#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dsyevd_(char *jobz, char *uplo, integer *n, doublereal * a, integer *lda, doublereal *w, doublereal *work, integer *lwork, integer *iwork, integer *liwork, 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 ======= DSYEVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. 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. Because of large use of BLAS of level 3, DSYEVD needs N**2 more workspace than DSYEVX. 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. A (input/output) DOUBLE PRECISION array, dimension (LDA, N) On entry, the symmetric 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, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then 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). W (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 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 N <= 1, LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + 2*N**2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. IWORK (workspace/output) INTEGER array, dimension (LIWORK) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. LIWORK (input) INTEGER The dimension of the array IWORK. If N <= 1, LIWORK must be at least 1. If JOBZ = 'N' and N > 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to 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 an intermediate tridiagonal form did not converge to zero. Further Details =============== Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Modified by Francoise Tisseur, University of Tennessee. ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__0 = 0; static doublereal c_b12 = 1.; static integer c__1 = 1; /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublereal d__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer inde; static doublereal anrm, rmin, rmax; static integer lopt; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); static doublereal sigma; extern logical lsame_(char *, char *); static integer iinfo, lwmin, liopt; static logical lower, wantz; static integer indwk2, llwrk2; extern doublereal dlamch_(char *); static integer iscale; extern /* Subroutine */ int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dstedc_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, integer *), dlacpy_( char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *); static doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *); static doublereal bignum; static integer indtau; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, integer *); extern doublereal dlansy_(char *, char *, integer *, doublereal *, integer *, doublereal *); static integer indwrk, liwmin; extern /* Subroutine */ int dormtr_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *), dsytrd_(char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *); static integer llwork; static doublereal smlnum; static logical lquery; static doublereal eps; #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --w; --work; --iwork; /* Function Body */ wantz = lsame_(jobz, "V"); lower = lsame_(uplo, "L"); lquery = *lwork == -1 || *liwork == -1; *info = 0; if (*n <= 1) { liwmin = 1; lwmin = 1; lopt = lwmin; liopt = liwmin; } else { if (wantz) { liwmin = *n * 5 + 3; /* Computing 2nd power */ i__1 = *n; lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); } else { liwmin = 1; lwmin = (*n << 1) + 1; } lopt = lwmin; liopt = liwmin; } if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (lower || lsame_(uplo, "U"))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*lda < max(1,*n)) { *info = -5; } else if (*lwork < lwmin && ! lquery) { *info = -8; } else if (*liwork < liwmin && ! lquery) { *info = -10; } if (*info == 0) { work[1] = (doublereal) lopt; iwork[1] = liopt; } if (*info != 0) { i__1 = -(*info); xerbla_("DSYEVD", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { w[1] = a_ref(1, 1); if (wantz) { a_ref(1, 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. */ anrm = dlansy_("M", uplo, n, &a[a_offset], lda, &work[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) { dlascl_(uplo, &c__0, &c__0, &c_b12, &sigma, n, n, &a[a_offset], lda, info); } /* Call DSYTRD to reduce symmetric matrix to tridiagonal form. */ inde = 1; indtau = inde + *n; indwrk = indtau + *n; llwork = *lwork - indwrk + 1; indwk2 = indwrk + *n * *n; llwrk2 = *lwork - indwk2 + 1; dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], & work[indwrk], &llwork, &iinfo); lopt = (integer) ((*n << 1) + work[indwrk]); /* For eigenvalues only, call DSTERF. For eigenvectors, first call DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the tridiagonal matrix, then call DORMTR to multiply it by the Householder transformations stored in A. */ if (! wantz) { dsterf_(n, &w[1], &work[inde], info); } else { dstedc_("I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], & llwrk2, &iwork[1], liwork, info); dormtr_("L", uplo, "N", n, n, &a[a_offset], lda, &work[indtau], &work[ indwrk], n, &work[indwk2], &llwrk2, &iinfo); dlacpy_("A", n, n, &work[indwrk], n, &a[a_offset], lda); /* Computing MAX Computing 2nd power */ i__3 = *n; i__1 = lopt, i__2 = *n * 6 + 1 + (i__3 * i__3 << 1); lopt = max(i__1,i__2); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { d__1 = 1. / sigma; dscal_(n, &d__1, &w[1], &c__1); } work[1] = (doublereal) lopt; iwork[1] = liopt; return 0; /* End of DSYEVD */ } /* dsyevd_ */ #undef a_ref