#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zlacn2_(integer *n, doublecomplex *v, doublecomplex *x, doublereal *est, integer *kase, integer *isave) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZLACN2 estimates the 1-norm of a square, complex matrix A. Reverse communication is used for evaluating matrix-vector products. Arguments ========= N (input) INTEGER The order of the matrix. N >= 1. V (workspace) COMPLEX*16 array, dimension (N) On the final return, V = A*W, where EST = norm(V)/norm(W) (W is not returned). X (input/output) COMPLEX*16 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 ZLACN2 must be re-called with all the other parameters unchanged. EST (input/output) DOUBLE PRECISION On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be unchanged from the previous call to ZLACN2. On exit, EST is an estimate (a lower bound) for norm(A). KASE (input/output) INTEGER On the initial call to ZLACN2, 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 ZLACN2, KASE will again be 0. ISAVE (input/output) INTEGER array, dimension (3) ISAVE is used to save variables between calls to ZLACN2 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. Last modified: April, 1999 This is a thread safe version of ZLACON, which uses the array ISAVE in place of a SAVE statement, as follows: ZLACON ZLACN2 JUMP ISAVE(1) J ISAVE(2) ITER ISAVE(3) ===================================================================== Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer i__1, i__2, i__3; doublereal d__1, d__2; doublecomplex z__1; /* Builtin functions */ double z_abs(doublecomplex *), d_imag(doublecomplex *); /* Local variables */ static integer i__; static doublereal temp, absxi; static integer jlast; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); extern integer izmax1_(integer *, doublecomplex *, integer *); extern doublereal dzsum1_(integer *, doublecomplex *, integer *), dlamch_( char *); static doublereal safmin, altsgn, estold; --isave; --x; --v; /* Function Body */ safmin = dlamch_("Safe minimum"); if (*kase == 0) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; d__1 = 1. / (doublereal) (*n); z__1.r = d__1, z__1.i = 0.; x[i__2].r = z__1.r, x[i__2].i = z__1.i; /* L10: */ } *kase = 1; isave[1] = 1; return 0; } switch (isave[1]) { case 1: goto L20; case 2: goto L40; case 3: goto L70; case 4: goto L90; case 5: goto L120; } /* ................ ENTRY (ISAVE( 1 ) = 1) FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X. */ L20: if (*n == 1) { v[1].r = x[1].r, v[1].i = x[1].i; *est = z_abs(&v[1]); /* ... QUIT */ goto L130; } *est = dzsum1_(n, &x[1], &c__1); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { absxi = z_abs(&x[i__]); if (absxi > safmin) { i__2 = i__; i__3 = i__; d__1 = x[i__3].r / absxi; d__2 = d_imag(&x[i__]) / absxi; z__1.r = d__1, z__1.i = d__2; x[i__2].r = z__1.r, x[i__2].i = z__1.i; } else { i__2 = i__; x[i__2].r = 1., x[i__2].i = 0.; } /* L30: */ } *kase = 2; isave[1] = 2; return 0; /* ................ ENTRY (ISAVE( 1 ) = 2) FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X. */ L40: isave[2] = izmax1_(n, &x[1], &c__1); isave[3] = 2; /* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */ L50: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; x[i__2].r = 0., x[i__2].i = 0.; /* L60: */ } i__1 = isave[2]; x[i__1].r = 1., x[i__1].i = 0.; *kase = 1; isave[1] = 3; return 0; /* ................ ENTRY (ISAVE( 1 ) = 3) X HAS BEEN OVERWRITTEN BY A*X. */ L70: zcopy_(n, &x[1], &c__1, &v[1], &c__1); estold = *est; *est = dzsum1_(n, &v[1], &c__1); /* TEST FOR CYCLING. */ if (*est <= estold) { goto L100; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { absxi = z_abs(&x[i__]); if (absxi > safmin) { i__2 = i__; i__3 = i__; d__1 = x[i__3].r / absxi; d__2 = d_imag(&x[i__]) / absxi; z__1.r = d__1, z__1.i = d__2; x[i__2].r = z__1.r, x[i__2].i = z__1.i; } else { i__2 = i__; x[i__2].r = 1., x[i__2].i = 0.; } /* L80: */ } *kase = 2; isave[1] = 4; return 0; /* ................ ENTRY (ISAVE( 1 ) = 4) X HAS BEEN OVERWRITTEN BY CTRANS(A)*X. */ L90: jlast = isave[2]; isave[2] = izmax1_(n, &x[1], &c__1); if (z_abs(&x[jlast]) != z_abs(&x[isave[2]]) && isave[3] < 5) { ++isave[3]; goto L50; } /* ITERATION COMPLETE. FINAL STAGE. */ L100: altsgn = 1.; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; d__1 = altsgn * ((doublereal) (i__ - 1) / (doublereal) (*n - 1) + 1.); z__1.r = d__1, z__1.i = 0.; x[i__2].r = z__1.r, x[i__2].i = z__1.i; altsgn = -altsgn; /* L110: */ } *kase = 1; isave[1] = 5; return 0; /* ................ ENTRY (ISAVE( 1 ) = 5) X HAS BEEN OVERWRITTEN BY A*X. */ L120: temp = dzsum1_(n, &x[1], &c__1) / (doublereal) (*n * 3) * 2.; if (temp > *est) { zcopy_(n, &x[1], &c__1, &v[1], &c__1); *est = temp; } L130: *kase = 0; return 0; /* End of ZLACN2 */ } /* zlacn2_ */