]));
}
double b_max = 0.0;
for (i = 0; i < N; i++)
{
b_max = Math.Max(b_max, Math.Abs(b[i]));
}
double eps = typeMethods.r8_epsilon();
double residn = resid_max / (N * a_max * b_max * eps);
time[2] = total;
time[3] = total switch
{
public static double dgeco(ref double[] a, int lda, int n, ref int[] ipvt, ref double[] z)
//****************************************************************************80
//
// Purpose:
//
// DGECO factors a real matrix and estimates its condition number.
//
// Discussion:
//
// If RCOND is not needed, DGEFA is slightly faster.
//
// To solve A * X = B, follow DGECO by DGESL.
//
// To compute inverse ( A ) * C, follow DGECO by DGESL.
//
// To compute determinant ( A ), follow DGECO by DGEDI.
//
// To compute inverse ( A ), follow DGECO by DGEDI.
//
// For the system A * X = B, relative perturbations in A and B
// of size EPSILON may cause relative perturbations in X of size
// EPSILON/RCOND.
//
// If RCOND is so small that the logical expression
// 1.0D+00 + RCOND == 1.0D+00
// is true, then A may be singular to working precision. In particular,
// RCOND is zero if exact singularity is detected or the estimate
// underflows.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 25 May 2005
//
// Author:
//
// Original FORTRAN77 version by Jack Dongarra, Cleve Moler, Jim Bunch,
// Pete Stewart.
// C++ version by John Burkardt.
//
// Reference:
//
// Jack Dongarra, Cleve Moler, Jim Bunch and Pete Stewart,
// LINPACK User's Guide,
// SIAM, (Society for Industrial and Applied Mathematics),
// 3600 University City Science Center,
// Philadelphia, PA, 19104-2688.
// ISBN 0-89871-172-X
//
// Parameters:
//
// Input/output, double A[LDA*N]. On input, a matrix to be
// factored. On output, the LU factorization of the matrix.
//
// Input, int LDA, the leading dimension of the array A.
//
// Input, int N, the order of the matrix A.
//
// Output, int IPVT[N], the pivot indices.
//
// Output, double Z[N], a work vector whose contents are usually
// unimportant. If A is close to a singular matrix, then Z is an
// approximate null vector in the sense that
// norm ( A * Z ) = RCOND * norm ( A ) * norm ( Z ).
//
// Output, double DGECO, the value of RCOND, an estimate
// of the reciprocal condition number of A.
//
{
int i;
int j;
int k;
int l;
double rcond;
double s;
double t;
//
// Compute the L1 norm of A.
//
double anorm = 0.0;
for (j = 1; j <= n; j++)
{
anorm = Math.Max(anorm, BLAS1D.dasum(n, a, 1, index: +0 + (j - 1) * lda));
}
//
// Compute the LU factorization.
//
DGEFA.dgefa(ref a, lda, n, ref ipvt);
//
// RCOND = 1 / ( norm(A) * (estimate of norm(inverse(A))) )
//
// estimate of norm(inverse(A)) = norm(Z) / norm(Y)
//
// where
// A * Z = Y
// and
// A' * Y = E
//
// The components of E are chosen to cause maximum local growth in the
// elements of W, where U'*W = E. The vectors are frequently rescaled
// to avoid overflow.
//
// Solve U' * W = E.
//
double ek = 1.0;
for (i = 1; i <= n; i++)
{
z[i - 1] = 0.0;
}
for (k = 1; k <= n; k++)
{
if (z[k - 1] != 0.0)
{
ek *= typeMethods.r8_sign(-z[k - 1]);
}
if (Math.Abs(a[k - 1 + (k - 1) * lda]) < Math.Abs(ek - z[k - 1]))
{
s = Math.Abs(a[k - 1 + (k - 1) * lda]) / Math.Abs(ek - z[k - 1]);
for (i = 1; i <= n; i++)
{
z[i - 1] = s * z[i - 1];
}
ek = s * ek;
}
double wk = ek - z[k - 1];
double wkm = -ek - z[k - 1];
s = Math.Abs(wk);
double sm = Math.Abs(wkm);
if (a[k - 1 + (k - 1) * lda] != 0.0)
{
wk /= a[k - 1 + (k - 1) * lda];
wkm /= a[k - 1 + (k - 1) * lda];
}
else
{
wk = 1.0;
wkm = 1.0;
}
if (k + 1 <= n)
{
for (j = k + 1; j <= n; j++)
{
sm += Math.Abs(z[j - 1] + wkm * a[k - 1 + (j - 1) * lda]);
z[j - 1] += wk * a[k - 1 + (j - 1) * lda];
s += Math.Abs(z[j - 1]);
}
if (s < sm)
{
t = wkm - wk;
wk = wkm;
for (i = k + 1; i <= n; i++)
{
z[i - 1] += t * a[k - 1 + (i - 1) * lda];
}
}
}
z[k - 1] = wk;
}
t = BLAS1D.dasum(n, z, 1);
for (i = 1; i <= n; i++)
{
z[i - 1] /= t;
}
//
// Solve L' * Y = W
//
for (k = n; 1 <= k; k--)
{
z[k - 1] += BLAS1D.ddot(n - k, a, 1, z, 1, xIndex: +k + (k - 1) * lda, yIndex: +k);
switch (Math.Abs(z[k - 1]))
{
case > 1.0:
{
t = Math.Abs(z[k - 1]);
for (i = 1; i <= n; i++)
{
z[i - 1] /= t;
}
break;
}
}
l = ipvt[k - 1];
t = z[l - 1];
z[l - 1] = z[k - 1];
z[k - 1] = t;
}
t = BLAS1D.dasum(n, z, 1);
for (i = 1; i <= n; i++)
{
z[i - 1] /= t;
}
double ynorm = 1.0;
//
// Solve L * V = Y.
//
for (k = 1; k <= n; k++)
{
l = ipvt[k - 1];
t = z[l - 1];
z[l - 1] = z[k - 1];
z[k - 1] = t;
for (i = k + 1; i <= n; i++)
{
z[i - 1] += t * a[i - 1 + (k - 1) * lda];
}
switch (Math.Abs(z[k - 1]))
{
case > 1.0:
{
ynorm /= Math.Abs(z[k - 1]);
t = Math.Abs(z[k - 1]);
for (i = 1; i <= n; i++)
{
z[i - 1] /= t;
}
break;
}
}
}
s = BLAS1D.dasum(n, z, 1);
for (i = 1; i <= n; i++)
{
z[i - 1] /= s;
}
ynorm /= s;
//
// Solve U * Z = V.
//
for (k = n; 1 <= k; k--)
{
if (Math.Abs(a[k - 1 + (k - 1) * lda]) < Math.Abs(z[k - 1]))
{
s = Math.Abs(a[k - 1 + (k - 1) * lda]) / Math.Abs(z[k - 1]);
for (i = 1; i <= n; i++)
{
z[i - 1] = s * z[i - 1];
}
ynorm = s * ynorm;
}
if (a[k - 1 + (k - 1) * lda] != 0.0)
{
z[k - 1] /= a[k - 1 + (k - 1) * lda];
}
else
{
z[k - 1] = 1.0;
}
for (i = 1; i <= k - 1; i++)
{
z[i - 1] -= z[k - 1] * a[i - 1 + (k - 1) * lda];
}
}
//
// Normalize Z in the L1 norm.
//
s = 1.0 / BLAS1D.dasum(n, z, 1);
for (i = 1; i <= n; i++)
{
z[i - 1] = s * z[i - 1];
}
ynorm = s * ynorm;
if (anorm != 0.0)
{
rcond = ynorm / anorm;
}
else
{
rcond = 0.0;
}
return(rcond);
}