#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cstedc_(char *compz, integer *n, real *d__, real *e, complex *z__, integer *ldz, complex *work, integer *lwork, real * rwork, integer *lrwork, integer *iwork, integer *liwork, integer * info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CSTEDC computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. The eigenvectors of a full or band complex Hermitian matrix can also be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this matrix to tridiagonal form. This code 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. See SLAED3 for details. Arguments ========= COMPZ (input) CHARACTER*1 = 'N': Compute eigenvalues only. = 'I': Compute eigenvectors of tridiagonal matrix also. = 'V': Compute eigenvectors of original Hermitian matrix also. On entry, Z contains the unitary matrix used to reduce the original matrix to tridiagonal form. N (input) INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0. D (input/output) REAL array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order. E (input/output) REAL array, dimension (N-1) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed. Z (input/output) COMPLEX array, dimension (LDZ,N) On entry, if COMPZ = 'V', then Z contains the unitary matrix used in the reduction to tridiagonal form. On exit, if INFO = 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors of the original Hermitian matrix, and if COMPZ = 'I', Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If COMPZ = 'N', then Z is not referenced. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1. If eigenvectors are desired, then LDZ >= max(1,N). WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1. If COMPZ = 'V' and N > 1, LWORK must be at least N*N. Note that for COMPZ = 'V', then if N is less than or equal to the minimum divide size, usually 25, then LWORK need only be 1. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. RWORK (workspace/output) REAL array, dimension (MAX(1,LRWORK)) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. LRWORK (input) INTEGER The dimension of the array RWORK. If COMPZ = 'N' or N <= 1, LRWORK must be at least 1. If COMPZ = 'V' and N > 1, LRWORK must be at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) = smallest integer k such that 2**k >= N. If COMPZ = 'I' and N > 1, LRWORK must be at least 1 + 4*N + 2*N**2 . Note that for COMPZ = 'I' or 'V', then if N is less than or equal to the minimum divide size, usually 25, then LRWORK need only be max(1,2*(N-1)). If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK 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 COMPZ = 'N' or N <= 1, LIWORK must be at least 1. If COMPZ = 'V' or N > 1, LIWORK must be at least 6 + 6*N + 5*N*lg N. If COMPZ = 'I' or N > 1, LIWORK must be at least 3 + 5*N . Note that for COMPZ = 'I' or 'V', then if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK 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: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1). Further Details =============== Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__9 = 9; static integer c__0 = 0; static integer c__2 = 2; static real c_b17 = 0.f; static real c_b18 = 1.f; static integer c__1 = 1; /* System generated locals */ integer z_dim1, z_offset, i__1, i__2, i__3, i__4; real r__1, r__2; /* Builtin functions */ double log(doublereal); integer pow_ii(integer *, integer *); double sqrt(doublereal); /* Local variables */ static integer i__, j, k, m; static real p; static integer ii, ll, lgn; static real eps, tiny; extern logical lsame_(char *, char *); extern /* Subroutine */ int cswap_(integer *, complex *, integer *, complex *, integer *); static integer lwmin; extern /* Subroutine */ int claed0_(integer *, integer *, real *, real *, complex *, integer *, complex *, integer *, real *, integer *, integer *); static integer start; extern /* Subroutine */ int clacrm_(integer *, integer *, complex *, integer *, real *, integer *, complex *, integer *, real *); extern doublereal slamch_(char *); extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); static integer finish; extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *), sstedc_(char *, integer *, real *, real *, real *, integer *, real *, integer *, integer *, integer *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *); static integer liwmin, icompz; extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, complex *, integer *, real *, integer *); static real orgnrm; extern doublereal slanst_(char *, integer *, real *, real *); extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *); static integer lrwmin; static logical lquery; static integer smlsiz; extern /* Subroutine */ int ssteqr_(char *, integer *, real *, real *, real *, integer *, real *, integer *); --d__; --e; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --rwork; --iwork; /* Function Body */ *info = 0; lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; if (lsame_(compz, "N")) { icompz = 0; } else if (lsame_(compz, "V")) { icompz = 1; } else if (lsame_(compz, "I")) { icompz = 2; } else { icompz = -1; } if (icompz < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { *info = -6; } if (*info == 0) { /* Compute the workspace requirements */ smlsiz = ilaenv_(&c__9, "CSTEDC", " ", &c__0, &c__0, &c__0, &c__0, ( ftnlen)6, (ftnlen)1); if (*n <= 1 || icompz == 0) { lwmin = 1; liwmin = 1; lrwmin = 1; } else if (*n <= smlsiz) { lwmin = 1; liwmin = 1; lrwmin = *n - 1 << 1; } else if (icompz == 1) { lgn = (integer) (log((real) (*n)) / log(2.f)); if (pow_ii(&c__2, &lgn) < *n) { ++lgn; } if (pow_ii(&c__2, &lgn) < *n) { ++lgn; } lwmin = *n * *n; /* Computing 2nd power */ i__1 = *n; lrwmin = *n * 3 + 1 + (*n << 1) * lgn + i__1 * i__1 * 3; liwmin = *n * 6 + 6 + *n * 5 * lgn; } else if (icompz == 2) { lwmin = 1; /* Computing 2nd power */ i__1 = *n; lrwmin = (*n << 2) + 1 + (i__1 * i__1 << 1); liwmin = *n * 5 + 3; } work[1].r = (real) lwmin, work[1].i = 0.f; rwork[1] = (real) lrwmin; iwork[1] = liwmin; if (*lwork < lwmin && ! lquery) { *info = -8; } else if (*lrwork < lrwmin && ! lquery) { *info = -10; } else if (*liwork < liwmin && ! lquery) { *info = -12; } } if (*info != 0) { i__1 = -(*info); xerbla_("CSTEDC", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { if (icompz != 0) { i__1 = z_dim1 + 1; z__[i__1].r = 1.f, z__[i__1].i = 0.f; } return 0; } /* If the following conditional clause is removed, then the routine will use the Divide and Conquer routine to compute only the eigenvalues, which requires (3N + 3N**2) real workspace and (2 + 5N + 2N lg(N)) integer workspace. Since on many architectures SSTERF is much faster than any other algorithm for finding eigenvalues only, it is used here as the default. If the conditional clause is removed, then information on the size of workspace needs to be changed. If COMPZ = 'N', use SSTERF to compute the eigenvalues. */ if (icompz == 0) { ssterf_(n, &d__[1], &e[1], info); goto L70; } /* If N is smaller than the minimum divide size (SMLSIZ+1), then solve the problem with another solver. */ if (*n <= smlsiz) { csteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1], info); } else { /* If COMPZ = 'I', we simply call SSTEDC instead. */ if (icompz == 2) { slaset_("Full", n, n, &c_b17, &c_b18, &rwork[1], n); ll = *n * *n + 1; i__1 = *lrwork - ll + 1; sstedc_("I", n, &d__[1], &e[1], &rwork[1], n, &rwork[ll], &i__1, & iwork[1], liwork, info); i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * z_dim1; i__4 = (j - 1) * *n + i__; z__[i__3].r = rwork[i__4], z__[i__3].i = 0.f; /* L10: */ } /* L20: */ } goto L70; } /* From now on, only option left to be handled is COMPZ = 'V', i.e. ICOMPZ = 1. Scale. */ orgnrm = slanst_("M", n, &d__[1], &e[1]); if (orgnrm == 0.f) { goto L70; } eps = slamch_("Epsilon"); start = 1; /* while ( START <= N ) */ L30: if (start <= *n) { /* Let FINISH be the position of the next subdiagonal entry such that E( FINISH ) <= TINY or FINISH = N if no such subdiagonal exists. The matrix identified by the elements between START and FINISH constitutes an independent sub-problem. */ finish = start; L40: if (finish < *n) { tiny = eps * sqrt((r__1 = d__[finish], dabs(r__1))) * sqrt(( r__2 = d__[finish + 1], dabs(r__2))); if ((r__1 = e[finish], dabs(r__1)) > tiny) { ++finish; goto L40; } } /* (Sub) Problem determined. Compute its size and solve it. */ m = finish - start + 1; if (m > smlsiz) { /* Scale. */ orgnrm = slanst_("M", &m, &d__[start], &e[start]); slascl_("G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[ start], &m, info); i__1 = m - 1; i__2 = m - 1; slascl_("G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[ start], &i__2, info); claed0_(n, &m, &d__[start], &e[start], &z__[start * z_dim1 + 1], ldz, &work[1], n, &rwork[1], &iwork[1], info); if (*info > 0) { *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % (m + 1) + start - 1; goto L70; } /* Scale back. */ slascl_("G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[ start], &m, info); } else { ssteqr_("I", &m, &d__[start], &e[start], &rwork[1], &m, & rwork[m * m + 1], info); clacrm_(n, &m, &z__[start * z_dim1 + 1], ldz, &rwork[1], &m, & work[1], n, &rwork[m * m + 1]); clacpy_("A", n, &m, &work[1], n, &z__[start * z_dim1 + 1], ldz); if (*info > 0) { *info = start * (*n + 1) + finish; goto L70; } } start = finish + 1; goto L30; } /* endwhile If the problem split any number of times, then the eigenvalues will not be properly ordered. Here we permute the eigenvalues (and the associated eigenvectors) into ascending order. */ if (m != *n) { /* Use Selection Sort to minimize swaps of eigenvectors */ i__1 = *n; for (ii = 2; ii <= i__1; ++ii) { i__ = ii - 1; k = i__; p = d__[i__]; i__2 = *n; for (j = ii; j <= i__2; ++j) { if (d__[j] < p) { k = j; p = d__[j]; } /* L50: */ } if (k != i__) { d__[k] = d__[i__]; d__[i__] = p; cswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], &c__1); } /* L60: */ } } } L70: work[1].r = (real) lwmin, work[1].i = 0.f; rwork[1] = (real) lrwmin; iwork[1] = liwmin; return 0; /* End of CSTEDC */ } /* cstedc_ */