#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int ssterf_(integer *n, real *d__, real *e, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SSTERF computes all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm. Arguments ========= N (input) INTEGER The order of the matrix. N >= 0. D (input/output) REAL array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order. E (input/output) REAL array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: the algorithm failed to find all of the eigenvalues in a total of 30*N iterations; if INFO = i, then i elements of E have not converged to zero. ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__0 = 0; static integer c__1 = 1; static real c_b32 = 1.f; /* System generated locals */ integer i__1; real r__1, r__2, r__3; /* Builtin functions */ double sqrt(doublereal), r_sign(real *, real *); /* Local variables */ static real c__; static integer i__, l, m; static real p, r__, s; static integer l1; static real bb, rt1, rt2, eps, rte; static integer lsv; static real eps2, oldc; static integer lend, jtot; extern /* Subroutine */ int slae2_(real *, real *, real *, real *, real *) ; static real gamma, alpha, sigma, anorm; extern doublereal slapy2_(real *, real *); static integer iscale; static real oldgam; extern doublereal slamch_(char *); static real safmin; extern /* Subroutine */ int xerbla_(char *, integer *); static real safmax; extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *); static integer lendsv; static real ssfmin; static integer nmaxit; static real ssfmax; extern doublereal slanst_(char *, integer *, real *, real *); extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *); --e; --d__; /* Function Body */ *info = 0; /* Quick return if possible */ if (*n < 0) { *info = -1; i__1 = -(*info); xerbla_("SSTERF", &i__1); return 0; } if (*n <= 1) { return 0; } /* Determine the unit roundoff for this environment. */ eps = slamch_("E"); /* Computing 2nd power */ r__1 = eps; eps2 = r__1 * r__1; safmin = slamch_("S"); safmax = 1.f / safmin; ssfmax = sqrt(safmax) / 3.f; ssfmin = sqrt(safmin) / eps2; /* Compute the eigenvalues of the tridiagonal matrix. */ nmaxit = *n * 30; sigma = 0.f; jtot = 0; /* Determine where the matrix splits and choose QL or QR iteration for each block, according to whether top or bottom diagonal element is smaller. */ l1 = 1; L10: if (l1 > *n) { goto L170; } if (l1 > 1) { e[l1 - 1] = 0.f; } i__1 = *n - 1; for (m = l1; m <= i__1; ++m) { if ((r__3 = e[m], dabs(r__3)) <= sqrt((r__1 = d__[m], dabs(r__1))) * sqrt((r__2 = d__[m + 1], dabs(r__2))) * eps) { e[m] = 0.f; goto L30; } /* L20: */ } m = *n; L30: l = l1; lsv = l; lend = m; lendsv = lend; l1 = m + 1; if (lend == l) { goto L10; } /* Scale submatrix in rows and columns L to LEND */ i__1 = lend - l + 1; anorm = slanst_("I", &i__1, &d__[l], &e[l]); iscale = 0; if (anorm > ssfmax) { iscale = 1; i__1 = lend - l + 1; slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, info); i__1 = lend - l; slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, info); } else if (anorm < ssfmin) { iscale = 2; i__1 = lend - l + 1; slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, info); i__1 = lend - l; slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, info); } i__1 = lend - 1; for (i__ = l; i__ <= i__1; ++i__) { /* Computing 2nd power */ r__1 = e[i__]; e[i__] = r__1 * r__1; /* L40: */ } /* Choose between QL and QR iteration */ if ((r__1 = d__[lend], dabs(r__1)) < (r__2 = d__[l], dabs(r__2))) { lend = lsv; l = lendsv; } if (lend >= l) { /* QL Iteration Look for small subdiagonal element. */ L50: if (l != lend) { i__1 = lend - 1; for (m = l; m <= i__1; ++m) { if ((r__2 = e[m], dabs(r__2)) <= eps2 * (r__1 = d__[m] * d__[ m + 1], dabs(r__1))) { goto L70; } /* L60: */ } } m = lend; L70: if (m < lend) { e[m] = 0.f; } p = d__[l]; if (m == l) { goto L90; } /* If remaining matrix is 2 by 2, use SLAE2 to compute its eigenvalues. */ if (m == l + 1) { rte = sqrt(e[l]); slae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2); d__[l] = rt1; d__[l + 1] = rt2; e[l] = 0.f; l += 2; if (l <= lend) { goto L50; } goto L150; } if (jtot == nmaxit) { goto L150; } ++jtot; /* Form shift. */ rte = sqrt(e[l]); sigma = (d__[l + 1] - p) / (rte * 2.f); r__ = slapy2_(&sigma, &c_b32); sigma = p - rte / (sigma + r_sign(&r__, &sigma)); c__ = 1.f; s = 0.f; gamma = d__[m] - sigma; p = gamma * gamma; /* Inner loop */ i__1 = l; for (i__ = m - 1; i__ >= i__1; --i__) { bb = e[i__]; r__ = p + bb; if (i__ != m - 1) { e[i__ + 1] = s * r__; } oldc = c__; c__ = p / r__; s = bb / r__; oldgam = gamma; alpha = d__[i__]; gamma = c__ * (alpha - sigma) - s * oldgam; d__[i__ + 1] = oldgam + (alpha - gamma); if (c__ != 0.f) { p = gamma * gamma / c__; } else { p = oldc * bb; } /* L80: */ } e[l] = s * p; d__[l] = sigma + gamma; goto L50; /* Eigenvalue found. */ L90: d__[l] = p; ++l; if (l <= lend) { goto L50; } goto L150; } else { /* QR Iteration Look for small superdiagonal element. */ L100: i__1 = lend + 1; for (m = l; m >= i__1; --m) { if ((r__2 = e[m - 1], dabs(r__2)) <= eps2 * (r__1 = d__[m] * d__[ m - 1], dabs(r__1))) { goto L120; } /* L110: */ } m = lend; L120: if (m > lend) { e[m - 1] = 0.f; } p = d__[l]; if (m == l) { goto L140; } /* If remaining matrix is 2 by 2, use SLAE2 to compute its eigenvalues. */ if (m == l - 1) { rte = sqrt(e[l - 1]); slae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2); d__[l] = rt1; d__[l - 1] = rt2; e[l - 1] = 0.f; l += -2; if (l >= lend) { goto L100; } goto L150; } if (jtot == nmaxit) { goto L150; } ++jtot; /* Form shift. */ rte = sqrt(e[l - 1]); sigma = (d__[l - 1] - p) / (rte * 2.f); r__ = slapy2_(&sigma, &c_b32); sigma = p - rte / (sigma + r_sign(&r__, &sigma)); c__ = 1.f; s = 0.f; gamma = d__[m] - sigma; p = gamma * gamma; /* Inner loop */ i__1 = l - 1; for (i__ = m; i__ <= i__1; ++i__) { bb = e[i__]; r__ = p + bb; if (i__ != m) { e[i__ - 1] = s * r__; } oldc = c__; c__ = p / r__; s = bb / r__; oldgam = gamma; alpha = d__[i__ + 1]; gamma = c__ * (alpha - sigma) - s * oldgam; d__[i__] = oldgam + (alpha - gamma); if (c__ != 0.f) { p = gamma * gamma / c__; } else { p = oldc * bb; } /* L130: */ } e[l - 1] = s * p; d__[l] = sigma + gamma; goto L100; /* Eigenvalue found. */ L140: d__[l] = p; --l; if (l >= lend) { goto L100; } goto L150; } /* Undo scaling if necessary */ L150: if (iscale == 1) { i__1 = lendsv - lsv + 1; slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], n, info); } if (iscale == 2) { i__1 = lendsv - lsv + 1; slascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], n, info); } /* Check for no convergence to an eigenvalue after a total of N*MAXIT iterations. */ if (jtot < nmaxit) { goto L10; } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { if (e[i__] != 0.f) { ++(*info); } /* L160: */ } goto L180; /* Sort eigenvalues in increasing order. */ L170: slasrt_("I", n, &d__[1], info); L180: return 0; /* End of SSTERF */ } /* ssterf_ */