/* Subroutine */ int cheevr_(char *jobz, char *range, char *uplo, integer *n, complex *a, integer *lda, real *vl, real *vu, integer *il, integer * iu, real *abstol, integer *m, real *w, complex *z__, integer *ldz, integer *isuppz, complex *work, integer *lwork, real *rwork, integer * lrwork, integer *iwork, integer *liwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2; real r__1, r__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ integer i__, j, nb, jj; real eps, vll, vuu, tmp1, anrm; integer imax; real rmin, rmax; logical test; integer itmp1, indrd, indre; real sigma; extern logical lsame_(char *, char *); integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); char order[1]; integer indwk; extern /* Subroutine */ int cswap_(integer *, complex *, integer *, complex *, integer *); integer lwmin; logical lower; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *); logical wantz, alleig, indeig; integer iscale, ieeeok, indibl, indrdd, indifl, indree; logical valeig; extern doublereal slamch_(char *); extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer *, real *, real *, complex *, complex *, integer *, integer *), csscal_(integer *, real *, complex *, integer *); real safmin; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *); real abstll, bignum; integer indtau, indisp; extern /* Subroutine */ int cstein_(integer *, real *, real *, integer *, real *, integer *, integer *, complex *, integer *, real *, integer *, integer *, integer *); integer indiwo, indwkn; extern doublereal clansy_(char *, char *, integer *, complex *, integer *, real *); extern /* Subroutine */ int cstemr_(char *, char *, integer *, real *, real *, real *, real *, integer *, integer *, integer *, real *, complex *, integer *, integer *, integer *, logical *, real *, integer *, integer *, integer *, integer *); integer indrwk, liwmin; logical tryrac; extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *); integer lrwmin, llwrkn, llwork, nsplit; real smlnum; extern /* Subroutine */ int cunmtr_(char *, char *, char *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *), sstebz_( char *, char *, integer *, real *, real *, integer *, integer *, real *, real *, real *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *); logical lquery; integer lwkopt, llrwork; /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CHEEVR 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. */ /* CHEEVR first reduces the matrix A to tridiagonal form T with a call */ /* to CHETRD. Then, whenever possible, CHEEVR calls CSTEMR to compute */ /* the eigenspectrum using Relatively Robust Representations. CSTEMR */ /* computes eigenvalues by the dqds algorithm, while orthogonal */ /* eigenvectors are computed from various "good" L D L^T representations */ /* (also known as Relatively Robust Representations). Gram-Schmidt */ /* orthogonalization is avoided as far as possible. More specifically, */ /* the various steps of the algorithm are as follows. */ /* For each unreduced block (submatrix) of T, */ /* (a) Compute T - sigma I = L D L^T, so that L and D */ /* define all the wanted eigenvalues to high relative accuracy. */ /* This means that small relative changes in the entries of D and L */ /* cause only small relative changes in the eigenvalues and */ /* eigenvectors. The standard (unfactored) representation of the */ /* tridiagonal matrix T does not have this property in general. */ /* (b) Compute the eigenvalues to suitable accuracy. */ /* If the eigenvectors are desired, the algorithm attains full */ /* accuracy of the computed eigenvalues only right before */ /* the corresponding vectors have to be computed, see steps c) and d). */ /* (c) For each cluster of close eigenvalues, select a new */ /* shift close to the cluster, find a new factorization, and refine */ /* the shifted eigenvalues to suitable accuracy. */ /* (d) For each eigenvalue with a large enough relative separation compute */ /* the corresponding eigenvector by forming a rank revealing twisted */ /* factorization. Go back to (c) for any clusters that remain. */ /* The desired accuracy of the output can be specified by the input */ /* parameter ABSTOL. */ /* For more details, see DSTEMR's documentation and: */ /* - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations */ /* to compute orthogonal eigenvectors of symmetric tridiagonal matrices," */ /* Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. */ /* - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and */ /* Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, */ /* 2004. Also LAPACK Working Note 154. */ /* - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric */ /* tridiagonal eigenvalue/eigenvector problem", */ /* Computer Science Division Technical Report No. UCB/CSD-97-971, */ /* UC Berkeley, May 1997. */ /* Note 1 : CHEEVR calls CSTEMR when the full spectrum is requested */ /* on machines which conform to the ieee-754 floating point standard. */ /* CHEEVR calls SSTEBZ and CSTEIN on non-ieee machines and */ /* when partial spectrum requests are made. */ /* Normal execution of CSTEMR may create NaNs and infinities and */ /* hence may abort due to a floating point exception in environments */ /* which do not handle NaNs and infinities in the ieee standard default */ /* manner. */ /* 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. */ /* ********* For RANGE = 'V' or 'I' and IU - IL < N - 1, SSTEBZ and */ /* ********* CSTEIN are called */ /* 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 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) REAL */ /* VU (input) REAL */ /* 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) REAL */ /* 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. */ /* See "Computing Small Singular Values of Bidiagonal Matrices */ /* with Guaranteed High Relative Accuracy," by Demmel and */ /* Kahan, LAPACK Working Note #3. */ /* If high relative accuracy is important, set ABSTOL to */ /* SLAMCH( 'Safe minimum' ). Doing so will guarantee that */ /* eigenvalues are computed to high relative accuracy when */ /* possible in future releases. The current code does not */ /* make any guarantees about high relative accuracy, but */ /* furutre releases will. See J. Barlow and J. Demmel, */ /* "Computing Accurate Eigensystems of Scaled Diagonally */ /* Dominant Matrices", LAPACK Working Note #7, for a discussion */ /* of which matrices define their eigenvalues to high relative */ /* accuracy. */ /* 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) REAL array, dimension (N) */ /* The first M elements contain the selected eigenvalues in */ /* ascending order. */ /* Z (output) COMPLEX 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 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). */ /* ISUPPZ (output) INTEGER array, dimension ( 2*max(1,M) ) */ /* The support of the eigenvectors in Z, i.e., the indices */ /* indicating the nonzero elements in Z. The i-th eigenvector */ /* is nonzero only in elements ISUPPZ( 2*i-1 ) through */ /* ISUPPZ( 2*i ). */ /* ********* Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 */ /* WORK (workspace/output) COMPLEX array, dimension (MAX(1,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). */ /* For optimal efficiency, LWORK >= (NB+1)*N, */ /* where NB is the max of the blocksize for CHETRD and for */ /* CUNMTR as returned by ILAENV. */ /* 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 */ /* (and minimal) LRWORK. */ /* LRWORK (input) INTEGER */ /* The length of the array RWORK. LRWORK >= max(1,24*N). */ /* 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 */ /* (and minimal) LIWORK. */ /* LIWORK (input) INTEGER */ /* The dimension of the array IWORK. LIWORK >= max(1,10*N). */ /* 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: Internal error */ /* Further Details */ /* =============== */ /* Based on contributions by */ /* Inderjit Dhillon, IBM Almaden, USA */ /* Osni Marques, LBNL/NERSC, USA */ /* Ken Stanley, Computer Science Division, University of */ /* California at Berkeley, USA */ /* Jason Riedy, Computer Science Division, University of */ /* California at Berkeley, USA */ /* ===================================================================== */ /* .. 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; --isuppz; --work; --rwork; --iwork; /* Function Body */ ieeeok = ilaenv_(&c__10, "CHEEVR", "N", &c__1, &c__2, &c__3, &c__4); lower = lsame_(uplo, "L"); wantz = lsame_(jobz, "V"); alleig = lsame_(range, "A"); valeig = lsame_(range, "V"); indeig = lsame_(range, "I"); lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; /* Computing MAX */ i__1 = 1, i__2 = *n * 24; lrwmin = max(i__1,i__2); /* Computing MAX */ i__1 = 1, i__2 = *n * 10; liwmin = max(i__1,i__2); /* Computing MAX */ i__1 = 1, i__2 = *n << 1; lwmin = max(i__1,i__2); *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) { nb = ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1); /* Computing MAX */ i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMTR", uplo, n, &c_n1, &c_n1, & c_n1); nb = max(i__1,i__2); /* Computing MAX */ i__1 = (nb + 1) * *n; lwkopt = max(i__1,lwmin); work[1].r = (real) lwkopt, work[1].i = 0.f; rwork[1] = (real) lrwmin; iwork[1] = liwmin; if (*lwork < lwmin && ! lquery) { *info = -18; } else if (*lrwork < lrwmin && ! lquery) { *info = -20; } else if (*liwork < liwmin && ! lquery) { *info = -22; } } if (*info != 0) { i__1 = -(*info); xerbla_("CHEEVR", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { work[1].r = 1.f, work[1].i = 0.f; return 0; } if (*n == 1) { work[1].r = 2.f, work[1].i = 0.f; if (alleig || indeig) { *m = 1; i__1 = a_dim1 + 1; w[1] = a[i__1].r; } else { 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.f, z__[i__1].i = 0.f; } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum"); eps = slamch_("Precision"); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); /* Computing MIN */ r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin)); rmax = dmin(r__1,r__2); /* Scale matrix to allowable range, if necessary. */ iscale = 0; abstll = *abstol; if (valeig) { vll = *vl; vuu = *vu; } anrm = clansy_("M", uplo, n, &a[a_offset], lda, &rwork[1]); if (anrm > 0.f && 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; csscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1); /* L10: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { csscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1); /* L20: */ } } if (*abstol > 0.f) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Initialize indices into workspaces. Note: The IWORK indices are */ /* used only if SSTERF or CSTEMR fail. */ /* WORK(INDTAU:INDTAU+N-1) stores the complex scalar factors of the */ /* elementary reflectors used in CHETRD. */ indtau = 1; /* INDWK is the starting offset of the remaining complex workspace, */ /* and LLWORK is the remaining complex workspace size. */ indwk = indtau + *n; llwork = *lwork - indwk + 1; /* RWORK(INDRD:INDRD+N-1) stores the real tridiagonal's diagonal */ /* entries. */ indrd = 1; /* RWORK(INDRE:INDRE+N-1) stores the off-diagonal entries of the */ /* tridiagonal matrix from CHETRD. */ indre = indrd + *n; /* RWORK(INDRDD:INDRDD+N-1) is a copy of the diagonal entries over */ /* -written by CSTEMR (the SSTERF path copies the diagonal to W). */ indrdd = indre + *n; /* RWORK(INDREE:INDREE+N-1) is a copy of the off-diagonal entries over */ /* -written while computing the eigenvalues in SSTERF and CSTEMR. */ indree = indrdd + *n; /* INDRWK is the starting offset of the left-over real workspace, and */ /* LLRWORK is the remaining workspace size. */ indrwk = indree + *n; llrwork = *lrwork - indrwk + 1; /* IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in SSTEBZ and */ /* stores the block indices of each of the M<=N eigenvalues. */ indibl = 1; /* IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in SSTEBZ and */ /* stores the starting and finishing indices of each block. */ indisp = indibl + *n; /* IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors */ /* that corresponding to eigenvectors that fail to converge in */ /* SSTEIN. This information is discarded; if any fail, the driver */ /* returns INFO > 0. */ indifl = indisp + *n; /* INDIWO is the offset of the remaining integer workspace. */ indiwo = indisp + *n; /* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */ chetrd_(uplo, n, &a[a_offset], lda, &rwork[indrd], &rwork[indre], &work[ indtau], &work[indwk], &llwork, &iinfo); /* If all eigenvalues are desired */ /* then call SSTERF or CSTEMR and CUNMTR. */ test = FALSE_; if (indeig) { if (*il == 1 && *iu == *n) { test = TRUE_; } } if ((alleig || test) && ieeeok == 1) { if (! wantz) { scopy_(n, &rwork[indrd], &c__1, &w[1], &c__1); i__1 = *n - 1; scopy_(&i__1, &rwork[indre], &c__1, &rwork[indree], &c__1); ssterf_(n, &w[1], &rwork[indree], info); } else { i__1 = *n - 1; scopy_(&i__1, &rwork[indre], &c__1, &rwork[indree], &c__1); scopy_(n, &rwork[indrd], &c__1, &rwork[indrdd], &c__1); if (*abstol <= *n * 2.f * eps) { tryrac = TRUE_; } else { tryrac = FALSE_; } cstemr_(jobz, "A", n, &rwork[indrdd], &rwork[indree], vl, vu, il, iu, m, &w[1], &z__[z_offset], ldz, n, &isuppz[1], &tryrac, &rwork[indrwk], &llrwork, &iwork[1], liwork, info); /* Apply unitary matrix used in reduction to tridiagonal */ /* form to eigenvectors returned by CSTEIN. */ if (wantz && *info == 0) { indwkn = indwk; llwrkn = *lwork - indwkn + 1; cunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau] , &z__[z_offset], ldz, &work[indwkn], &llwrkn, &iinfo); } } if (*info == 0) { *m = *n; goto L30; } *info = 0; } /* Otherwise, call SSTEBZ and, if eigenvectors are desired, CSTEIN. */ /* Also call SSTEBZ and CSTEIN if CSTEMR fails. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &rwork[indrd], & rwork[indre], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], & rwork[indrwk], &iwork[indiwo], info); if (wantz) { cstein_(n, &rwork[indrd], &rwork[indre], m, &w[1], &iwork[indibl], & iwork[indisp], &z__[z_offset], ldz, &rwork[indrwk], &iwork[ indiwo], &iwork[indifl], info); /* Apply unitary matrix used in reduction to tridiagonal */ /* form to eigenvectors returned by CSTEIN. */ indwkn = indwk; llwrkn = *lwork - indwkn + 1; cunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau], &z__[ z_offset], ldz, &work[indwkn], &llwrkn, &iinfo); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L30: if (iscale == 1) { if (*info == 0) { imax = *m; } else { imax = *info - 1; } r__1 = 1.f / sigma; sscal_(&imax, &r__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]; } /* 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; cswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], &c__1); } /* L50: */ } } /* Set WORK(1) to optimal workspace size. */ work[1].r = (real) lwkopt, work[1].i = 0.f; rwork[1] = (real) lrwmin; iwork[1] = liwmin; return 0; /* End of CHEEVR */ } /* cheevr_ */
/* Subroutine */ int cheev_(char *jobz, char *uplo, integer *n, complex *a, integer *lda, real *w, complex *work, integer *lwork, real *rwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; real r__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ integer nb; real eps; integer inde; real anrm; integer imax; real rmin, rmax, sigma; extern logical lsame_(char *, char *); integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); logical lower, wantz; extern real clanhe_(char *, char *, integer *, complex *, integer *, real *); integer iscale; extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, real *, integer *, integer *, complex *, integer *, integer *); extern real slamch_(char *); extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer *, real *, real *, complex *, complex *, integer *, integer *); real safmin; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *); real bignum; integer indtau, indwrk; extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, complex *, integer *, real *, integer *), cungtr_(char *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), ssterf_(integer *, real *, real *, integer *); integer llwork; real smlnum; integer lwkopt; logical lquery; /* -- 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; --work; --rwork; /* Function Body */ wantz = lsame_(jobz, "V"); lower = lsame_(uplo, "L"); lquery = *lwork == -1; *info = 0; 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; } if (*info == 0) { nb = ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1); /* Computing MAX */ i__1 = 1; i__2 = (nb + 1) * *n; // , expr subst lwkopt = max(i__1,i__2); work[1].r = (real) lwkopt; work[1].i = 0.f; // , expr subst /* Computing MAX */ i__1 = 1; i__2 = (*n << 1) - 1; // , expr subst if (*lwork < max(i__1,i__2) && ! lquery) { *info = -8; } } if (*info != 0) { i__1 = -(*info); xerbla_("CHEEV ", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { i__1 = a_dim1 + 1; w[1] = a[i__1].r; work[1].r = 1.f; work[1].i = 0.f; // , expr subst if (wantz) { i__1 = a_dim1 + 1; a[i__1].r = 1.f; a[i__1].i = 0.f; // , expr subst } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum"); eps = slamch_("Precision"); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); rmax = sqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = clanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]); iscale = 0; if (anrm > 0.f && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { clascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, info); } /* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */ inde = 1; indtau = 1; indwrk = indtau + *n; llwork = *lwork - indwrk + 1; chetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], & work[indwrk], &llwork, &iinfo); /* For eigenvalues only, call SSTERF. For eigenvectors, first call */ /* CUNGTR to generate the unitary matrix, then call CSTEQR. */ if (! wantz) { ssterf_(n, &w[1], &rwork[inde], info); } else { cungtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], & llwork, &iinfo); indwrk = inde + *n; csteqr_(jobz, n, &w[1], &rwork[inde], &a[a_offset], lda, &rwork[ indwrk], info); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { if (*info == 0) { imax = *n; } else { imax = *info - 1; } r__1 = 1.f / sigma; sscal_(&imax, &r__1, &w[1], &c__1); } /* Set WORK(1) to optimal complex workspace size. */ work[1].r = (real) lwkopt; work[1].i = 0.f; // , expr subst return 0; /* End of CHEEV */ }
/* Subroutine */ int cheev_(char *jobz, char *uplo, integer *n, complex *a, integer *lda, real *w, complex *work, integer *lwork, real *rwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; real r__1; complex q__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer nb; static real eps; static integer inde; static real anrm; static integer imax; static real rmin, rmax; static integer lopt; static real sigma; extern logical lsame_(char *, char *, ftnlen, ftnlen); static integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); static logical lower, wantz; extern doublereal clanhe_(char *, char *, integer *, complex *, integer *, real *, ftnlen, ftnlen); static integer iscale; extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, real *, integer *, integer *, complex *, integer *, integer *, ftnlen); extern doublereal slamch_(char *, ftnlen); extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer *, real *, real *, complex *, complex *, integer *, integer *, ftnlen); static real safmin; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); static real bignum; static integer indtau, indwrk; extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, complex *, integer *, real *, integer *, ftnlen), cungtr_(char *, integer *, complex *, integer *, complex *, complex *, integer *, integer *, ftnlen), ssterf_(integer *, real *, real *, integer *); static integer llwork; static real smlnum; static integer lwkopt; static logical lquery; /* -- 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 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CHEEV computes all eigenvalues and, optionally, eigenvectors of a */ /* complex Hermitian matrix A. */ /* 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) COMPLEX 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, 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) REAL array, dimension (N) */ /* If INFO = 0, the eigenvalues in ascending order. */ /* WORK (workspace/output) COMPLEX 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 CHETRD returned by ILAENV. */ /* 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. */ /* RWORK (workspace) REAL 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 */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --w; --work; --rwork; /* Function Body */ wantz = lsame_(jobz, "V", (ftnlen)1, (ftnlen)1); lower = lsame_(uplo, "L", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; *info = 0; if (! (wantz || lsame_(jobz, "N", (ftnlen)1, (ftnlen)1))) { *info = -1; } else if (! (lower || lsame_(uplo, "U", (ftnlen)1, (ftnlen)1))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*lda < max(1,*n)) { *info = -5; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = (*n << 1) - 1; if (*lwork < max(i__1,i__2) && ! lquery) { *info = -8; } } if (*info == 0) { nb = ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ i__1 = 1, i__2 = (nb + 1) * *n; lwkopt = max(i__1,i__2); work[1].r = (real) lwkopt, work[1].i = 0.f; } if (*info != 0) { i__1 = -(*info); xerbla_("CHEEV ", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { work[1].r = 1.f, work[1].i = 0.f; return 0; } if (*n == 1) { i__1 = a_dim1 + 1; w[1] = a[i__1].r; work[1].r = 3.f, work[1].i = 0.f; if (wantz) { i__1 = a_dim1 + 1; a[i__1].r = 1.f, a[i__1].i = 0.f; } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum", (ftnlen)12); eps = slamch_("Precision", (ftnlen)9); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); rmax = sqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = clanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, ( ftnlen)1); iscale = 0; if (anrm > 0.f && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { clascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, info, (ftnlen)1); } /* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */ inde = 1; indtau = 1; indwrk = indtau + *n; llwork = *lwork - indwrk + 1; chetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], & work[indwrk], &llwork, &iinfo, (ftnlen)1); i__1 = indwrk; q__1.r = *n + work[i__1].r, q__1.i = work[i__1].i; lopt = q__1.r; /* For eigenvalues only, call SSTERF. For eigenvectors, first call */ /* CUNGTR to generate the unitary matrix, then call CSTEQR. */ if (! wantz) { ssterf_(n, &w[1], &rwork[inde], info); } else { cungtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], & llwork, &iinfo, (ftnlen)1); indwrk = inde + *n; csteqr_(jobz, n, &w[1], &rwork[inde], &a[a_offset], lda, &rwork[ indwrk], info, (ftnlen)1); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { if (*info == 0) { imax = *n; } else { imax = *info - 1; } r__1 = 1.f / sigma; sscal_(&imax, &r__1, &w[1], &c__1); } /* Set WORK(1) to optimal complex workspace size. */ work[1].r = (real) lwkopt, work[1].i = 0.f; return 0; /* End of CHEEV */ } /* cheev_ */
/* Subroutine */ int cheevd_(char *jobz, char *uplo, integer *n, complex *a, integer *lda, real *w, complex *work, integer *lwork, real *rwork, integer *lrwork, integer *iwork, integer *liwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; real r__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ real eps; integer inde; real anrm; integer imax; real rmin, rmax; integer lopt; real sigma; extern logical lsame_(char *, char *); integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); integer lwmin, liopt; logical lower; integer llrwk, lropt; logical wantz; integer indwk2, llwrk2; extern doublereal clanhe_(char *, char *, integer *, complex *, integer *, real *); integer iscale; extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, real *, integer *, integer *, complex *, integer *, integer *), cstedc_(char *, integer *, real *, real *, complex *, integer *, complex *, integer *, real *, integer *, integer *, integer *, integer *); extern doublereal slamch_(char *); extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer *, real *, real *, complex *, complex *, integer *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *); real safmin; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *); real bignum; integer indtau, indrwk, indwrk, liwmin; extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *); integer lrwmin; extern /* Subroutine */ int cunmtr_(char *, char *, char *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *); integer llwork; real smlnum; logical lquery; /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CHEEVD computes all eigenvalues and, optionally, eigenvectors of a */ /* complex Hermitian 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. */ /* 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) COMPLEX 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, 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) REAL array, dimension (N) */ /* If INFO = 0, the eigenvalues in ascending order. */ /* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */ /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* LWORK (input) INTEGER */ /* The length of the array WORK. */ /* If N <= 1, LWORK must be at least 1. */ /* If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. */ /* If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. */ /* 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 (LRWORK) */ /* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */ /* LRWORK (input) INTEGER */ /* The dimension of the array RWORK. */ /* If N <= 1, LRWORK must be at least 1. */ /* If JOBZ = 'N' and N > 1, LRWORK must be at least N. */ /* If JOBZ = 'V' and N > 1, LRWORK must be at least */ /* 1 + 5*N + 2*N**2. */ /* 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 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 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: if INFO = i and JOBZ = 'N', then the algorithm failed */ /* to converge; i off-diagonal elements of an intermediate */ /* tridiagonal form did not converge to zero; */ /* if INFO = i and JOBZ = 'V', then 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 */ /* Modified description of INFO. Sven, 16 Feb 05. */ /* ===================================================================== */ /* .. 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; --work; --rwork; --iwork; /* Function Body */ wantz = lsame_(jobz, "V"); lower = lsame_(uplo, "L"); lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; *info = 0; 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; } if (*info == 0) { if (*n <= 1) { lwmin = 1; lrwmin = 1; liwmin = 1; lopt = lwmin; lropt = lrwmin; liopt = liwmin; } else { if (wantz) { lwmin = (*n << 1) + *n * *n; /* Computing 2nd power */ i__1 = *n; lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1); liwmin = *n * 5 + 3; } else { lwmin = *n + 1; lrwmin = *n; liwmin = 1; } /* Computing MAX */ i__1 = lwmin, i__2 = *n + ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1); lopt = max(i__1,i__2); lropt = lrwmin; liopt = liwmin; } work[1].r = (real) lopt, work[1].i = 0.f; rwork[1] = (real) lropt; iwork[1] = liopt; 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_("CHEEVD", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { i__1 = a_dim1 + 1; w[1] = a[i__1].r; if (wantz) { i__1 = a_dim1 + 1; a[i__1].r = 1.f, a[i__1].i = 0.f; } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum"); eps = slamch_("Precision"); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); rmax = sqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = clanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]); iscale = 0; if (anrm > 0.f && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { clascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, info); } /* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */ inde = 1; indtau = 1; indwrk = indtau + *n; indrwk = inde + *n; indwk2 = indwrk + *n * *n; llwork = *lwork - indwrk + 1; llwrk2 = *lwork - indwk2 + 1; llrwk = *lrwork - indrwk + 1; chetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], & work[indwrk], &llwork, &iinfo); /* For eigenvalues only, call SSTERF. For eigenvectors, first call */ /* CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */ /* tridiagonal matrix, then call CUNMTR to multiply it to the */ /* Householder transformations represented as Householder vectors in */ /* A. */ if (! wantz) { ssterf_(n, &w[1], &rwork[inde], info); } else { cstedc_("I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2], &llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info); cunmtr_("L", uplo, "N", n, n, &a[a_offset], lda, &work[indtau], &work[ indwrk], n, &work[indwk2], &llwrk2, &iinfo); clacpy_("A", n, n, &work[indwrk], n, &a[a_offset], lda); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { if (*info == 0) { imax = *n; } else { imax = *info - 1; } r__1 = 1.f / sigma; sscal_(&imax, &r__1, &w[1], &c__1); } work[1].r = (real) lopt, work[1].i = 0.f; rwork[1] = (real) lropt; iwork[1] = liopt; return 0; /* End of CHEEVD */ } /* cheevd_ */
int main(void) { /* Local scalars */ char uplo, uplo_i; lapack_int n, n_i; lapack_int lda, lda_i; lapack_int lda_r; lapack_int lwork, lwork_i; lapack_int info, info_i; lapack_int i; int failed; /* Local arrays */ lapack_complex_float *a = NULL, *a_i = NULL; float *d = NULL, *d_i = NULL; float *e = NULL, *e_i = NULL; lapack_complex_float *tau = NULL, *tau_i = NULL; lapack_complex_float *work = NULL, *work_i = NULL; lapack_complex_float *a_save = NULL; float *d_save = NULL; float *e_save = NULL; lapack_complex_float *tau_save = NULL; lapack_complex_float *a_r = NULL; /* Iniitialize the scalar parameters */ init_scalars_chetrd( &uplo, &n, &lda, &lwork ); lda_r = n+2; uplo_i = uplo; n_i = n; lda_i = lda; lwork_i = lwork; /* Allocate memory for the LAPACK routine arrays */ a = (lapack_complex_float *) LAPACKE_malloc( lda*n * sizeof(lapack_complex_float) ); d = (float *)LAPACKE_malloc( n * sizeof(float) ); e = (float *)LAPACKE_malloc( (n-1) * sizeof(float) ); tau = (lapack_complex_float *) LAPACKE_malloc( (n-1) * sizeof(lapack_complex_float) ); work = (lapack_complex_float *) LAPACKE_malloc( lwork * sizeof(lapack_complex_float) ); /* Allocate memory for the C interface function arrays */ a_i = (lapack_complex_float *) LAPACKE_malloc( lda*n * sizeof(lapack_complex_float) ); d_i = (float *)LAPACKE_malloc( n * sizeof(float) ); e_i = (float *)LAPACKE_malloc( (n-1) * sizeof(float) ); tau_i = (lapack_complex_float *) LAPACKE_malloc( (n-1) * sizeof(lapack_complex_float) ); work_i = (lapack_complex_float *) LAPACKE_malloc( lwork * sizeof(lapack_complex_float) ); /* Allocate memory for the backup arrays */ a_save = (lapack_complex_float *) LAPACKE_malloc( lda*n * sizeof(lapack_complex_float) ); d_save = (float *)LAPACKE_malloc( n * sizeof(float) ); e_save = (float *)LAPACKE_malloc( (n-1) * sizeof(float) ); tau_save = (lapack_complex_float *) LAPACKE_malloc( (n-1) * sizeof(lapack_complex_float) ); /* Allocate memory for the row-major arrays */ a_r = (lapack_complex_float *) LAPACKE_malloc( n*(n+2) * sizeof(lapack_complex_float) ); /* Initialize input arrays */ init_a( lda*n, a ); init_d( n, d ); init_e( (n-1), e ); init_tau( (n-1), tau ); init_work( lwork, work ); /* Backup the ouptut arrays */ for( i = 0; i < lda*n; i++ ) { a_save[i] = a[i]; } for( i = 0; i < n; i++ ) { d_save[i] = d[i]; } for( i = 0; i < (n-1); i++ ) { e_save[i] = e[i]; } for( i = 0; i < (n-1); i++ ) { tau_save[i] = tau[i]; } /* Call the LAPACK routine */ chetrd_( &uplo, &n, a, &lda, d, e, tau, work, &lwork, &info ); /* Initialize input data, call the column-major middle-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a_save[i]; } for( i = 0; i < n; i++ ) { d_i[i] = d_save[i]; } for( i = 0; i < (n-1); i++ ) { e_i[i] = e_save[i]; } for( i = 0; i < (n-1); i++ ) { tau_i[i] = tau_save[i]; } for( i = 0; i < lwork; i++ ) { work_i[i] = work[i]; } info_i = LAPACKE_chetrd_work( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i, d_i, e_i, tau_i, work_i, lwork_i ); failed = compare_chetrd( a, a_i, d, d_i, e, e_i, tau, tau_i, info, info_i, lda, n ); if( failed == 0 ) { printf( "PASSED: column-major middle-level interface to chetrd\n" ); } else { printf( "FAILED: column-major middle-level interface to chetrd\n" ); } /* Initialize input data, call the column-major high-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a_save[i]; } for( i = 0; i < n; i++ ) { d_i[i] = d_save[i]; } for( i = 0; i < (n-1); i++ ) { e_i[i] = e_save[i]; } for( i = 0; i < (n-1); i++ ) { tau_i[i] = tau_save[i]; } for( i = 0; i < lwork; i++ ) { work_i[i] = work[i]; } info_i = LAPACKE_chetrd( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i, d_i, e_i, tau_i ); failed = compare_chetrd( a, a_i, d, d_i, e, e_i, tau, tau_i, info, info_i, lda, n ); if( failed == 0 ) { printf( "PASSED: column-major high-level interface to chetrd\n" ); } else { printf( "FAILED: column-major high-level interface to chetrd\n" ); } /* Initialize input data, call the row-major middle-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a_save[i]; } for( i = 0; i < n; i++ ) { d_i[i] = d_save[i]; } for( i = 0; i < (n-1); i++ ) { e_i[i] = e_save[i]; } for( i = 0; i < (n-1); i++ ) { tau_i[i] = tau_save[i]; } for( i = 0; i < lwork; i++ ) { work_i[i] = work[i]; } LAPACKE_cge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 ); info_i = LAPACKE_chetrd_work( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r, d_i, e_i, tau_i, work_i, lwork_i ); LAPACKE_cge_trans( LAPACK_ROW_MAJOR, n, n, a_r, n+2, a_i, lda ); failed = compare_chetrd( a, a_i, d, d_i, e, e_i, tau, tau_i, info, info_i, lda, n ); if( failed == 0 ) { printf( "PASSED: row-major middle-level interface to chetrd\n" ); } else { printf( "FAILED: row-major middle-level interface to chetrd\n" ); } /* Initialize input data, call the row-major high-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a_save[i]; } for( i = 0; i < n; i++ ) { d_i[i] = d_save[i]; } for( i = 0; i < (n-1); i++ ) { e_i[i] = e_save[i]; } for( i = 0; i < (n-1); i++ ) { tau_i[i] = tau_save[i]; } for( i = 0; i < lwork; i++ ) { work_i[i] = work[i]; } /* Init row_major arrays */ LAPACKE_cge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 ); info_i = LAPACKE_chetrd( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r, d_i, e_i, tau_i ); LAPACKE_cge_trans( LAPACK_ROW_MAJOR, n, n, a_r, n+2, a_i, lda ); failed = compare_chetrd( a, a_i, d, d_i, e, e_i, tau, tau_i, info, info_i, lda, n ); if( failed == 0 ) { printf( "PASSED: row-major high-level interface to chetrd\n" ); } else { printf( "FAILED: row-major high-level interface to chetrd\n" ); } /* Release memory */ if( a != NULL ) { LAPACKE_free( a ); } if( a_i != NULL ) { LAPACKE_free( a_i ); } if( a_r != NULL ) { LAPACKE_free( a_r ); } if( a_save != NULL ) { LAPACKE_free( a_save ); } if( d != NULL ) { LAPACKE_free( d ); } if( d_i != NULL ) { LAPACKE_free( d_i ); } if( d_save != NULL ) { LAPACKE_free( d_save ); } if( e != NULL ) { LAPACKE_free( e ); } if( e_i != NULL ) { LAPACKE_free( e_i ); } if( e_save != NULL ) { LAPACKE_free( e_save ); } if( tau != NULL ) { LAPACKE_free( tau ); } if( tau_i != NULL ) { LAPACKE_free( tau_i ); } if( tau_save != NULL ) { LAPACKE_free( tau_save ); } if( work != NULL ) { LAPACKE_free( work ); } if( work_i != NULL ) { LAPACKE_free( work_i ); } return 0; }
/* Subroutine */ int cheevx_(char *jobz, char *range, char *uplo, integer *n, complex *a, integer *lda, real *vl, real *vu, integer *il, integer * iu, real *abstol, integer *m, real *w, complex *z__, integer *ldz, complex *work, integer *lwork, real *rwork, integer *iwork, integer * ifail, integer *info) { /* System generated locals */ integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2; real r__1, r__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ integer i__, j, nb, jj; real eps, vll, vuu, tmp1; integer indd, inde; real anrm; integer imax; real rmin, rmax; logical test; integer itmp1, indee; real sigma; extern logical lsame_(char *, char *); integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); char order[1]; extern /* Subroutine */ int cswap_(integer *, complex *, integer *, complex *, integer *); logical lower; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *); logical wantz; extern doublereal clanhe_(char *, char *, integer *, complex *, integer *, real *); logical alleig, indeig; integer iscale, indibl; logical valeig; extern doublereal slamch_(char *); extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer *, real *, real *, complex *, complex *, integer *, integer *), csscal_(integer *, real *, complex *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *); real safmin; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *); real abstll, bignum; integer indiwk, indisp, indtau; extern /* Subroutine */ int cstein_(integer *, real *, real *, integer *, real *, integer *, integer *, complex *, integer *, real *, integer *, integer *, integer *); integer indrwk, indwrk, lwkmin; extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, complex *, integer *, real *, integer *), cungtr_(char *, integer *, complex *, integer *, complex *, complex *, integer *, integer *), ssterf_(integer *, real *, real *, integer *), cunmtr_(char *, char *, char *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *, integer *); integer nsplit, llwork; real smlnum; extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *, real *, integer *, integer *, real *, real *, real *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *); integer lwkopt; logical lquery; /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CHEEVX 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 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) REAL */ /* VU (input) REAL */ /* 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) REAL */ /* 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*SLAMCH('S'), not zero. */ /* If this routine returns with INFO>0, indicating that some */ /* eigenvectors did not converge, try setting ABSTOL to */ /* 2*SLAMCH('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) REAL array, dimension (N) */ /* On normal exit, the first M elements contain the selected */ /* eigenvalues in ascending order. */ /* Z (output) COMPLEX 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 array, dimension (MAX(1,LWORK)) */ /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* LWORK (input) INTEGER */ /* The length of the array WORK. LWORK >= 1, when N <= 1; */ /* otherwise 2*N. */ /* For optimal efficiency, LWORK >= (NB+1)*N, */ /* where NB is the max of the blocksize for CHETRD and for */ /* CUNMTR as returned by ILAENV. */ /* 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. */ /* RWORK (workspace) REAL 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 */ 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 = (real) lwkmin, work[1].i = 0.f; } else { lwkmin = *n << 1; nb = ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1); /* Computing MAX */ i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMTR", uplo, n, &c_n1, &c_n1, &c_n1); nb = max(i__1,i__2); /* Computing MAX */ i__1 = 1, i__2 = (nb + 1) * *n; lwkopt = max(i__1,i__2); work[1].r = (real) lwkopt, work[1].i = 0.f; } if (*lwork < lwkmin && ! lquery) { *info = -17; } } if (*info != 0) { i__1 = -(*info); xerbla_("CHEEVX", &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.f, z__[i__1].i = 0.f; } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum"); eps = slamch_("Precision"); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); /* Computing MIN */ r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin)); rmax = dmin(r__1,r__2); /* Scale matrix to allowable range, if necessary. */ iscale = 0; abstll = *abstol; if (valeig) { vll = *vl; vuu = *vu; } anrm = clanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]); if (anrm > 0.f && 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; csscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1); /* L10: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { csscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1); /* L20: */ } } if (*abstol > 0.f) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */ indd = 1; inde = indd + *n; indrwk = inde + *n; indtau = 1; indwrk = indtau + *n; llwork = *lwork - indwrk + 1; chetrd_(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 SSTERF or CUNGTR and CSTEQR. If this fails for */ /* some eigenvalue, then try SSTEBZ. */ test = FALSE_; if (indeig) { if (*il == 1 && *iu == *n) { test = TRUE_; } } if ((alleig || test) && *abstol <= 0.f) { scopy_(n, &rwork[indd], &c__1, &w[1], &c__1); indee = indrwk + (*n << 1); if (! wantz) { i__1 = *n - 1; scopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); ssterf_(n, &w[1], &rwork[indee], info); } else { clacpy_("A", n, n, &a[a_offset], lda, &z__[z_offset], ldz); cungtr_(uplo, n, &z__[z_offset], ldz, &work[indtau], &work[indwrk] , &llwork, &iinfo); i__1 = *n - 1; scopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); csteqr_(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 SSTEBZ and, if eigenvectors are desired, CSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwk = indisp + *n; sstebz_(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) { cstein_(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 CSTEIN. */ cunmtr_("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; } r__1 = 1.f / sigma; sscal_(&imax, &r__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; cswap_(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 = (real) lwkopt, work[1].i = 0.f; return 0; /* End of CHEEVX */ } /* cheevx_ */