/** ======================================================================* 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 sstein_(integer *n, real *d, real *e, integer *m, real *	w, integer *iblock, integer *isplit, real *z, integer *ldz, real *	work, integer *iwork, integer *ifail, integer *info){/*  -- LAPACK 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       =======       SSTEIN 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).       Arguments       =========       N       (input) INTEGER               The order of the matrix.  N >= 0.       D       (input) REAL array, dimension (N)               The n diagonal elements of the tridiagonal matrix T.       E       (input) REAL array, dimension (N)               The (n-1) subdiagonal elements of the tridiagonal matrix               T, in elements 1 to N-1.  E(N) need not be set.       M       (input) INTEGER               The number of eigenvectors to be found.  0 <= M <= N.       W       (input) REAL 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 SSTEBZ with ORDER = 'B' is expected here. )       IBLOCK  (input) 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 SSTEBZ is expected here. )       ISPLIT  (input) 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 SSTEBZ is expected here. )       Z       (output) REAL 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.       LDZ     (input) INTEGER               The leading dimension of the array Z.  LDZ >= max(1,N).       WORK    (workspace) REAL array, dimension (5*N)       IWORK   (workspace) INTEGER array, dimension (N)       IFAIL   (output) 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.       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                    in MAXITS iterations.  Their indices are stored in                    array IFAIL.       Internal Parameters       ===================       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.       =====================================================================          Test the input parameters.          Parameter adjustments          Function Body */    /* Table of constant values */    static integer c__2 = 2;    static integer c__1 = 1;    static integer c_n1 = -1;        /* System generated locals */    integer z_dim1, z_offset, i__1, i__2, i__3;    real r__1, r__2, r__3, r__4, r__5;    /* Builtin functions */    double sqrt(doublereal);    /* Local variables */    static integer jblk, nblk, jmax;    extern doublereal sdot_(integer *, real *, integer *, real *, integer *), 	    snrm2_(integer *, real *, integer *);    static integer i, j, iseed[4], gpind, iinfo;    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);    static integer b1;    extern doublereal sasum_(integer *, real *, integer *);    static integer j1;    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 	    integer *);    static real ortol;    extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, 	    real *, integer *);    static integer indrv1, indrv2, indrv3, indrv4, indrv5, bn;    static real xj;    extern doublereal slamch_(char *);    extern /* Subroutine */ int xerbla_(char *, integer *), slagtf_(	    integer *, real *, real *, real *, real *, real *, real *, 	    integer *, integer *);    static integer nrmchk;    extern integer isamax_(integer *, real *, integer *);    extern /* Subroutine */ int slagts_(integer *, integer *, real *, real *, 	    real *, real *, integer *, real *, real *, integer *);    static integer blksiz;    static real onenrm, pertol;    extern /* Subroutine */ int slarnv_(integer *, integer *, integer *, real 	    *);    static real stpcrt, scl, eps, ctr, sep, nrm, tol;    static integer its;    static real xjm, eps1;#define ISEED(I) iseed[(I)]#define D(I) d[(I)-1]#define E(I) e[(I)-1]#define W(I) w[(I)-1]#define IBLOCK(I) iblock[(I)-1]#define ISPLIT(I) isplit[(I)-1]#define WORK(I) work[(I)-1]#define IWORK(I) iwork[(I)-1]#define IFAIL(I) ifail[(I)-1]#define Z(I,J) z[(I)-1 + ((J)-1)* ( *ldz)]    *info = 0;    i__1 = *m;    for (i = 1; i <= *m; ++i) {	IFAIL(i) = 0;/* L10: */    }    if (*n < 0) {	*info = -1;    } else if (*m < 0 || *m > *n) {	*info = -4;    } else if (*ldz < max(1,*n)) {	*info = -9;    } else {	i__1 = *m;	for (j = 2; j <= *m; ++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_("SSTEIN", &i__1);	return 0;    }/*     Quick return if possible */    if (*n == 0 || *m == 0) {	return 0;    } else if (*n == 1) {	Z(1,1) = 1.f;	return 0;    }/*     Get machine constants. */    eps = slamch_("Precision");/*     Initialize seed for random number generator SLARNV. */    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 <= IBLOCK(*m); ++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 = b1;/*        Compute reorthogonalization criterion and stopping criterion. */	onenrm = (r__1 = D(b1), dabs(r__1)) + (r__2 = E(b1), dabs(r__2));/* Computing MAX */	r__3 = onenrm, r__4 = (r__1 = D(bn), dabs(r__1)) + (r__2 = E(bn - 1), 		dabs(r__2));	onenrm = dmax(r__3,r__4);	i__2 = bn - 1;	for (i = b1 + 1; i <= bn-1; ++i) {/* Computing MAX */	    r__4 = onenrm, r__5 = (r__1 = D(i), dabs(r__1)) + (r__2 = E(i - 1)		    , dabs(r__2)) + (r__3 = E(i), dabs(r__3));	    onenrm = dmax(r__4,r__5);/* L50: */	}	ortol = onenrm * .001f;	stpcrt = sqrt(.1f / blksiz);/*        Loop through eigenvalues of block nblk. */L60:	jblk = 0;	i__2 = *m;	for (j = j1; j <= *m; ++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.f;		goto L120;	    }/*           If eigenvalues j and j-1 are too close, add a relatively                small perturbation. */	    if (jblk > 1) {		eps1 = (r__1 = eps * xj, dabs(r__1));		pertol = eps1 * 10.f;		sep = xj - xjm;		if (sep < pertol) {		    xj = xjm + pertol;		}	    }	    its = 0;	    nrmchk = 0;/*           Get random starting vector. */	    slarnv_(&c__2, iseed, &blksiz, &WORK(indrv1 + 1));/*           Copy the matrix T so it won't be destroyed in factorization. */	    scopy_(&blksiz, &D(b1), &c__1, &WORK(indrv4 + 1), &c__1);	    i__3 = blksiz - 1;	    scopy_(&i__3, &E(b1), &c__1, &WORK(indrv2 + 2), &c__1);	    i__3 = blksiz - 1;	    scopy_(&i__3, &E(b1), &c__1, &WORK(indrv3 + 1), &c__1);/*           Compute LU factors with partial pivoting  ( PT = LU ) */	    tol = 0.f;	    slagtf_(&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.      Computing MAX */	    r__2 = eps, r__3 = (r__1 = WORK(indrv4 + blksiz), dabs(r__1));	    scl = blksiz * onenrm * dmax(r__2,r__3) / sasum_(&blksiz, &WORK(		    indrv1 + 1), &c__1);	    sscal_(&blksiz, &scl, &WORK(indrv1 + 1), &c__1);/*           Solve the system LU = Pb. */	    slagts_(&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 ((r__1 = xj - xjm, dabs(r__1)) > ortol) {		gpind = j;	    }	    if (gpind != j) {		i__3 = j - 1;		for (i = gpind; i <= j-1; ++i) {		    ctr = -(doublereal)sdot_(&blksiz, &WORK(indrv1 + 1), &			    c__1, &Z(b1,i), &c__1);		    saxpy_(&blksiz, &ctr, &Z(b1,i), &c__1, &WORK(			    indrv1 + 1), &c__1);/* L80: */		}	    }/*           Check the infinity norm of the iterate. */L90:	    jmax = isamax_(&blksiz, &WORK(indrv1 + 1), &c__1);	    nrm = (r__1 = WORK(indrv1 + jmax), dabs(r__1));/*           Continue for additional iterations after norm reaches                stopping criterion. */	    if (nrm < stpcrt) {		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.f / snrm2_(&blksiz, &WORK(indrv1 + 1), &c__1);	    jmax = isamax_(&blksiz, &WORK(indrv1 + 1), &c__1);	    if (WORK(indrv1 + jmax) < 0.f) {		scl = -(doublereal)scl;	    }	    sscal_(&blksiz, &scl, &WORK(indrv1 + 1), &c__1);L120:	    i__3 = *n;	    for (i = 1; i <= *n; ++i) {		Z(i,j) = 0.f;/* L130: */	    }	    i__3 = blksiz;	    for (i = 1; i <= blksiz; ++i) {		Z(b1+i-1,j) = WORK(indrv1 + i);/* L140: */	    }/*           Save the shift to check eigenvalue spacing at next                iteration. */	    xjm = xj;/* L150: */	}L160:	;    }    return 0;/*     End of SSTEIN */} /* sstein_ */