#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 int logical; typedef short int shortlogical; 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 pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(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);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #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)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief \b DSTEIN */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DSTEIN + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, */ /* IWORK, IFAIL, INFO ) */ /* INTEGER INFO, LDZ, M, N */ /* INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), */ /* $ IWORK( * ) */ /* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DSTEIN computes the eigenvectors of a real symmetric tridiagonal */ /* > matrix T corresponding to specified eigenvalues, using inverse */ /* > iteration. */ /* > */ /* > The maximum number of iterations allowed for each eigenvector is */ /* > specified by an internal parameter MAXITS (currently set to 5). */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] D */ /* > \verbatim */ /* > D is DOUBLE PRECISION array, dimension (N) */ /* > The n diagonal elements of the tridiagonal matrix T. */ /* > \endverbatim */ /* > */ /* > \param[in] E */ /* > \verbatim */ /* > E is DOUBLE PRECISION array, dimension (N-1) */ /* > The (n-1) subdiagonal elements of the tridiagonal matrix */ /* > T, in elements 1 to N-1. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of eigenvectors to be found. 0 <= M <= N. */ /* > \endverbatim */ /* > */ /* > \param[in] W */ /* > \verbatim */ /* > W is DOUBLE PRECISION array, dimension (N) */ /* > The first M elements of W contain the eigenvalues for */ /* > which eigenvectors are to be computed. The eigenvalues */ /* > should be grouped by split-off block and ordered from */ /* > smallest to largest within the block. ( The output array */ /* > W from DSTEBZ with ORDER = 'B' is expected here. ) */ /* > \endverbatim */ /* > */ /* > \param[in] IBLOCK */ /* > \verbatim */ /* > IBLOCK is INTEGER array, dimension (N) */ /* > The submatrix indices associated with the corresponding */ /* > eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to */ /* > the first submatrix from the top, =2 if W(i) belongs to */ /* > the second submatrix, etc. ( The output array IBLOCK */ /* > from DSTEBZ is expected here. ) */ /* > \endverbatim */ /* > */ /* > \param[in] ISPLIT */ /* > \verbatim */ /* > ISPLIT is INTEGER array, dimension (N) */ /* > The splitting points, at which T breaks up into submatrices. */ /* > The first submatrix consists of rows/columns 1 to */ /* > ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 */ /* > through ISPLIT( 2 ), etc. */ /* > ( The output array ISPLIT from DSTEBZ is expected here. ) */ /* > \endverbatim */ /* > */ /* > \param[out] Z */ /* > \verbatim */ /* > Z is DOUBLE PRECISION array, dimension (LDZ, M) */ /* > The computed eigenvectors. The eigenvector associated */ /* > with the eigenvalue W(i) is stored in the i-th column of */ /* > Z. Any vector which fails to converge is set to its current */ /* > iterate after MAXITS iterations. */ /* > \endverbatim */ /* > */ /* > \param[in] LDZ */ /* > \verbatim */ /* > LDZ is INTEGER */ /* > The leading dimension of the array Z. LDZ >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension (5*N) */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[out] IFAIL */ /* > \verbatim */ /* > IFAIL is INTEGER array, dimension (M) */ /* > On normal exit, all elements of IFAIL are zero. */ /* > If one or more eigenvectors fail to converge after */ /* > MAXITS iterations, then their indices are stored in */ /* > array IFAIL. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit. */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > > 0: if INFO = i, then i eigenvectors failed to converge */ /* > in MAXITS iterations. Their indices are stored in */ /* > array IFAIL. */ /* > \endverbatim */ /* > \par Internal Parameters: */ /* ========================= */ /* > */ /* > \verbatim */ /* > MAXITS INTEGER, default = 5 */ /* > The maximum number of iterations performed. */ /* > */ /* > EXTRA INTEGER, default = 2 */ /* > The number of iterations performed after norm growth */ /* > criterion is satisfied, should be at least 1. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup doubleOTHERcomputational */ /* ===================================================================== */ /* Subroutine */ int dstein_(integer *n, doublereal *d__, doublereal *e, integer *m, doublereal *w, integer *iblock, integer *isplit, doublereal *z__, integer *ldz, doublereal *work, integer *iwork, integer *ifail, integer *info) { /* System generated locals */ integer z_dim1, z_offset, i__1, i__2, i__3; doublereal d__1, d__2, d__3, d__4, d__5; /* Local variables */ integer jblk, nblk; extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); integer jmax; extern doublereal dnrm2_(integer *, doublereal *, integer *); integer i__, j; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); integer iseed[4], gpind, iinfo; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer b1; extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); integer j1; doublereal ortol; integer indrv1, indrv2, indrv3, indrv4, indrv5, bn; extern doublereal dlamch_(char *); extern /* Subroutine */ int dlagtf_(integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer * , integer *); doublereal xj; extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dlagts_( integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *); integer nrmchk; extern /* Subroutine */ int dlarnv_(integer *, integer *, integer *, doublereal *); integer blksiz; doublereal onenrm, dtpcrt, pertol, scl, eps, sep, nrm, tol; integer its; doublereal xjm, ztr, eps1; /* -- LAPACK computational 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 */ /* ===================================================================== */ /* Test the input parameters. */ /* Parameter adjustments */ --d__; --e; --w; --iblock; --isplit; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --work; --iwork; --ifail; /* Function Body */ *info = 0; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { ifail[i__] = 0; /* L10: */ } if (*n < 0) { *info = -1; } else if (*m < 0 || *m > *n) { *info = -4; } else if (*ldz < f2cmax(1,*n)) { *info = -9; } else { i__1 = *m; for (j = 2; j <= i__1; ++j) { if (iblock[j] < iblock[j - 1]) { *info = -6; goto L30; } if (iblock[j] == iblock[j - 1] && w[j] < w[j - 1]) { *info = -5; goto L30; } /* L20: */ } L30: ; } if (*info != 0) { i__1 = -(*info); xerbla_("DSTEIN", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0 || *m == 0) { return 0; } else if (*n == 1) { z__[z_dim1 + 1] = 1.; return 0; } /* Get machine constants. */ eps = dlamch_("Precision"); /* Initialize seed for random number generator DLARNV. */ for (i__ = 1; i__ <= 4; ++i__) { iseed[i__ - 1] = 1; /* L40: */ } /* Initialize pointers. */ indrv1 = 0; indrv2 = indrv1 + *n; indrv3 = indrv2 + *n; indrv4 = indrv3 + *n; indrv5 = indrv4 + *n; /* Compute eigenvectors of matrix blocks. */ j1 = 1; i__1 = iblock[*m]; for (nblk = 1; nblk <= i__1; ++nblk) { /* Find starting and ending indices of block nblk. */ if (nblk == 1) { b1 = 1; } else { b1 = isplit[nblk - 1] + 1; } bn = isplit[nblk]; blksiz = bn - b1 + 1; if (blksiz == 1) { goto L60; } gpind = j1; /* Compute reorthogonalization criterion and stopping criterion. */ onenrm = (d__1 = d__[b1], abs(d__1)) + (d__2 = e[b1], abs(d__2)); /* Computing MAX */ d__3 = onenrm, d__4 = (d__1 = d__[bn], abs(d__1)) + (d__2 = e[bn - 1], abs(d__2)); onenrm = f2cmax(d__3,d__4); i__2 = bn - 1; for (i__ = b1 + 1; i__ <= i__2; ++i__) { /* Computing MAX */ d__4 = onenrm, d__5 = (d__1 = d__[i__], abs(d__1)) + (d__2 = e[ i__ - 1], abs(d__2)) + (d__3 = e[i__], abs(d__3)); onenrm = f2cmax(d__4,d__5); /* L50: */ } ortol = onenrm * .001; dtpcrt = sqrt(.1 / blksiz); /* Loop through eigenvalues of block nblk. */ L60: jblk = 0; i__2 = *m; for (j = j1; j <= i__2; ++j) { if (iblock[j] != nblk) { j1 = j; goto L160; } ++jblk; xj = w[j]; /* Skip all the work if the block size is one. */ if (blksiz == 1) { work[indrv1 + 1] = 1.; goto L120; } /* If eigenvalues j and j-1 are too close, add a relatively */ /* small perturbation. */ if (jblk > 1) { eps1 = (d__1 = eps * xj, abs(d__1)); pertol = eps1 * 10.; sep = xj - xjm; if (sep < pertol) { xj = xjm + pertol; } } its = 0; nrmchk = 0; /* Get random starting vector. */ dlarnv_(&c__2, iseed, &blksiz, &work[indrv1 + 1]); /* Copy the matrix T so it won't be destroyed in factorization. */ dcopy_(&blksiz, &d__[b1], &c__1, &work[indrv4 + 1], &c__1); i__3 = blksiz - 1; dcopy_(&i__3, &e[b1], &c__1, &work[indrv2 + 2], &c__1); i__3 = blksiz - 1; dcopy_(&i__3, &e[b1], &c__1, &work[indrv3 + 1], &c__1); /* Compute LU factors with partial pivoting ( PT = LU ) */ tol = 0.; dlagtf_(&blksiz, &work[indrv4 + 1], &xj, &work[indrv2 + 2], &work[ indrv3 + 1], &tol, &work[indrv5 + 1], &iwork[1], &iinfo); /* Update iteration count. */ L70: ++its; if (its > 5) { goto L100; } /* Normalize and scale the righthand side vector Pb. */ jmax = idamax_(&blksiz, &work[indrv1 + 1], &c__1); /* Computing MAX */ d__3 = eps, d__4 = (d__1 = work[indrv4 + blksiz], abs(d__1)); scl = blksiz * onenrm * f2cmax(d__3,d__4) / (d__2 = work[indrv1 + jmax], abs(d__2)); dscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1); /* Solve the system LU = Pb. */ dlagts_(&c_n1, &blksiz, &work[indrv4 + 1], &work[indrv2 + 2], & work[indrv3 + 1], &work[indrv5 + 1], &iwork[1], &work[ indrv1 + 1], &tol, &iinfo); /* Reorthogonalize by modified Gram-Schmidt if eigenvalues are */ /* close enough. */ if (jblk == 1) { goto L90; } if ((d__1 = xj - xjm, abs(d__1)) > ortol) { gpind = j; } if (gpind != j) { i__3 = j - 1; for (i__ = gpind; i__ <= i__3; ++i__) { ztr = -ddot_(&blksiz, &work[indrv1 + 1], &c__1, &z__[b1 + i__ * z_dim1], &c__1); daxpy_(&blksiz, &ztr, &z__[b1 + i__ * z_dim1], &c__1, & work[indrv1 + 1], &c__1); /* L80: */ } } /* Check the infinity norm of the iterate. */ L90: jmax = idamax_(&blksiz, &work[indrv1 + 1], &c__1); nrm = (d__1 = work[indrv1 + jmax], abs(d__1)); /* Continue for additional iterations after norm reaches */ /* stopping criterion. */ if (nrm < dtpcrt) { goto L70; } ++nrmchk; if (nrmchk < 3) { goto L70; } goto L110; /* If stopping criterion was not satisfied, update info and */ /* store eigenvector number in array ifail. */ L100: ++(*info); ifail[*info] = j; /* Accept iterate as jth eigenvector. */ L110: scl = 1. / dnrm2_(&blksiz, &work[indrv1 + 1], &c__1); jmax = idamax_(&blksiz, &work[indrv1 + 1], &c__1); if (work[indrv1 + jmax] < 0.) { scl = -scl; } dscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1); L120: i__3 = *n; for (i__ = 1; i__ <= i__3; ++i__) { z__[i__ + j * z_dim1] = 0.; /* L130: */ } i__3 = blksiz; for (i__ = 1; i__ <= i__3; ++i__) { z__[b1 + i__ - 1 + j * z_dim1] = work[indrv1 + i__]; /* L140: */ } /* Save the shift to check eigenvalue spacing at next */ /* iteration. */ xjm = xj; /* L150: */ } L160: ; } return 0; /* End of DSTEIN */ } /* dstein_ */