#include #include #include #include #include #ifdef complex #undef complex #endif #ifdef I #undef I #endif #if defined(_WIN64) typedef long long BLASLONG; typedef unsigned long long BLASULONG; #else typedef long BLASLONG; typedef unsigned long BLASULONG; #endif #ifdef LAPACK_ILP64 typedef BLASLONG blasint; #if defined(_WIN64) #define blasabs(x) llabs(x) #else #define blasabs(x) labs(x) #endif #else typedef int blasint; #define blasabs(x) abs(x) #endif typedef blasint integer; typedef unsigned int uinteger; typedef char *address; typedef short int shortint; typedef float real; typedef double doublereal; typedef struct { real r, i; } complex; typedef struct { doublereal r, i; } doublecomplex; #ifdef _MSC_VER static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;} static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;} static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;} static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;} #else static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;} static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;} static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;} static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;} #endif #define pCf(z) (*_pCf(z)) #define pCd(z) (*_pCd(z)) typedef blasint logical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #ifdef _MSC_VER #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);} #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimagf(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle() continue; #define myceiling(w) {ceil(w)} #define myhuge(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* -- translated by f2c (version 20000121). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ /* Table of constant values */ static integer c__1 = 1; static real c_b11 = 1.f; /* > \brief \b SLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matr ix-vector products. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SLACON + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SLACON( N, V, X, ISGN, EST, KASE ) */ /* INTEGER KASE, N */ /* REAL EST */ /* INTEGER ISGN( * ) */ /* REAL V( * ), X( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SLACON estimates the 1-norm of a square, real matrix A. */ /* > Reverse communication is used for evaluating matrix-vector products. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix. N >= 1. */ /* > \endverbatim */ /* > */ /* > \param[out] V */ /* > \verbatim */ /* > V is REAL array, dimension (N) */ /* > On the final return, V = A*W, where EST = norm(V)/norm(W) */ /* > (W is not returned). */ /* > \endverbatim */ /* > */ /* > \param[in,out] X */ /* > \verbatim */ /* > X is REAL array, dimension (N) */ /* > On an intermediate return, X should be overwritten by */ /* > A * X, if KASE=1, */ /* > A**T * X, if KASE=2, */ /* > and SLACON must be re-called with all the other parameters */ /* > unchanged. */ /* > \endverbatim */ /* > */ /* > \param[out] ISGN */ /* > \verbatim */ /* > ISGN is INTEGER array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[in,out] EST */ /* > \verbatim */ /* > EST is REAL */ /* > On entry with KASE = 1 or 2 and JUMP = 3, EST should be */ /* > unchanged from the previous call to SLACON. */ /* > On exit, EST is an estimate (a lower bound) for norm(A). */ /* > \endverbatim */ /* > */ /* > \param[in,out] KASE */ /* > \verbatim */ /* > KASE is INTEGER */ /* > On the initial call to SLACON, 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**T * X. */ /* > On the final return from SLACON, KASE will again be 0. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup realOTHERauxiliary */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Nick Higham, University of Manchester. \n */ /* > Originally named SONEST, dated March 16, 1988. */ /* > \par References: */ /* ================ */ /* > */ /* > 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. */ /* > */ /* ===================================================================== */ /* Subroutine */ void slacon_(integer *n, real *v, real *x, integer *isgn, real *est, integer *kase) { /* System generated locals */ integer i__1; real r__1; /* Local variables */ static integer iter; static real temp; static integer jump, i__, j, jlast; extern real sasum_(integer *, real *, integer *); extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *, integer *); extern integer isamax_(integer *, real *, integer *); static real altsgn, estold; /* -- LAPACK auxiliary routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* December 2016 */ /* ===================================================================== */ /* Parameter adjustments */ --isgn; --x; --v; /* Function Body */ if (*kase == 0) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { x[i__] = 1.f / (real) (*n); /* L10: */ } *kase = 1; jump = 1; return; } 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[1] = x[1]; *est = abs(v[1]); /* ... QUIT */ goto L150; } *est = sasum_(n, &x[1], &c__1); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { x[i__] = r_sign(&c_b11, &x[i__]); isgn[i__] = i_nint(&x[i__]); /* L30: */ } *kase = 2; jump = 2; return; /* ................ ENTRY (JUMP = 2) */ /* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */ L40: j = isamax_(n, &x[1], &c__1); iter = 2; /* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */ L50: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { x[i__] = 0.f; /* L60: */ } x[j] = 1.f; *kase = 1; jump = 3; return; /* ................ ENTRY (JUMP = 3) */ /* X HAS BEEN OVERWRITTEN BY A*X. */ L70: scopy_(n, &x[1], &c__1, &v[1], &c__1); estold = *est; *est = sasum_(n, &v[1], &c__1); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { r__1 = r_sign(&c_b11, &x[i__]); if (i_nint(&r__1) != isgn[i__]) { goto L90; } /* L80: */ } /* REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED. */ goto L120; L90: /* TEST FOR CYCLING. */ if (*est <= estold) { goto L120; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { x[i__] = r_sign(&c_b11, &x[i__]); isgn[i__] = i_nint(&x[i__]); /* L100: */ } *kase = 2; jump = 4; return; /* ................ ENTRY (JUMP = 4) */ /* X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */ L110: jlast = j; j = isamax_(n, &x[1], &c__1); if (x[jlast] != (r__1 = x[j], abs(r__1)) && iter < 5) { ++iter; goto L50; } /* ITERATION COMPLETE. FINAL STAGE. */ L120: altsgn = 1.f; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { x[i__] = altsgn * ((real) (i__ - 1) / (real) (*n - 1) + 1.f); altsgn = -altsgn; /* L130: */ } *kase = 1; jump = 5; return; /* ................ ENTRY (JUMP = 5) */ /* X HAS BEEN OVERWRITTEN BY A*X. */ L140: temp = sasum_(n, &x[1], &c__1) / (real) (*n * 3) * 2.f; if (temp > *est) { scopy_(n, &x[1], &c__1, &v[1], &c__1); *est = temp; } L150: *kase = 0; return; /* End of SLACON */ } /* slacon_ */