#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dstevd_(char *jobz, integer *n, doublereal *d__, doublereal *e, doublereal *z__, integer *ldz, doublereal *work, integer *lwork, integer *iwork, integer *liwork, integer *info) { /* -- LAPACK driver routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DSTEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. Arguments ========= JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. N (input) INTEGER The order of the matrix. N >= 0. D (input/output) DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A. On exit, if INFO = 0, the eigenvalues in ascending order. E (input/output) DOUBLE PRECISION array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A, stored in elements 1 to N-1 of E. On exit, the contents of E are destroyed. Z (output) DOUBLE PRECISION 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 D(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/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. If JOBZ = 'N' or N <= 1 then LWORK must be at least 1. If JOBZ = 'V' and N > 1 then LWORK must be at least ( 1 + 4*N + N**2 ). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. LIWORK (input) INTEGER The dimension of the array IWORK. If JOBZ = 'N' or N <= 1 then LIWORK must be at least 1. If JOBZ = 'V' and N > 1 then LIWORK must be at least 3+5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. 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 E 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 doublereal eps, rmin, rmax, tnrm; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); static doublereal sigma; extern logical lsame_(char *, char *); static integer lwmin; static logical wantz; extern doublereal dlamch_(char *); static integer iscale; extern /* Subroutine */ int dstedc_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, integer *); static doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *); static doublereal bignum; extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *); extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, integer *); static integer liwmin; static doublereal smlnum; static logical lquery; --d__; --e; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --iwork; /* Function Body */ wantz = lsame_(jobz, "V"); lquery = *lwork == -1 || *liwork == -1; *info = 0; liwmin = 1; lwmin = 1; if (*n > 1 && wantz) { /* Computing 2nd power */ i__1 = *n; lwmin = (*n << 2) + 1 + i__1 * i__1; liwmin = *n * 5 + 3; } if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -6; } if (*info == 0) { work[1] = (doublereal) lwmin; iwork[1] = liwmin; if (*lwork < lwmin && ! lquery) { *info = -8; } else if (*liwork < liwmin && ! lquery) { *info = -10; } } if (*info != 0) { i__1 = -(*info); xerbla_("DSTEVD", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { if (wantz) { z__[z_dim1 + 1] = 1.; } 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. */ iscale = 0; tnrm = dlanst_("M", n, &d__[1], &e[1]); if (tnrm > 0. && tnrm < rmin) { iscale = 1; sigma = rmin / tnrm; } else if (tnrm > rmax) { iscale = 1; sigma = rmax / tnrm; } if (iscale == 1) { dscal_(n, &sigma, &d__[1], &c__1); i__1 = *n - 1; dscal_(&i__1, &sigma, &e[1], &c__1); } /* For eigenvalues only, call DSTERF. For eigenvalues and eigenvectors, call DSTEDC. */ if (! wantz) { dsterf_(n, &d__[1], &e[1], info); } else { dstedc_("I", n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], lwork, &iwork[1], liwork, info); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { d__1 = 1. / sigma; dscal_(n, &d__1, &d__[1], &c__1); } work[1] = (doublereal) lwmin; iwork[1] = liwmin; return 0; /* End of DSTEVD */ } /* dstevd_ */