/** ======================================================================* NIST Guide to Available Math Software.* Fullsource for module SSYEVX.C from package CLAPACK.* Retrieved from NETLIB on Fri Mar 10 14:23:44 2000.* ======================================================================*/#include <f2c.h>/* Subroutine */ int ssyevx_(char *jobz, char *range, char *uplo, integer *n, 	real *a, integer *lda, real *vl, real *vu, integer *il, integer *iu, 	real *abstol, integer *m, real *w, real *z, integer *ldz, real *work, 	integer *lwork, integer *iwork, integer *ifail, integer *info){/*  -- LAPACK driver routine (version 2.0) --          Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,          Courant Institute, Argonne National Lab, and Rice University          September 30, 1994       Purpose       =======       SSYEVX computes selected eigenvalues and, optionally, eigenvectors       of a real symmetric matrix A.  Eigenvalues and eigenvectors can be       selected by specifying either a range of values or a range of indices       for the desired eigenvalues.       Arguments       =========       JOBZ    (input) CHARACTER*1               = 'N':  Compute eigenvalues only;               = 'V':  Compute eigenvalues and eigenvectors.       RANGE   (input) CHARACTER*1               = 'A': all eigenvalues will be found.               = 'V': all eigenvalues in the half-open interval (VL,VU]                      will be found.               = 'I': the IL-th through IU-th eigenvalues will be found.       UPLO    (input) CHARACTER*1               = 'U':  Upper triangle of A is stored;               = 'L':  Lower triangle of A is stored.       N       (input) INTEGER               The order of the matrix A.  N >= 0.       A       (input/output) REAL array, dimension (LDA, N)               On entry, the symmetric matrix A.  If UPLO = 'U', the               leading N-by-N upper triangular part of A contains the               upper triangular part of the matrix A.  If UPLO = 'L',               the leading N-by-N lower triangular part of A contains               the lower triangular part of the matrix A.               On exit, the lower triangle (if UPLO='L') or the upper               triangle (if UPLO='U') of A, including the diagonal, is               destroyed.       LDA     (input) INTEGER               The leading dimension of the array A.  LDA >= max(1,N).       VL      (input) REAL       VU      (input) REAL               If RANGE='V', the lower and upper bounds of the interval to               be searched for eigenvalues. VL < VU.               Not referenced if RANGE = 'A' or 'I'.       IL      (input) INTEGER       IU      (input) INTEGER               If RANGE='I', the indices (in ascending order) of the               smallest and largest eigenvalues to be returned.               1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.               Not referenced if RANGE = 'A' or 'V'.       ABSTOL  (input) REAL               The absolute error tolerance for the eigenvalues.               An approximate eigenvalue is accepted as converged               when it is determined to lie in an interval [a,b]               of width less than or equal to                       ABSTOL + EPS *   max( |a|,|b| ) ,               where EPS is the machine precision.  If ABSTOL is less than               or equal to zero, then  EPS*|T|  will be used in its place,               where |T| is the 1-norm of the tridiagonal matrix obtained               by reducing A to tridiagonal form.               Eigenvalues will be computed most accurately when ABSTOL is               set to twice the underflow threshold 2*SLAMCH('S'), not zero.               If this routine returns with INFO>0, indicating that some               eigenvectors did not converge, try setting ABSTOL to               2*SLAMCH('S').               See "Computing Small Singular Values of Bidiagonal Matrices               with Guaranteed High Relative Accuracy," by Demmel and               Kahan, LAPACK Working Note #3.       M       (output) INTEGER               The total number of eigenvalues found.  0 <= M <= N.               If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.       W       (output) REAL array, dimension (N)               On normal exit, the first M elements contain the selected               eigenvalues in ascending order.       Z       (output) REAL array, dimension (LDZ, max(1,M))               If JOBZ = 'V', then if INFO = 0, the first M columns of Z               contain the orthonormal eigenvectors of the matrix A               corresponding to the selected eigenvalues, with the i-th               column of Z holding the eigenvector associated with W(i).               If an eigenvector fails to converge, then that column of Z               contains the latest approximation to the eigenvector, and the               index of the eigenvector is returned in IFAIL.               If JOBZ = 'N', then Z is not referenced.               Note: the user must ensure that at least max(1,M) columns are               supplied in the array Z; if RANGE = 'V', the exact value of M               is not known in advance and an upper bound must be used.       LDZ     (input) INTEGER               The leading dimension of the array Z.  LDZ >= 1, and if               JOBZ = 'V', LDZ >= max(1,N).       WORK    (workspace/output) REAL array, dimension (LWORK)               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.       LWORK   (input) INTEGER               The length of the array WORK.  LWORK >= max(1,8*N).               For optimal efficiency, LWORK >= (NB+3)*N,               where NB is the blocksize for SSYTRD returned by ILAENV.       IWORK   (workspace) INTEGER array, dimension (5*N)       IFAIL   (output) INTEGER array, dimension (N)               If JOBZ = 'V', then if INFO = 0, the first M elements of               IFAIL are zero.  If INFO > 0, then IFAIL contains the               indices of the eigenvectors that failed to converge.               If JOBZ = 'N', then IFAIL is not referenced.       INFO    (output) 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.                     Their indices are stored in array IFAIL.      =====================================================================          Test the input parameters.          Parameter adjustments          Function Body */    /* Table of constant values */    static integer c__1 = 1;        /* System generated locals */    integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2;    real r__1, r__2;    /* Builtin functions */    double sqrt(doublereal);    /* Local variables */    static integer indd, inde;    static real anrm;    static integer imax;    static real rmin, rmax;    static integer lopt, itmp1, i, j, indee;    static real sigma;    extern logical lsame_(char *, char *);    static integer iinfo;    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);    static char order[1];    static logical lower;    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 	    integer *), sswap_(integer *, real *, integer *, real *, integer *	    );    static logical wantz;    static integer jj;    static logical alleig, indeig;    static integer iscale, indibl;    static logical valeig;    extern doublereal slamch_(char *);    static real safmin;    extern /* Subroutine */ int xerbla_(char *, integer *);    static real abstll, bignum;    static integer indtau, indisp, indiwo, indwkn;    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 	    integer *, real *, integer *);    static integer indwrk;    extern /* Subroutine */ int sstein_(integer *, real *, real *, integer *, 	    real *, integer *, integer *, real *, integer *, real *, integer *	    , integer *, integer *), ssterf_(integer *, real *, real *, 	    integer *);    static integer llwrkn, llwork, nsplit;    static real smlnum;    extern doublereal slansy_(char *, char *, integer *, real *, integer *, 	    real *);    extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *, 	    real *, integer *, integer *, real *, real *, real *, integer *, 	    integer *, real *, integer *, integer *, real *, integer *, 	    integer *), sorgtr_(char *, integer *, real *, 	    integer *, real *, real *, integer *, integer *), ssteqr_(	    char *, integer *, real *, real *, real *, integer *, real *, 	    integer *), sormtr_(char *, char *, char *, integer *, 	    integer *, real *, integer *, real *, real *, integer *, real *, 	    integer *, integer *), ssytrd_(char *, 	    integer *, real *, integer *, real *, real *, real *, real *, 	    integer *, integer *);    static real eps, vll, vuu, tmp1;#define W(I) w[(I)-1]#define WORK(I) work[(I)-1]#define IWORK(I) iwork[(I)-1]#define IFAIL(I) ifail[(I)-1]#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]#define Z(I,J) z[(I)-1 + ((J)-1)* ( *ldz)]    lower = lsame_(uplo, "L");    wantz = lsame_(jobz, "V");    alleig = lsame_(range, "A");    valeig = lsame_(range, "V");    indeig = lsame_(range, "I");    *info = 0;    if (! (wantz || lsame_(jobz, "N"))) {	*info = -1;    } else if (! (alleig || valeig || indeig)) {	*info = -2;    } else if (! (lower || lsame_(uplo, "U"))) {	*info = -3;    } else if (*n < 0) {	*info = -4;    } else if (*lda < max(1,*n)) {	*info = -6;    } else if (valeig && *n > 0 && *vu <= *vl) {	*info = -8;    } else if (indeig && *il < 1) {	*info = -9;    } else if (indeig && (*iu < min(*n,*il) || *iu > *n)) {	*info = -10;    } else if (*ldz < 1 || wantz && *ldz < *n) {	*info = -15;    } else /* if(complicated condition) */ {/* Computing MAX */	i__1 = 1, i__2 = *n << 3;	if (*lwork < max(i__1,i__2)) {	    *info = -17;	}    }    if (*info != 0) {	i__1 = -(*info);	xerbla_("SSYEVX", &i__1);	return 0;    }/*     Quick return if possible */    *m = 0;    if (*n == 0) {	WORK(1) = 1.f;	return 0;    }    if (*n == 1) {	WORK(1) = 7.f;	if (alleig || indeig) {	    *m = 1;	    W(1) = A(1,1);	} else {	    if (*vl < A(1,1) && *vu >= A(1,1)) {		*m = 1;		W(1) = A(1,1);	    }	}	if (wantz) {	    Z(1,1) = 1.f;	}	return 0;    }/*     Get machine constants. */    safmin = slamch_("Safe minimum");    eps = slamch_("Precision");    smlnum = safmin / eps;    bignum = 1.f / smlnum;    rmin = sqrt(smlnum);/* Computing MIN */    r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin));    rmax = dmin(r__1,r__2);/*     Scale matrix to allowable range, if necessary. */    iscale = 0;    abstll = *abstol;    if (valeig) {	vll = *vl;	vuu = *vu;    }    anrm = slansy_("M", uplo, n, &A(1,1), lda, &WORK(1));    if (anrm > 0.f && anrm < rmin) {	iscale = 1;	sigma = rmin / anrm;    } else if (anrm > rmax) {	iscale = 1;	sigma = rmax / anrm;    }    if (iscale == 1) {	if (lower) {	    i__1 = *n;	    for (j = 1; j <= *n; ++j) {		i__2 = *n - j + 1;		sscal_(&i__2, &sigma, &A(j,j), &c__1);/* L10: */	    }	} else {	    i__1 = *n;	    for (j = 1; j <= *n; ++j) {		sscal_(&j, &sigma, &A(1,j), &c__1);/* L20: */	    }	}	if (*abstol > 0.f) {	    abstll = *abstol * sigma;	}	if (valeig) {	    vll = *vl * sigma;	    vuu = *vu * sigma;	}    }/*     Call SSYTRD to reduce symmetric matrix to tridiagonal form. */    indtau = 1;    inde = indtau + *n;    indd = inde + *n;    indwrk = indd + *n;    llwork = *lwork - indwrk + 1;    ssytrd_(uplo, n, &A(1,1), lda, &WORK(indd), &WORK(inde), &WORK(	    indtau), &WORK(indwrk), &llwork, &iinfo);    lopt = *n * 3 + WORK(indwrk);/*     If all eigenvalues are desired and ABSTOL is less than or equal to          zero, then call SSTERF or SORGTR and SSTEQR.  If this fails for          some eigenvalue, then try SSTEBZ. */    if ((alleig || indeig && *il == 1 && *iu == *n) && *abstol <= 0.f) {	scopy_(n, &WORK(indd), &c__1, &W(1), &c__1);	indee = indwrk + (*n << 1);	if (! wantz) {	    i__1 = *n - 1;	    scopy_(&i__1, &WORK(inde), &c__1, &WORK(indee), &c__1);	    ssterf_(n, &W(1), &WORK(indee), info);	} else {	    slacpy_("A", n, n, &A(1,1), lda, &Z(1,1), ldz);	    sorgtr_(uplo, n, &Z(1,1), ldz, &WORK(indtau), &WORK(indwrk), 		    &llwork, &iinfo);	    i__1 = *n - 1;	    scopy_(&i__1, &WORK(inde), &c__1, &WORK(indee), &c__1);	    ssteqr_(jobz, n, &W(1), &WORK(indee), &Z(1,1), ldz, &WORK(		    indwrk), info);	    if (*info == 0) {		i__1 = *n;		for (i = 1; i <= *n; ++i) {		    IFAIL(i) = 0;/* L30: */		}	    }	}	if (*info == 0) {	    *m = *n;	    goto L40;	}	*info = 0;    }/*     Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN. */    if (wantz) {	*(unsigned char *)order = 'B';    } else {	*(unsigned char *)order = 'E';    }    indibl = 1;    indisp = indibl + *n;    indiwo = indisp + *n;    sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &WORK(indd), &WORK(	    inde), m, &nsplit, &W(1), &IWORK(indibl), &IWORK(indisp), &WORK(	    indwrk), &IWORK(indiwo), info);    if (wantz) {	sstein_(n, &WORK(indd), &WORK(inde), m, &W(1), &IWORK(indibl), &IWORK(		indisp), &Z(1,1), ldz, &WORK(indwrk), &IWORK(indiwo), &		IFAIL(1), info);/*        Apply orthogonal matrix used in reduction to tridiagonal             form to eigenvectors returned by SSTEIN. */	indwkn = inde;	llwrkn = *lwork - indwkn + 1;	sormtr_("L", uplo, "N", n, m, &A(1,1), lda, &WORK(indtau), &Z(1,1), ldz, &WORK(indwkn), &llwrkn, &iinfo);    }/*     If matrix was scaled, then rescale eigenvalues appropriately. */L40:    if (iscale == 1) {	if (*info == 0) {	    imax = *m;	} else {	    imax = *info - 1;	}	r__1 = 1.f / sigma;	sscal_(&imax, &r__1, &W(1), &c__1);    }/*     If eigenvalues are not in order, then sort them, along with          eigenvectors. */    if (wantz) {	i__1 = *m - 1;	for (j = 1; j <= *m-1; ++j) {	    i = 0;	    tmp1 = W(j);	    i__2 = *m;	    for (jj = j + 1; jj <= *m; ++jj) {		if (W(jj) < tmp1) {		    i = jj;		    tmp1 = W(jj);		}/* L50: */	    }	    if (i != 0) {		itmp1 = IWORK(indibl + i - 1);		W(i) = W(j);		IWORK(indibl + i - 1) = IWORK(indibl + j - 1);		W(j) = tmp1;		IWORK(indibl + j - 1) = itmp1;		sswap_(n, &Z(1,i), &c__1, &Z(1,j), &			c__1);		if (*info != 0) {		    itmp1 = IFAIL(i);		    IFAIL(i) = IFAIL(j);		    IFAIL(j) = itmp1;		}	    }/* L60: */	}    }/*     Set WORK(1) to optimal workspace size.      Computing MAX */    i__1 = *n * 7;    WORK(1) = (real) max(i__1,lopt);    return 0;/*     End of SSYEVX */} /* ssyevx_ */