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author | shmel1k <shmel1k@ydb.tech> | 2022-09-02 12:44:59 +0300 |
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committer | shmel1k <shmel1k@ydb.tech> | 2022-09-02 12:44:59 +0300 |
commit | 90d450f74722da7859d6f510a869f6c6908fd12f (patch) | |
tree | 538c718dedc76cdfe37ad6d01ff250dd930d9278 /contrib/libs/clapack/dsyevr.c | |
parent | 01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff) | |
download | ydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz |
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/dsyevr.c')
-rw-r--r-- | contrib/libs/clapack/dsyevr.c | 652 |
1 files changed, 652 insertions, 0 deletions
diff --git a/contrib/libs/clapack/dsyevr.c b/contrib/libs/clapack/dsyevr.c new file mode 100644 index 0000000000..4574299fb7 --- /dev/null +++ b/contrib/libs/clapack/dsyevr.c @@ -0,0 +1,652 @@ +/* dsyevr.f -- translated by f2c (version 20061008). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#include "f2c.h" +#include "blaswrap.h" + +/* Table of constant values */ + +static integer c__10 = 10; +static integer c__1 = 1; +static integer c__2 = 2; +static integer c__3 = 3; +static integer c__4 = 4; +static integer c_n1 = -1; + +/* Subroutine */ int dsyevr_(char *jobz, char *range, char *uplo, integer *n, + doublereal *a, integer *lda, doublereal *vl, doublereal *vu, integer * + il, integer *iu, doublereal *abstol, integer *m, doublereal *w, + doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2; + doublereal d__1, d__2; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer i__, j, nb, jj; + doublereal eps, vll, vuu, tmp1; + integer indd, inde; + doublereal anrm; + integer imax; + doublereal rmin, rmax; + integer inddd, indee; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + doublereal sigma; + extern logical lsame_(char *, char *); + integer iinfo; + char order[1]; + integer indwk; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *), dswap_(integer *, doublereal *, integer + *, doublereal *, integer *); + integer lwmin; + logical lower, wantz; + extern doublereal dlamch_(char *); + logical alleig, indeig; + integer iscale, ieeeok, indibl, indifl; + logical valeig; + doublereal safmin; + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *); + extern /* Subroutine */ int xerbla_(char *, integer *); + doublereal abstll, bignum; + integer indtau, indisp; + extern /* Subroutine */ int dstein_(integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *, integer *, integer *), + dsterf_(integer *, doublereal *, doublereal *, integer *); + integer indiwo, indwkn; + extern doublereal dlansy_(char *, char *, integer *, doublereal *, + integer *, doublereal *); + extern /* Subroutine */ int dstebz_(char *, char *, integer *, doublereal + *, doublereal *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, integer *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *), + dstemr_(char *, char *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, integer *, + logical *, doublereal *, integer *, integer *, integer *, integer + *); + integer liwmin; + logical tryrac; + extern /* Subroutine */ int dormtr_(char *, char *, char *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *); + integer llwrkn, llwork, nsplit; + doublereal smlnum; + extern /* Subroutine */ int dsytrd_(char *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + 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 */ +/* ======= */ + +/* DSYEVR computes selected eigenvalues and, optionally, eigenvectors */ +/* of a real symmetric matrix A. Eigenvalues and eigenvectors can be */ +/* selected by specifying either a range of values or a range of */ +/* indices for the desired eigenvalues. */ + +/* DSYEVR first reduces the matrix A to tridiagonal form T with a call */ +/* to DSYTRD. Then, whenever possible, DSYEVR calls DSTEMR to compute */ +/* the eigenspectrum using Relatively Robust Representations. DSTEMR */ +/* 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 : DSYEVR calls DSTEMR when the full spectrum is requested */ +/* on machines which conform to the ieee-754 floating point standard. */ +/* DSYEVR calls DSTEBZ and SSTEIN on non-ieee machines and */ +/* when partial spectrum requests are made. */ + +/* Normal execution of DSTEMR 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, DSTEBZ and */ +/* ********* DSTEIN 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) 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, 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) 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 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 */ +/* DLAMCH( '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 */ +/* future 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) DOUBLE PRECISION array, dimension (N) */ +/* The first M elements contain the selected eigenvalues in */ +/* ascending order. */ + +/* Z (output) DOUBLE PRECISION 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. */ +/* Supplying N columns is always safe. */ + +/* 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) DOUBLE PRECISION 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. LWORK >= max(1,26*N). */ +/* For optimal efficiency, LWORK >= (NB+6)*N, */ +/* where NB is the max of the blocksize for DSYTRD and DORMTR */ +/* 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. */ + +/* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */ +/* On exit, if INFO = 0, IWORK(1) returns the optimal LWORK. */ + +/* 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 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: 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; + --iwork; + + /* Function Body */ + ieeeok = ilaenv_(&c__10, "DSYEVR", "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 || *liwork == -1; + +/* Computing MAX */ + i__1 = 1, i__2 = *n * 26; + lwmin = max(i__1,i__2); +/* Computing MAX */ + i__1 = 1, i__2 = *n * 10; + liwmin = 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; + } else if (*lwork < lwmin && ! lquery) { + *info = -18; + } else if (*liwork < liwmin && ! lquery) { + *info = -20; + } + } + + if (*info == 0) { + nb = ilaenv_(&c__1, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1); +/* Computing MAX */ + i__1 = nb, i__2 = ilaenv_(&c__1, "DORMTR", 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] = (doublereal) lwkopt; + iwork[1] = liwmin; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_("DSYEVR", &i__1); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + *m = 0; + if (*n == 0) { + work[1] = 1.; + return 0; + } + + if (*n == 1) { + work[1] = 7.; + if (alleig || indeig) { + *m = 1; + w[1] = a[a_dim1 + 1]; + } else { + if (*vl < a[a_dim1 + 1] && *vu >= a[a_dim1 + 1]) { + *m = 1; + w[1] = a[a_dim1 + 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); +/* 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; + vll = *vl; + vuu = *vu; + anrm = dlansy_("M", uplo, n, &a[a_offset], lda, &work[1]); + if (anrm > 0. && 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; + dscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1); +/* L10: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + dscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1); +/* L20: */ + } + } + if (*abstol > 0.) { + abstll = *abstol * sigma; + } + if (valeig) { + vll = *vl * sigma; + vuu = *vu * sigma; + } + } +/* Initialize indices into workspaces. Note: The IWORK indices are */ +/* used only if DSTERF or DSTEMR fail. */ +/* WORK(INDTAU:INDTAU+N-1) stores the scalar factors of the */ +/* elementary reflectors used in DSYTRD. */ + indtau = 1; +/* WORK(INDD:INDD+N-1) stores the tridiagonal's diagonal entries. */ + indd = indtau + *n; +/* WORK(INDE:INDE+N-1) stores the off-diagonal entries of the */ +/* tridiagonal matrix from DSYTRD. */ + inde = indd + *n; +/* WORK(INDDD:INDDD+N-1) is a copy of the diagonal entries over */ +/* -written by DSTEMR (the DSTERF path copies the diagonal to W). */ + inddd = inde + *n; +/* WORK(INDEE:INDEE+N-1) is a copy of the off-diagonal entries over */ +/* -written while computing the eigenvalues in DSTERF and DSTEMR. */ + indee = inddd + *n; +/* INDWK is the starting offset of the left-over workspace, and */ +/* LLWORK is the remaining workspace size. */ + indwk = indee + *n; + llwork = *lwork - indwk + 1; +/* IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in DSTEBZ and */ +/* stores the block indices of each of the M<=N eigenvalues. */ + indibl = 1; +/* IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in DSTEBZ 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 */ +/* DSTEIN. 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 DSYTRD to reduce symmetric matrix to tridiagonal form. */ + + dsytrd_(uplo, n, &a[a_offset], lda, &work[indd], &work[inde], &work[ + indtau], &work[indwk], &llwork, &iinfo); + +/* If all eigenvalues are desired */ +/* then call DSTERF or DSTEMR and DORMTR. */ + + if ((alleig || indeig && *il == 1 && *iu == *n) && ieeeok == 1) { + if (! wantz) { + dcopy_(n, &work[indd], &c__1, &w[1], &c__1); + i__1 = *n - 1; + dcopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1); + dsterf_(n, &w[1], &work[indee], info); + } else { + i__1 = *n - 1; + dcopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1); + dcopy_(n, &work[indd], &c__1, &work[inddd], &c__1); + + if (*abstol <= *n * 2. * eps) { + tryrac = TRUE_; + } else { + tryrac = FALSE_; + } + dstemr_(jobz, "A", n, &work[inddd], &work[indee], vl, vu, il, iu, + m, &w[1], &z__[z_offset], ldz, n, &isuppz[1], &tryrac, & + work[indwk], lwork, &iwork[1], liwork, info); + + + +/* Apply orthogonal matrix used in reduction to tridiagonal */ +/* form to eigenvectors returned by DSTEIN. */ + + if (wantz && *info == 0) { + indwkn = inde; + llwrkn = *lwork - indwkn + 1; + dormtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau] +, &z__[z_offset], ldz, &work[indwkn], &llwrkn, &iinfo); + } + } + + + if (*info == 0) { +/* Everything worked. Skip DSTEBZ/DSTEIN. IWORK(:) are */ +/* undefined. */ + *m = *n; + goto L30; + } + *info = 0; + } + +/* Otherwise, call DSTEBZ and, if eigenvectors are desired, DSTEIN. */ +/* Also call DSTEBZ and DSTEIN if DSTEMR fails. */ + + if (wantz) { + *(unsigned char *)order = 'B'; + } else { + *(unsigned char *)order = 'E'; + } + dstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &work[indd], &work[ + inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[ + indwk], &iwork[indiwo], info); + + if (wantz) { + dstein_(n, &work[indd], &work[inde], m, &w[1], &iwork[indibl], &iwork[ + indisp], &z__[z_offset], ldz, &work[indwk], &iwork[indiwo], & + iwork[indifl], info); + +/* Apply orthogonal matrix used in reduction to tridiagonal */ +/* form to eigenvectors returned by DSTEIN. */ + + indwkn = inde; + llwrkn = *lwork - indwkn + 1; + dormtr_("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. */ + +/* Jump here if DSTEMR/DSTEIN succeeded. */ +L30: + 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. Note: We do not sort the IFAIL portion of IWORK. */ +/* It may not be initialized (if DSTEMR/DSTEIN succeeded), and we do */ +/* not return this detailed information to the user. */ + + 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) { + w[i__] = w[j]; + w[j] = tmp1; + dswap_(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] = (doublereal) lwkopt; + iwork[1] = liwmin; + + return 0; + +/* End of DSYEVR */ + +} /* dsyevr_ */ |