/* Subroutine */ int zhpev_(char *jobz, char *uplo, integer *n, doublecomplex *ap, doublereal *w, doublecomplex *z__, integer *ldz, doublecomplex * work, doublereal *rwork, 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 March 31, 1993 Purpose ======= ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage. Arguments ========= JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. 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. 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 orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(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 >= max(1,N). WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1)) RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2)) INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. ===================================================================== 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; doublereal d__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer inde; static doublereal anrm; static integer imax; static doublereal rmin, rmax; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); static doublereal sigma; extern logical lsame_(char *, char *); static integer iinfo; static logical wantz; extern doublereal dlamch_(char *); static integer iscale; static doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_( integer *, doublereal *, doublecomplex *, integer *); static doublereal bignum; static integer indtau; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, integer *); extern doublereal zlanhp_(char *, char *, integer *, doublecomplex *, doublereal *); static integer indrwk, indwrk; static doublereal smlnum; extern /* Subroutine */ int zhptrd_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublecomplex *, integer *), zsteqr_(char *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, doublereal *, integer *), zupgtr_(char *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *); static doublereal eps; #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; /* Function Body */ wantz = lsame_(jobz, "V"); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (lsame_(uplo, "L") || lsame_(uplo, "U"))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -7; } if (*info != 0) { i__1 = -(*info); xerbla_("ZHPEV ", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { w[1] = ap[1].r; rwork[1] = 1.; if (wantz) { i__1 = z___subscr(1, 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); rmax = sqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = zlanhp_("M", uplo, n, &ap[1], &rwork[1]); iscale = 0; 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); } /* Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form. */ inde = 1; indtau = 1; zhptrd_(uplo, n, &ap[1], &w[1], &rwork[inde], &work[indtau], &iinfo); /* For eigenvalues only, call DSTERF. For eigenvectors, first call ZUPGTR to generate the orthogonal matrix, then call ZSTEQR. */ if (! wantz) { dsterf_(n, &w[1], &rwork[inde], info); } else { indwrk = indtau + *n; zupgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, &work[ indwrk], &iinfo); indrwk = inde + *n; zsteqr_(jobz, n, &w[1], &rwork[inde], &z__[z_offset], ldz, &rwork[ indrwk], info); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { if (*info == 0) { imax = *n; } else { imax = *info - 1; } d__1 = 1. / sigma; dscal_(&imax, &d__1, &w[1], &c__1); } return 0; /* End of ZHPEV */ } /* zhpev_ */
int zhpev_(char *jobz, char *uplo, int *n, doublecomplex *ap, double *w, doublecomplex *z__, int *ldz, doublecomplex * work, double *rwork, int *info) { /* System generated locals */ int z_dim1, z_offset, i__1; double d__1; /* Builtin functions */ double sqrt(double); /* Local variables */ double eps; int inde; double anrm; int imax; double rmin, rmax; extern int dscal_(int *, double *, double *, int *); double sigma; extern int lsame_(char *, char *); int iinfo; int wantz; extern double dlamch_(char *); int iscale; double safmin; extern int xerbla_(char *, int *), zdscal_( int *, double *, doublecomplex *, int *); double bignum; int indtau; extern int dsterf_(int *, double *, double *, int *); extern double zlanhp_(char *, char *, int *, doublecomplex *, double *); int indrwk, indwrk; double smlnum; extern int zhptrd_(char *, int *, doublecomplex *, double *, double *, doublecomplex *, int *), zsteqr_(char *, int *, double *, double *, doublecomplex *, int *, double *, int *), zupgtr_(char *, int *, doublecomplex *, doublecomplex *, doublecomplex *, int *, doublecomplex *, int *); /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a */ /* complex Hermitian matrix in packed storage. */ /* Arguments */ /* ========= */ /* JOBZ (input) CHARACTER*1 */ /* = 'N': Compute eigenvalues only; */ /* = 'V': Compute eigenvalues and eigenvectors. */ /* 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. */ /* 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 orthonormal */ /* eigenvectors of the matrix A, with the i-th column of Z */ /* holding the eigenvector associated with W(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 >= MAX(1,N). */ /* WORK (workspace) COMPLEX*16 array, dimension (MAX(1, 2*N-1)) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension (MAX(1, 3*N-2)) */ /* INFO (output) INTEGER */ /* = 0: successful exit. */ /* < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > 0: if INFO = i, the algorithm failed to converge; i */ /* off-diagonal elements of an intermediate tridiagonal */ /* form did not converge to zero. */ /* ===================================================================== */ /* .. 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; /* Function Body */ wantz = lsame_(jobz, "V"); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (lsame_(uplo, "L") || lsame_(uplo, "U"))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -7; } if (*info != 0) { i__1 = -(*info); xerbla_("ZHPEV ", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { w[1] = ap[1].r; rwork[1] = 1.; 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); rmax = sqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = zlanhp_("M", uplo, n, &ap[1], &rwork[1]); iscale = 0; 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); } /* Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form. */ inde = 1; indtau = 1; zhptrd_(uplo, n, &ap[1], &w[1], &rwork[inde], &work[indtau], &iinfo); /* For eigenvalues only, call DSTERF. For eigenvectors, first call */ /* ZUPGTR to generate the orthogonal matrix, then call ZSTEQR. */ if (! wantz) { dsterf_(n, &w[1], &rwork[inde], info); } else { indwrk = indtau + *n; zupgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, &work[ indwrk], &iinfo); indrwk = inde + *n; zsteqr_(jobz, n, &w[1], &rwork[inde], &z__[z_offset], ldz, &rwork[ indrwk], info); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { if (*info == 0) { imax = *n; } else { imax = *info - 1; } d__1 = 1. / sigma; dscal_(&imax, &d__1, &w[1], &c__1); } return 0; /* End of ZHPEV */ } /* zhpev_ */
/* 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 zhpev_(char *jobz, char *uplo, integer *n, doublecomplex *ap, doublereal *w, doublecomplex *z__, integer *ldz, doublecomplex * work, doublereal *rwork, integer *info) { /* System generated locals */ integer z_dim1, z_offset, i__1; doublereal d__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ doublereal eps; integer inde; doublereal anrm; integer imax; doublereal rmin, rmax; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal sigma; extern logical lsame_(char *, char *); integer iinfo; logical wantz; extern doublereal dlamch_(char *); integer iscale; doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_( integer *, doublereal *, doublecomplex *, integer *); doublereal bignum; integer indtau; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, integer *); extern doublereal zlanhp_(char *, char *, integer *, doublecomplex *, doublereal *); integer indrwk, indwrk; doublereal smlnum; extern /* Subroutine */ int zhptrd_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublecomplex *, integer *), zsteqr_(char *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, doublereal *, integer *), zupgtr_(char *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, 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 */ --ap; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --rwork; /* Function Body */ wantz = lsame_(jobz, "V"); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (lsame_(uplo, "L") || lsame_(uplo, "U"))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -7; } if (*info != 0) { i__1 = -(*info); xerbla_("ZHPEV ", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { w[1] = ap[1].r; rwork[1] = 1.; 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); rmax = sqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = zlanhp_("M", uplo, n, &ap[1], &rwork[1]); iscale = 0; 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); } /* Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form. */ inde = 1; indtau = 1; zhptrd_(uplo, n, &ap[1], &w[1], &rwork[inde], &work[indtau], &iinfo); /* For eigenvalues only, call DSTERF. For eigenvectors, first call */ /* ZUPGTR to generate the orthogonal matrix, then call ZSTEQR. */ if (! wantz) { dsterf_(n, &w[1], &rwork[inde], info); } else { indwrk = indtau + *n; zupgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, &work[ indwrk], &iinfo); indrwk = inde + *n; zsteqr_(jobz, n, &w[1], &rwork[inde], &z__[z_offset], ldz, &rwork[ indrwk], info); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { if (*info == 0) { imax = *n; } else { imax = *info - 1; } d__1 = 1. / sigma; dscal_(&imax, &d__1, &w[1], &c__1); } return 0; /* End of ZHPEV */ }