#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int chpevx_(char *jobz, char *range, char *uplo, integer *n, complex *ap, real *vl, real *vu, integer *il, integer *iu, real * abstol, integer *m, real *w, complex *z__, integer *ldz, complex * work, real *rwork, integer *iwork, integer *ifail, integer *info) { /* -- LAPACK driver routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= CHPEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. Eigenvalues/vectors 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. AP (input/output) COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. 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 AP 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) If INFO = 0, the selected eigenvalues in ascending order. Z (output) COMPLEX 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) COMPLEX array, dimension (2*N) RWORK (workspace) REAL array, dimension (7*N) 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 */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer 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 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]; extern /* Subroutine */ int cswap_(integer *, complex *, integer *, complex *, integer *), scopy_(integer *, real *, integer *, real * , integer *); static logical wantz; static integer jj; static logical alleig, indeig; static integer iscale, indibl; extern doublereal clanhp_(char *, char *, integer *, complex *, real *); static logical valeig; extern doublereal slamch_(char *); extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer *); static real safmin; extern /* Subroutine */ int xerbla_(char *, integer *); static real abstll, bignum; static integer indiwk, indisp, indtau; extern /* Subroutine */ int chptrd_(char *, integer *, complex *, real *, real *, complex *, integer *), cstein_(integer *, real *, real *, integer *, real *, integer *, integer *, complex *, integer *, real *, integer *, integer *, integer *); static integer indrwk, indwrk; extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, complex *, integer *, real *, integer *), cupgtr_(char *, integer *, complex *, complex *, complex *, integer *, complex *, integer *), ssterf_(integer *, real *, real *, integer *); static integer nsplit; extern /* Subroutine */ int cupmtr_(char *, char *, char *, integer *, integer *, complex *, complex *, complex *, integer *, complex *, integer *); static real smlnum; extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *, real *, integer *, integer *, real *, real *, real *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *); static real eps, vll, vuu, tmp1; #define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1 #define z___ref(a_1,a_2) z__[z___subscr(a_1,a_2)] --ap; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --work; --rwork; --iwork; --ifail; /* Function Body */ 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 (! (lsame_(uplo, "L") || lsame_(uplo, "U"))) { *info = -3; } else if (*n < 0) { *info = -4; } else { if (valeig) { if (*n > 0 && *vu <= *vl) { *info = -7; } } else if (indeig) { if (*il < 1 || *il > max(1,*n)) { *info = -8; } else if (*iu < min(*n,*il) || *iu > *n) { *info = -9; } } } if (*info == 0) { if (*ldz < 1 || wantz && *ldz < *n) { *info = -14; } } if (*info != 0) { i__1 = -(*info); xerbla_("CHPEVX", &i__1); return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { return 0; } if (*n == 1) { if (alleig || indeig) { *m = 1; w[1] = ap[1].r; } else { if (*vl < ap[1].r && *vu >= ap[1].r) { *m = 1; w[1] = ap[1].r; } } if (wantz) { i__1 = z___subscr(1, 1); z__[i__1].r = 1.f, z__[i__1].i = 0.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; } else { vll = 0.f; vuu = 0.f; } anrm = clanhp_("M", uplo, n, &ap[1], &rwork[1]); if (anrm > 0.f && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { i__1 = *n * (*n + 1) / 2; csscal_(&i__1, &sigma, &ap[1], &c__1); if (*abstol > 0.f) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Call CHPTRD to reduce Hermitian packed matrix to tridiagonal form. */ indd = 1; inde = indd + *n; indrwk = inde + *n; indtau = 1; indwrk = indtau + *n; chptrd_(uplo, n, &ap[1], &rwork[indd], &rwork[inde], &work[indtau], & iinfo); /* If all eigenvalues are desired and ABSTOL is less than or equal to zero, then call SSTERF or CUPGTR and CSTEQR. If this fails for some eigenvalue, then try SSTEBZ. */ if ((alleig || indeig && *il == 1 && *iu == *n) && *abstol <= 0.f) { scopy_(n, &rwork[indd], &c__1, &w[1], &c__1); indee = indrwk + (*n << 1); if (! wantz) { i__1 = *n - 1; scopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); ssterf_(n, &w[1], &rwork[indee], info); } else { cupgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, & work[indwrk], &iinfo); i__1 = *n - 1; scopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); csteqr_(jobz, n, &w[1], &rwork[indee], &z__[z_offset], ldz, & rwork[indrwk], info); if (*info == 0) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { ifail[i__] = 0; /* L10: */ } } } if (*info == 0) { *m = *n; goto L20; } *info = 0; } /* Otherwise, call SSTEBZ and, if eigenvectors are desired, CSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwk = indisp + *n; sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &rwork[indd], & rwork[inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], & rwork[indrwk], &iwork[indiwk], info); if (wantz) { cstein_(n, &rwork[indd], &rwork[inde], m, &w[1], &iwork[indibl], & iwork[indisp], &z__[z_offset], ldz, &rwork[indrwk], &iwork[ indiwk], &ifail[1], info); /* Apply unitary matrix used in reduction to tridiagonal form to eigenvectors returned by CSTEIN. */ indwrk = indtau + *n; cupmtr_("L", uplo, "N", n, m, &ap[1], &work[indtau], &z__[z_offset], ldz, &work[indwrk], info); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L20: 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 <= i__1; ++j) { i__ = 0; tmp1 = w[j]; i__2 = *m; for (jj = j + 1; jj <= i__2; ++jj) { if (w[jj] < tmp1) { i__ = jj; tmp1 = w[jj]; } /* L30: */ } 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; cswap_(n, &z___ref(1, i__), &c__1, &z___ref(1, j), &c__1); if (*info != 0) { itmp1 = ifail[i__]; ifail[i__] = ifail[j]; ifail[j] = itmp1; } } /* L40: */ } } return 0; /* End of CHPEVX */ } /* chpevx_ */ #undef z___ref #undef z___subscr