/* Subroutine */ int zheevx_(char *jobz, char *range, char *uplo, integer *n, doublecomplex *a, integer *lda, doublereal *vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer *m, doublereal * w, doublecomplex *z__, integer *ldz, doublecomplex *work, integer * lwork, doublereal *rwork, integer *iwork, integer *ifail, integer * info) { /* System generated locals */ integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2; doublereal d__1, d__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ integer i__, j, nb, jj; doublereal eps, vll, vuu, tmp1; integer indd, inde; doublereal anrm; integer imax; doublereal rmin, rmax; logical test; integer itmp1, indee; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal sigma; extern logical lsame_(char *, char *); integer iinfo; char order[1]; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); logical lower, wantz; extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); extern doublereal dlamch_(char *); logical alleig, indeig; integer iscale, indibl; logical valeig; doublereal safmin; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_( integer *, doublereal *, doublecomplex *, integer *); doublereal abstll, bignum; extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); integer indiwk, indisp, indtau; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, integer *), dstebz_(char *, char *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); integer indrwk, indwrk; extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublecomplex *, integer *, integer *); integer lwkmin; extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); integer llwork, nsplit; doublereal smlnum; extern /* Subroutine */ int zstein_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, integer *, integer *); integer lwkopt; logical lquery; extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, doublereal *, integer *), zungtr_(char *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *), zunmtr_(char *, char *, char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *); /* -- LAPACK driver routine (version 3.4.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* November 2011 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --rwork; --iwork; --ifail; /* Function Body */ lower = lsame_(uplo, "L"); wantz = lsame_(jobz, "V"); alleig = lsame_(range, "A"); valeig = lsame_(range, "V"); indeig = lsame_(range, "I"); lquery = *lwork == -1; *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) { if (*n > 0 && *vu <= *vl) { *info = -8; } } else if (indeig) { if (*il < 1 || *il > max(1,*n)) { *info = -9; } else if (*iu < min(*n,*il) || *iu > *n) { *info = -10; } } } if (*info == 0) { if (*ldz < 1 || wantz && *ldz < *n) { *info = -15; } } if (*info == 0) { if (*n <= 1) { lwkmin = 1; work[1].r = (doublereal) lwkmin; work[1].i = 0.; // , expr subst } else { lwkmin = *n << 1; nb = ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1); /* Computing MAX */ i__1 = nb; i__2 = ilaenv_(&c__1, "ZUNMTR", uplo, n, &c_n1, &c_n1, &c_n1); // , expr subst nb = max(i__1,i__2); /* Computing MAX */ i__1 = 1; i__2 = (nb + 1) * *n; // , expr subst lwkopt = max(i__1,i__2); work[1].r = (doublereal) lwkopt; work[1].i = 0.; // , expr subst } if (*lwork < lwkmin && ! lquery) { *info = -17; } } if (*info != 0) { i__1 = -(*info); xerbla_("ZHEEVX", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { return 0; } if (*n == 1) { if (alleig || indeig) { *m = 1; i__1 = a_dim1 + 1; w[1] = a[i__1].r; } else if (valeig) { i__1 = a_dim1 + 1; i__2 = a_dim1 + 1; if (*vl < a[i__1].r && *vu >= a[i__2].r) { *m = 1; i__1 = a_dim1 + 1; w[1] = a[i__1].r; } } if (wantz) { i__1 = z_dim1 + 1; z__[i__1].r = 1.; z__[i__1].i = 0.; // , expr subst } return 0; } /* Get machine constants. */ safmin = dlamch_("Safe minimum"); eps = dlamch_("Precision"); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = sqrt(smlnum); /* Computing MIN */ d__1 = sqrt(bignum); d__2 = 1. / sqrt(sqrt(safmin)); // , expr subst rmax = min(d__1,d__2); /* Scale matrix to allowable range, if necessary. */ iscale = 0; abstll = *abstol; if (valeig) { vll = *vl; vuu = *vu; } anrm = zlanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]); if (anrm > 0. && 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 <= i__1; ++j) { i__2 = *n - j + 1; zdscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1); /* L10: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { zdscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1); /* L20: */ } } if (*abstol > 0.) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */ indd = 1; inde = indd + *n; indrwk = inde + *n; indtau = 1; indwrk = indtau + *n; llwork = *lwork - indwrk + 1; zhetrd_(uplo, n, &a[a_offset], lda, &rwork[indd], &rwork[inde], &work[ indtau], &work[indwrk], &llwork, &iinfo); /* If all eigenvalues are desired and ABSTOL is less than or equal to */ /* zero, then call DSTERF or ZUNGTR and ZSTEQR. If this fails for */ /* some eigenvalue, then try DSTEBZ. */ test = FALSE_; if (indeig) { if (*il == 1 && *iu == *n) { test = TRUE_; } } if ((alleig || test) && *abstol <= 0.) { dcopy_(n, &rwork[indd], &c__1, &w[1], &c__1); indee = indrwk + (*n << 1); if (! wantz) { i__1 = *n - 1; dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); dsterf_(n, &w[1], &rwork[indee], info); } else { zlacpy_("A", n, n, &a[a_offset], lda, &z__[z_offset], ldz); zungtr_(uplo, n, &z__[z_offset], ldz, &work[indtau], &work[indwrk] , &llwork, &iinfo); i__1 = *n - 1; dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); zsteqr_(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; /* L30: */ } } } if (*info == 0) { *m = *n; goto L40; } *info = 0; } /* Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwk = indisp + *n; dstebz_(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) { zstein_(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 ZSTEIN. */ zunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau], &z__[ z_offset], ldz, &work[indwrk], &llwork, &iinfo); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L40: if (iscale == 1) { if (*info == 0) { imax = *m; } else { imax = *info - 1; } d__1 = 1. / sigma; dscal_(&imax, &d__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]; } /* 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; zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], &c__1); if (*info != 0) { itmp1 = ifail[i__]; ifail[i__] = ifail[j]; ifail[j] = itmp1; } } /* L60: */ } } /* Set WORK(1) to optimal complex workspace size. */ work[1].r = (doublereal) lwkopt; work[1].i = 0.; // , expr subst return 0; /* End of ZHEEVX */ }
/* Subroutine */ int zheevx_(char *jobz, char *range, char *uplo, integer *n, doublecomplex *a, integer *lda, doublereal *vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer *m, doublereal * w, doublecomplex *z, integer *ldz, doublecomplex *work, integer * lwork, doublereal *rwork, 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 ======= ZHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian 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) COMPLEX*16 array, dimension (LDA, N) On entry, the Hermitian 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) DOUBLE PRECISION VU (input) DOUBLE PRECISION 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) DOUBLE PRECISION 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*DLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('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) DOUBLE PRECISION array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order. Z (output) COMPLEX*16 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) COMPLEX*16 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(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for ZHETRD returned by ILAENV. RWORK (workspace) DOUBLE PRECISION 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 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; doublereal d__1, d__2; doublecomplex z__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer indd, inde; static doublereal anrm; static integer imax; static doublereal rmin, rmax; static integer lopt, itmp1, i, j, indee; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); static doublereal sigma; extern logical lsame_(char *, char *); static integer iinfo; static char order[1]; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); static logical lower, wantz; extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); static integer jj; extern doublereal dlamch_(char *); static logical alleig, indeig; static integer iscale, indibl; static logical valeig; static doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_( integer *, doublereal *, doublecomplex *, integer *); static doublereal abstll, bignum; extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); static integer indiwk, indisp, indtau; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, integer *), dstebz_(char *, char *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); static integer indrwk, indwrk; extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); static integer llwork, nsplit; static doublereal smlnum; extern /* Subroutine */ int zstein_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, integer *, integer *), zsteqr_(char *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, doublereal *, integer *), zungtr_(char *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *), zunmtr_(char *, char *, char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *); static doublereal eps, vll, vuu, tmp1; #define W(I) w[(I)-1] #define WORK(I) work[(I)-1] #define RWORK(I) rwork[(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 << 1) - 1; if (*lwork < max(i__1,i__2)) { *info = -17; } } if (*info != 0) { i__1 = -(*info); xerbla_("ZHEEVX", &i__1); return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { WORK(1).r = 1., WORK(1).i = 0.; return 0; } if (*n == 1) { WORK(1).r = 1., WORK(1).i = 0.; if (alleig || indeig) { *m = 1; i__1 = a_dim1 + 1; W(1) = A(1,1).r; } else if (valeig) { i__1 = a_dim1 + 1; i__2 = a_dim1 + 1; if (*vl < A(1,1).r && *vu >= A(1,1).r) { *m = 1; i__1 = a_dim1 + 1; W(1) = A(1,1).r; } } if (wantz) { i__1 = z_dim1 + 1; Z(1,1).r = 1., Z(1,1).i = 0.; } return 0; } /* Get machine constants. */ safmin = dlamch_("Safe minimum"); eps = dlamch_("Precision"); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = sqrt(smlnum); /* Computing MIN */ d__1 = sqrt(bignum), d__2 = 1. / sqrt(sqrt(safmin)); rmax = min(d__1,d__2); /* Scale matrix to allowable range, if necessary. */ iscale = 0; abstll = *abstol; if (valeig) { vll = *vl; vuu = *vu; } anrm = zlanhe_("M", uplo, n, &A(1,1), lda, &RWORK(1)); if (anrm > 0. && 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; zdscal_(&i__2, &sigma, &A(j,j), &c__1); /* L10: */ } } else { i__1 = *n; for (j = 1; j <= *n; ++j) { zdscal_(&j, &sigma, &A(1,j), &c__1); /* L20: */ } } if (*abstol > 0.) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */ indd = 1; inde = indd + *n; indrwk = inde + *n; indtau = 1; indwrk = indtau + *n; llwork = *lwork - indwrk + 1; zhetrd_(uplo, n, &A(1,1), lda, &RWORK(indd), &RWORK(inde), &WORK( indtau), &WORK(indwrk), &llwork, &iinfo); i__1 = indwrk; z__1.r = *n + WORK(indwrk).r, z__1.i = WORK(indwrk).i; lopt = (integer) z__1.r; /* If all eigenvalues are desired and ABSTOL is less than or equal to zero, then call DSTERF or ZUNGTR and ZSTEQR. If this fails for some eigenvalue, then try DSTEBZ. */ if ((alleig || indeig && *il == 1 && *iu == *n) && *abstol <= 0.) { dcopy_(n, &RWORK(indd), &c__1, &W(1), &c__1); indee = indrwk + (*n << 1); if (! wantz) { i__1 = *n - 1; dcopy_(&i__1, &RWORK(inde), &c__1, &RWORK(indee), &c__1); dsterf_(n, &W(1), &RWORK(indee), info); } else { zlacpy_("A", n, n, &A(1,1), lda, &Z(1,1), ldz); zungtr_(uplo, n, &Z(1,1), ldz, &WORK(indtau), &WORK(indwrk), &llwork, &iinfo); i__1 = *n - 1; dcopy_(&i__1, &RWORK(inde), &c__1, &RWORK(indee), &c__1); zsteqr_(jobz, n, &W(1), &RWORK(indee), &Z(1,1), ldz, &RWORK( indrwk), 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 DSTEBZ and, if eigenvectors are desired, ZSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwk = indisp + *n; dstebz_(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) { zstein_(n, &RWORK(indd), &RWORK(inde), m, &W(1), &IWORK(indibl), & IWORK(indisp), &Z(1,1), ldz, &RWORK(indrwk), &IWORK( indiwk), &IFAIL(1), info); /* Apply unitary matrix used in reduction to tridiagonal form to eigenvectors returned by ZSTEIN. */ zunmtr_("L", uplo, "N", n, m, &A(1,1), lda, &WORK(indtau), &Z(1,1), ldz, &WORK(indwrk), &llwork, &iinfo); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L40: if (iscale == 1) { if (*info == 0) { imax = *m; } else { imax = *info - 1; } d__1 = 1. / sigma; dscal_(&imax, &d__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; zswap_(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 complex workspace size. Computing MAX */ i__1 = (*n << 1) - 1; d__1 = (doublereal) max(i__1,lopt); WORK(1).r = d__1, WORK(1).i = 0.; return 0; /* End of ZHEEVX */ } /* zheevx_ */
/* Subroutine */ int zhpevx_(char *jobz, char *range, char *uplo, integer *n, doublecomplex *ap, doublereal *vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer *m, doublereal *w, doublecomplex *z__, integer *ldz, doublecomplex *work, doublereal * rwork, integer *iwork, integer *ifail, integer *info) { /* System generated locals */ integer z_dim1, z_offset, i__1, i__2; doublereal d__1, d__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ integer i__, j, jj; doublereal eps, vll, vuu, tmp1; integer indd, inde; doublereal anrm; integer imax; doublereal rmin, rmax; logical test; integer itmp1, indee; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal sigma; extern logical lsame_(char *, char *); integer iinfo; char order[1]; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); logical wantz; extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); extern doublereal dlamch_(char *); logical alleig, indeig; integer iscale, indibl; logical valeig; doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_( integer *, doublereal *, doublecomplex *, integer *); doublereal abstll, bignum; integer indiwk, indisp, indtau; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, integer *), dstebz_(char *, char *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); extern doublereal zlanhp_(char *, char *, integer *, doublecomplex *, doublereal *); integer indrwk, indwrk, nsplit; doublereal smlnum; extern /* Subroutine */ int zhptrd_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublecomplex *, integer *), zstein_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, integer *, integer *), zsteqr_(char *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, doublereal *, integer *), zupgtr_(char *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), zupmtr_(char *, char *, char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *); /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZHPEVX 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*16 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) DOUBLE PRECISION */ /* VU (input) DOUBLE PRECISION */ /* 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) DOUBLE PRECISION */ /* 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*DLAMCH('S'), not zero. */ /* If this routine returns with INFO>0, indicating that some */ /* eigenvectors did not converge, try setting ABSTOL to */ /* 2*DLAMCH('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) DOUBLE PRECISION array, dimension (N) */ /* If INFO = 0, the selected eigenvalues in ascending order. */ /* Z (output) COMPLEX*16 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*16 array, dimension (2*N) */ /* RWORK (workspace) DOUBLE PRECISION 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. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ --ap; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; 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_("ZHPEVX", &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_dim1 + 1; z__[i__1].r = 1., z__[i__1].i = 0.; } return 0; } /* Get machine constants. */ safmin = dlamch_("Safe minimum"); eps = dlamch_("Precision"); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = sqrt(smlnum); /* Computing MIN */ d__1 = sqrt(bignum), d__2 = 1. / sqrt(sqrt(safmin)); rmax = min(d__1,d__2); /* Scale matrix to allowable range, if necessary. */ iscale = 0; abstll = *abstol; if (valeig) { vll = *vl; vuu = *vu; } else { vll = 0.; vuu = 0.; } anrm = zlanhp_("M", uplo, n, &ap[1], &rwork[1]); if (anrm > 0. && 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; zdscal_(&i__1, &sigma, &ap[1], &c__1); if (*abstol > 0.) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form. */ indd = 1; inde = indd + *n; indrwk = inde + *n; indtau = 1; indwrk = indtau + *n; zhptrd_(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 DSTERF or ZUPGTR and ZSTEQR. If this fails */ /* for some eigenvalue, then try DSTEBZ. */ test = FALSE_; if (indeig) { if (*il == 1 && *iu == *n) { test = TRUE_; } } if ((alleig || test) && *abstol <= 0.) { dcopy_(n, &rwork[indd], &c__1, &w[1], &c__1); indee = indrwk + (*n << 1); if (! wantz) { i__1 = *n - 1; dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); dsterf_(n, &w[1], &rwork[indee], info); } else { zupgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, & work[indwrk], &iinfo); i__1 = *n - 1; dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); zsteqr_(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 DSTEBZ and, if eigenvectors are desired, ZSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwk = indisp + *n; dstebz_(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) { zstein_(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 ZSTEIN. */ indwrk = indtau + *n; zupmtr_("L", uplo, "N", n, m, &ap[1], &work[indtau], &z__[z_offset], ldz, &work[indwrk], &iinfo); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L20: if (iscale == 1) { if (*info == 0) { imax = *m; } else { imax = *info - 1; } d__1 = 1. / sigma; dscal_(&imax, &d__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; zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], &c__1); if (*info != 0) { itmp1 = ifail[i__]; ifail[i__] = ifail[j]; ifail[j] = itmp1; } } /* L40: */ } } return 0; /* End of ZHPEVX */ } /* zhpevx_ */
/* Subroutine */ int zhbgvx_(char *jobz, char *range, char *uplo, integer *n, integer *ka, integer *kb, doublecomplex *ab, integer *ldab, doublecomplex *bb, integer *ldbb, doublecomplex *q, integer *ldq, doublereal *vl, doublereal *vu, integer *il, integer *iu, doublereal * abstol, integer *m, doublereal *w, doublecomplex *z__, integer *ldz, doublecomplex *work, doublereal *rwork, integer *iwork, integer * ifail, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, bb_dim1, bb_offset, q_dim1, q_offset, z_dim1, z_offset, i__1, i__2; /* Local variables */ integer i__, j, jj; doublereal tmp1; integer indd, inde; char vect[1]; logical test; integer itmp1, indee; extern logical lsame_(char *, char *); integer iinfo; char order[1]; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); logical upper, wantz; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); logical alleig, indeig; integer indibl; logical valeig; extern /* Subroutine */ int xerbla_(char *, integer *); integer indiwk, indisp; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, integer *), dstebz_(char *, char *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), zhbtrd_(char *, char *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, doublecomplex *, integer *); integer indrwk, indwrk; extern /* Subroutine */ int zhbgst_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublereal *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); integer nsplit; extern /* Subroutine */ int zpbstf_(char *, integer *, integer *, doublecomplex *, integer *, integer *), zstein_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, integer *, integer *), zsteqr_(char *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, doublereal *, integer *); /* -- LAPACK driver routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZHBGVX computes all the eigenvalues, and optionally, the eigenvectors */ /* of a complex generalized Hermitian-definite banded eigenproblem, of */ /* the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian */ /* and banded, and B is also positive definite. Eigenvalues and */ /* eigenvectors can be selected by specifying either all eigenvalues, */ /* 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 triangles of A and B are stored; */ /* = 'L': Lower triangles of A and B are stored. */ /* N (input) INTEGER */ /* The order of the matrices A and B. N >= 0. */ /* KA (input) INTEGER */ /* The number of superdiagonals of the matrix A if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KA >= 0. */ /* KB (input) INTEGER */ /* The number of superdiagonals of the matrix B if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KB >= 0. */ /* AB (input/output) COMPLEX*16 array, dimension (LDAB, N) */ /* On entry, the upper or lower triangle of the Hermitian band */ /* matrix A, stored in the first ka+1 rows of the array. The */ /* j-th column of A is stored in the j-th column of the array AB */ /* as follows: */ /* if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; */ /* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). */ /* On exit, the contents of AB are destroyed. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= KA+1. */ /* BB (input/output) COMPLEX*16 array, dimension (LDBB, N) */ /* On entry, the upper or lower triangle of the Hermitian band */ /* matrix B, stored in the first kb+1 rows of the array. The */ /* j-th column of B is stored in the j-th column of the array BB */ /* as follows: */ /* if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; */ /* if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). */ /* On exit, the factor S from the split Cholesky factorization */ /* B = S**H*S, as returned by ZPBSTF. */ /* LDBB (input) INTEGER */ /* The leading dimension of the array BB. LDBB >= KB+1. */ /* Q (output) COMPLEX*16 array, dimension (LDQ, N) */ /* If JOBZ = 'V', the n-by-n matrix used in the reduction of */ /* A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x, */ /* and consequently C to tridiagonal form. */ /* If JOBZ = 'N', the array Q is not referenced. */ /* LDQ (input) INTEGER */ /* The leading dimension of the array Q. If JOBZ = 'N', */ /* LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N). */ /* VL (input) DOUBLE PRECISION */ /* VU (input) DOUBLE PRECISION */ /* 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) DOUBLE PRECISION */ /* 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*DLAMCH('S'), not zero. */ /* If this routine returns with INFO>0, indicating that some */ /* eigenvectors did not converge, try setting ABSTOL to */ /* 2*DLAMCH('S'). */ /* 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) DOUBLE PRECISION array, dimension (N) */ /* If INFO = 0, the eigenvalues in ascending order. */ /* Z (output) COMPLEX*16 array, dimension (LDZ, N) */ /* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */ /* eigenvectors, with the i-th column of Z holding the */ /* eigenvector associated with W(i). The eigenvectors are */ /* normalized so that Z**H*B*Z = I. */ /* If JOBZ = 'N', then Z is not referenced. */ /* LDZ (input) INTEGER */ /* The leading dimension of the array Z. LDZ >= 1, and if */ /* JOBZ = 'V', LDZ >= N. */ /* WORK (workspace) COMPLEX*16 array, dimension (N) */ /* RWORK (workspace) DOUBLE PRECISION 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, and i is: */ /* <= N: then i eigenvectors failed to converge. Their */ /* indices are stored in array IFAIL. */ /* > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF */ /* returned INFO = i: B is not positive definite. */ /* The factorization of B could not be completed and */ /* no eigenvalues or eigenvectors were computed. */ /* Further Details */ /* =============== */ /* Based on contributions by */ /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; bb_dim1 = *ldbb; bb_offset = 1 + bb_dim1; bb -= bb_offset; q_dim1 = *ldq; q_offset = 1 + q_dim1; q -= q_offset; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --rwork; --iwork; --ifail; /* Function Body */ wantz = lsame_(jobz, "V"); upper = lsame_(uplo, "U"); 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 (! (upper || lsame_(uplo, "L"))) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*ka < 0) { *info = -5; } else if (*kb < 0 || *kb > *ka) { *info = -6; } else if (*ldab < *ka + 1) { *info = -8; } else if (*ldbb < *kb + 1) { *info = -10; } else if (*ldq < 1 || wantz && *ldq < *n) { *info = -12; } else { if (valeig) { if (*n > 0 && *vu <= *vl) { *info = -14; } } else if (indeig) { if (*il < 1 || *il > max(1,*n)) { *info = -15; } else if (*iu < min(*n,*il) || *iu > *n) { *info = -16; } } } if (*info == 0) { if (*ldz < 1 || wantz && *ldz < *n) { *info = -21; } } if (*info != 0) { i__1 = -(*info); xerbla_("ZHBGVX", &i__1); return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { return 0; } /* Form a split Cholesky factorization of B. */ zpbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info); if (*info != 0) { *info = *n + *info; return 0; } /* Transform problem to standard eigenvalue problem. */ zhbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb, &q[q_offset], ldq, &work[1], &rwork[1], &iinfo); /* Solve the standard eigenvalue problem. */ /* Reduce Hermitian band matrix to tridiagonal form. */ indd = 1; inde = indd + *n; indrwk = inde + *n; indwrk = 1; if (wantz) { *(unsigned char *)vect = 'U'; } else { *(unsigned char *)vect = 'N'; } zhbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &rwork[indd], &rwork[ inde], &q[q_offset], ldq, &work[indwrk], &iinfo); /* If all eigenvalues are desired and ABSTOL is less than or equal */ /* to zero, then call DSTERF or ZSTEQR. If this fails for some */ /* eigenvalue, then try DSTEBZ. */ test = FALSE_; if (indeig) { if (*il == 1 && *iu == *n) { test = TRUE_; } } if ((alleig || test) && *abstol <= 0.) { dcopy_(n, &rwork[indd], &c__1, &w[1], &c__1); indee = indrwk + (*n << 1); i__1 = *n - 1; dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); if (! wantz) { dsterf_(n, &w[1], &rwork[indee], info); } else { zlacpy_("A", n, n, &q[q_offset], ldq, &z__[z_offset], ldz); zsteqr_(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 L30; } *info = 0; } /* Otherwise, call DSTEBZ and, if eigenvectors are desired, */ /* call ZSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwk = indisp + *n; dstebz_(range, order, n, vl, vu, il, iu, abstol, &rwork[indd], &rwork[ inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &rwork[ indrwk], &iwork[indiwk], info); if (wantz) { zstein_(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 ZSTEIN. */ i__1 = *m; for (j = 1; j <= i__1; ++j) { zcopy_(n, &z__[j * z_dim1 + 1], &c__1, &work[1], &c__1); zgemv_("N", n, n, &c_b2, &q[q_offset], ldq, &work[1], &c__1, & c_b1, &z__[j * z_dim1 + 1], &c__1); /* L20: */ } } L30: /* 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]; } /* L40: */ } 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; zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], &c__1); if (*info != 0) { itmp1 = ifail[i__]; ifail[i__] = ifail[j]; ifail[j] = itmp1; } } /* L50: */ } } return 0; /* End of ZHBGVX */ } /* zhbgvx_ */