#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 DLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DLAED0 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, */ /* WORK, IWORK, INFO ) */ /* INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ */ /* INTEGER IWORK( * ) */ /* DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), */ /* $ WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DLAED0 computes all eigenvalues and corresponding eigenvectors of a */ /* > symmetric tridiagonal matrix using the divide and conquer method. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] ICOMPQ */ /* > \verbatim */ /* > ICOMPQ is INTEGER */ /* > = 0: Compute eigenvalues only. */ /* > = 1: Compute eigenvectors of original dense symmetric matrix */ /* > also. On entry, Q contains the orthogonal matrix used */ /* > to reduce the original matrix to tridiagonal form. */ /* > = 2: Compute eigenvalues and eigenvectors of tridiagonal */ /* > matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] QSIZ */ /* > \verbatim */ /* > QSIZ is INTEGER */ /* > The dimension of the orthogonal matrix used to reduce */ /* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] D */ /* > \verbatim */ /* > D is DOUBLE PRECISION array, dimension (N) */ /* > On entry, the main diagonal of the tridiagonal matrix. */ /* > On exit, its eigenvalues. */ /* > \endverbatim */ /* > */ /* > \param[in] E */ /* > \verbatim */ /* > E is DOUBLE PRECISION array, dimension (N-1) */ /* > The off-diagonal elements of the tridiagonal matrix. */ /* > On exit, E has been destroyed. */ /* > \endverbatim */ /* > */ /* > \param[in,out] Q */ /* > \verbatim */ /* > Q is DOUBLE PRECISION array, dimension (LDQ, N) */ /* > On entry, Q must contain an N-by-N orthogonal matrix. */ /* > If ICOMPQ = 0 Q is not referenced. */ /* > If ICOMPQ = 1 On entry, Q is a subset of the columns of the */ /* > orthogonal matrix used to reduce the full */ /* > matrix to tridiagonal form corresponding to */ /* > the subset of the full matrix which is being */ /* > decomposed at this time. */ /* > If ICOMPQ = 2 On entry, Q will be the identity matrix. */ /* > On exit, Q contains the eigenvectors of the */ /* > tridiagonal matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] LDQ */ /* > \verbatim */ /* > LDQ is INTEGER */ /* > The leading dimension of the array Q. If eigenvectors are */ /* > desired, then LDQ >= f2cmax(1,N). In any case, LDQ >= 1. */ /* > \endverbatim */ /* > */ /* > \param[out] QSTORE */ /* > \verbatim */ /* > QSTORE is DOUBLE PRECISION array, dimension (LDQS, N) */ /* > Referenced only when ICOMPQ = 1. Used to store parts of */ /* > the eigenvector matrix when the updating matrix multiplies */ /* > take place. */ /* > \endverbatim */ /* > */ /* > \param[in] LDQS */ /* > \verbatim */ /* > LDQS is INTEGER */ /* > The leading dimension of the array QSTORE. If ICOMPQ = 1, */ /* > then LDQS >= f2cmax(1,N). In any case, LDQS >= 1. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, */ /* > If ICOMPQ = 0 or 1, the dimension of WORK must be at least */ /* > 1 + 3*N + 2*N*lg N + 3*N**2 */ /* > ( lg( N ) = smallest integer k */ /* > such that 2^k >= N ) */ /* > If ICOMPQ = 2, the dimension of WORK must be at least */ /* > 4*N + N**2. */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, */ /* > If ICOMPQ = 0 or 1, the dimension of IWORK must be at least */ /* > 6 + 6*N + 5*N*lg N. */ /* > ( lg( N ) = smallest integer k */ /* > such that 2^k >= N ) */ /* > If ICOMPQ = 2, the dimension of IWORK must be at least */ /* > 3 + 5*N. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit. */ /* > < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > > 0: The algorithm failed to compute an eigenvalue while */ /* > working on the submatrix lying in rows and columns */ /* > INFO/(N+1) through mod(INFO,N+1). */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup auxOTHERcomputational */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Jeff Rutter, Computer Science Division, University of California */ /* > at Berkeley, USA */ /* ===================================================================== */ /* Subroutine */ int dlaed0_(integer *icompq, integer *qsiz, integer *n, doublereal *d__, doublereal *e, doublereal *q, integer *ldq, doublereal *qstore, integer *ldqs, doublereal *work, integer *iwork, integer *info) { /* System generated locals */ integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2; doublereal d__1; /* Local variables */ doublereal temp; integer curr, i__, j, k; extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); integer iperm; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer indxq, iwrem; extern /* Subroutine */ int dlaed1_(integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *); integer iqptr; extern /* Subroutine */ int dlaed7_(integer *, integer *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, integer *); integer tlvls, iq; extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *); integer igivcl; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); integer igivnm, submat, curprb, subpbs, igivpt; extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *); integer curlvl, matsiz, iprmpt, smlsiz, lgn, msd2, smm1, spm1, spm2; /* -- 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; q_dim1 = *ldq; q_offset = 1 + q_dim1 * 1; q -= q_offset; qstore_dim1 = *ldqs; qstore_offset = 1 + qstore_dim1 * 1; qstore -= qstore_offset; --work; --iwork; /* Function Body */ *info = 0; if (*icompq < 0 || *icompq > 2) { *info = -1; } else if (*icompq == 1 && *qsiz < f2cmax(0,*n)) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ldq < f2cmax(1,*n)) { *info = -7; } else if (*ldqs < f2cmax(1,*n)) { *info = -9; } if (*info != 0) { i__1 = -(*info); xerbla_("DLAED0", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } smlsiz = ilaenv_(&c__9, "DLAED0", " ", &c__0, &c__0, &c__0, &c__0, ( ftnlen)6, (ftnlen)1); /* Determine the size and placement of the submatrices, and save in */ /* the leading elements of IWORK. */ iwork[1] = *n; subpbs = 1; tlvls = 0; L10: if (iwork[subpbs] > smlsiz) { for (j = subpbs; j >= 1; --j) { iwork[j * 2] = (iwork[j] + 1) / 2; iwork[(j << 1) - 1] = iwork[j] / 2; /* L20: */ } ++tlvls; subpbs <<= 1; goto L10; } i__1 = subpbs; for (j = 2; j <= i__1; ++j) { iwork[j] += iwork[j - 1]; /* L30: */ } /* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */ /* using rank-1 modifications (cuts). */ spm1 = subpbs - 1; i__1 = spm1; for (i__ = 1; i__ <= i__1; ++i__) { submat = iwork[i__] + 1; smm1 = submat - 1; d__[smm1] -= (d__1 = e[smm1], abs(d__1)); d__[submat] -= (d__1 = e[smm1], abs(d__1)); /* L40: */ } indxq = (*n << 2) + 3; if (*icompq != 2) { /* Set up workspaces for eigenvalues only/accumulate new vectors */ /* routine */ temp = log((doublereal) (*n)) / log(2.); lgn = (integer) temp; if (pow_ii(&c__2, &lgn) < *n) { ++lgn; } if (pow_ii(&c__2, &lgn) < *n) { ++lgn; } iprmpt = indxq + *n + 1; iperm = iprmpt + *n * lgn; iqptr = iperm + *n * lgn; igivpt = iqptr + *n + 2; igivcl = igivpt + *n * lgn; igivnm = 1; iq = igivnm + (*n << 1) * lgn; /* Computing 2nd power */ i__1 = *n; iwrem = iq + i__1 * i__1 + 1; /* Initialize pointers */ i__1 = subpbs; for (i__ = 0; i__ <= i__1; ++i__) { iwork[iprmpt + i__] = 1; iwork[igivpt + i__] = 1; /* L50: */ } iwork[iqptr] = 1; } /* Solve each submatrix eigenproblem at the bottom of the divide and */ /* conquer tree. */ curr = 0; i__1 = spm1; for (i__ = 0; i__ <= i__1; ++i__) { if (i__ == 0) { submat = 1; matsiz = iwork[1]; } else { submat = iwork[i__] + 1; matsiz = iwork[i__ + 1] - iwork[i__]; } if (*icompq == 2) { dsteqr_("I", &matsiz, &d__[submat], &e[submat], &q[submat + submat * q_dim1], ldq, &work[1], info); if (*info != 0) { goto L130; } } else { dsteqr_("I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 + iwork[iqptr + curr]], &matsiz, &work[1], info); if (*info != 0) { goto L130; } if (*icompq == 1) { dgemm_("N", "N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat * q_dim1 + 1], ldq, &work[iq - 1 + iwork[iqptr + curr]], &matsiz, &c_b24, &qstore[submat * qstore_dim1 + 1], ldqs); } /* Computing 2nd power */ i__2 = matsiz; iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; ++curr; } k = 1; i__2 = iwork[i__ + 1]; for (j = submat; j <= i__2; ++j) { iwork[indxq + j] = k; ++k; /* L60: */ } /* L70: */ } /* Successively merge eigensystems of adjacent submatrices */ /* into eigensystem for the corresponding larger matrix. */ /* while ( SUBPBS > 1 ) */ curlvl = 1; L80: if (subpbs > 1) { spm2 = subpbs - 2; i__1 = spm2; for (i__ = 0; i__ <= i__1; i__ += 2) { if (i__ == 0) { submat = 1; matsiz = iwork[2]; msd2 = iwork[1]; curprb = 0; } else { submat = iwork[i__] + 1; matsiz = iwork[i__ + 2] - iwork[i__]; msd2 = matsiz / 2; ++curprb; } /* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */ /* into an eigensystem of size MATSIZ. */ /* DLAED1 is used only for the full eigensystem of a tridiagonal */ /* matrix. */ /* DLAED7 handles the cases in which eigenvalues only or eigenvalues */ /* and eigenvectors of a full symmetric matrix (which was reduced to */ /* tridiagonal form) are desired. */ if (*icompq == 2) { dlaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1], ldq, &iwork[indxq + submat], &e[submat + msd2 - 1], & msd2, &work[1], &iwork[subpbs + 1], info); } else { dlaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[ submat], &qstore[submat * qstore_dim1 + 1], ldqs, & iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, & work[iq], &iwork[iqptr], &iwork[iprmpt], &iwork[iperm] , &iwork[igivpt], &iwork[igivcl], &work[igivnm], & work[iwrem], &iwork[subpbs + 1], info); } if (*info != 0) { goto L130; } iwork[i__ / 2 + 1] = iwork[i__ + 2]; /* L90: */ } subpbs /= 2; ++curlvl; goto L80; } /* end while */ /* Re-merge the eigenvalues/vectors which were deflated at the final */ /* merge step. */ if (*icompq == 1) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { j = iwork[indxq + i__]; work[i__] = d__[j]; dcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1], &c__1); /* L100: */ } dcopy_(n, &work[1], &c__1, &d__[1], &c__1); } else if (*icompq == 2) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { j = iwork[indxq + i__]; work[i__] = d__[j]; dcopy_(n, &q[j * q_dim1 + 1], &c__1, &work[*n * i__ + 1], &c__1); /* L110: */ } dcopy_(n, &work[1], &c__1, &d__[1], &c__1); dlacpy_("A", n, n, &work[*n + 1], n, &q[q_offset], ldq); } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { j = iwork[indxq + i__]; work[i__] = d__[j]; /* L120: */ } dcopy_(n, &work[1], &c__1, &d__[1], &c__1); } goto L140; L130: *info = submat * (*n + 1) + submat + matsiz - 1; L140: return 0; /* End of DLAED0 */ } /* dlaed0_ */