/*! @file clacon.c * \brief Estimates the 1-norm * *
* -- SuperLU routine (version 2.0) -- * Univ. of California Berkeley, Xerox Palo Alto Research Center, * and Lawrence Berkeley National Lab. * November 15, 1997 **/ #include
* Purpose * ======= * * CLACON estimates the 1-norm of a square matrix A. * Reverse communication is used for evaluating matrix-vector products. * * * Arguments * ========= * * N (input) INT * The order of the matrix. N >= 1. * * V (workspace) COMPLEX PRECISION array, dimension (N) * On the final return, V = A*W, where EST = norm(V)/norm(W) * (W is not returned). * * X (input/output) COMPLEX PRECISION array, dimension (N) * On an intermediate return, X should be overwritten by * A * X, if KASE=1, * A' * X, if KASE=2, * where A' is the conjugate transpose of A, * and CLACON must be re-called with all the other parameters * unchanged. * * * EST (output) FLOAT PRECISION * An estimate (a lower bound) for norm(A). * * KASE (input/output) INT * On the initial call to CLACON, KASE should be 0. * On an intermediate return, KASE will be 1 or 2, indicating * whether X should be overwritten by A * X or A' * X. * On the final return from CLACON, KASE will again be 0. * * Further Details * ======= ======= * * Contributed by Nick Higham, University of Manchester. * Originally named CONEST, dated March 16, 1988. * * Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of * a real or complex matrix, with applications to condition estimation", * ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988. * ===================================================================== **/ int clacon_(int *n, complex *v, complex *x, float *est, int *kase) { /* Table of constant values */ int c__1 = 1; complex zero = {0.0, 0.0}; complex one = {1.0, 0.0}; /* System generated locals */ float d__1; /* Local variables */ static int iter; static int jump, jlast; static float altsgn, estold; static int i, j; float temp; float safmin; extern float slamch_(char *); extern int icmax1_(int *, complex *, int *); extern double scsum1_(int *, complex *, int *); safmin = slamch_("Safe minimum"); if ( *kase == 0 ) { for (i = 0; i < *n; ++i) { x[i].r = 1. / (float) (*n); x[i].i = 0.; } *kase = 1; jump = 1; return 0; } switch (jump) { case 1: goto L20; case 2: goto L40; case 3: goto L70; case 4: goto L110; case 5: goto L140; } /* ................ ENTRY (JUMP = 1) FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X. */ L20: if (*n == 1) { v[0] = x[0]; *est = c_abs(&v[0]); /* ... QUIT */ goto L150; } *est = scsum1_(n, x, &c__1); for (i = 0; i < *n; ++i) { d__1 = c_abs(&x[i]); if (d__1 > safmin) { d__1 = 1 / d__1; x[i].r *= d__1; x[i].i *= d__1; } else { x[i] = one; } } *kase = 2; jump = 2; return 0; /* ................ ENTRY (JUMP = 2) FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */ L40: j = icmax1_(n, &x[0], &c__1); --j; iter = 2; /* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */ L50: for (i = 0; i < *n; ++i) x[i] = zero; x[j] = one; *kase = 1; jump = 3; return 0; /* ................ ENTRY (JUMP = 3) X HAS BEEN OVERWRITTEN BY A*X. */ L70: #ifdef _CRAY CCOPY(n, x, &c__1, v, &c__1); #else ccopy_(n, x, &c__1, v, &c__1); #endif estold = *est; *est = scsum1_(n, v, &c__1); L90: /* TEST FOR CYCLING. */ if (*est <= estold) goto L120; for (i = 0; i < *n; ++i) { d__1 = c_abs(&x[i]); if (d__1 > safmin) { d__1 = 1 / d__1; x[i].r *= d__1; x[i].i *= d__1; } else { x[i] = one; } } *kase = 2; jump = 4; return 0; /* ................ ENTRY (JUMP = 4) X HAS BEEN OVERWRITTEN BY TRANDPOSE(A)*X. */ L110: jlast = j; j = icmax1_(n, &x[0], &c__1); --j; if (x[jlast].r != (d__1 = x[j].r, fabs(d__1)) && iter < 5) { ++iter; goto L50; } /* ITERATION COMPLETE. FINAL STAGE. */ L120: altsgn = 1.; for (i = 1; i <= *n; ++i) { x[i-1].r = altsgn * ((float)(i - 1) / (float)(*n - 1) + 1.); x[i-1].i = 0.; altsgn = -altsgn; } *kase = 1; jump = 5; return 0; /* ................ ENTRY (JUMP = 5) X HAS BEEN OVERWRITTEN BY A*X. */ L140: temp = scsum1_(n, x, &c__1) / (float)(*n * 3) * 2.; if (temp > *est) { #ifdef _CRAY CCOPY(n, &x[0], &c__1, &v[0], &c__1); #else ccopy_(n, &x[0], &c__1, &v[0], &c__1); #endif *est = temp; } L150: *kase = 0; return 0; } /* clacon_ */