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#include "rb_lapack.h"
extern VOID zheevr_(char* jobz, char* range, char* uplo, integer* n, doublecomplex* a, integer* lda, doublereal* vl, doublereal* vu, integer* il, integer* iu, doublereal* abstol, integer* m, doublereal* w, doublecomplex* z, integer* ldz, integer* isuppz, doublecomplex* work, integer* lwork, doublereal* rwork, integer* lrwork, integer* iwork, integer* liwork, integer* info);
static VALUE
rblapack_zheevr(int argc, VALUE *argv, VALUE self){
VALUE rblapack_jobz;
char jobz;
VALUE rblapack_range;
char range;
VALUE rblapack_uplo;
char uplo;
VALUE rblapack_a;
doublecomplex *a;
VALUE rblapack_vl;
doublereal vl;
VALUE rblapack_vu;
doublereal vu;
VALUE rblapack_il;
integer il;
VALUE rblapack_iu;
integer iu;
VALUE rblapack_abstol;
doublereal abstol;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_lrwork;
integer lrwork;
VALUE rblapack_liwork;
integer liwork;
VALUE rblapack_m;
integer m;
VALUE rblapack_w;
doublereal *w;
VALUE rblapack_z;
doublecomplex *z;
VALUE rblapack_isuppz;
integer *isuppz;
VALUE rblapack_work;
doublecomplex *work;
VALUE rblapack_rwork;
doublereal *rwork;
VALUE rblapack_iwork;
integer *iwork;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
doublecomplex *a_out__;
integer lda;
integer n;
integer ldz;
VALUE rblapack_options;
if (argc > 0 && TYPE(argv[argc-1]) == T_HASH) {
argc--;
rblapack_options = argv[argc];
if (rb_hash_aref(rblapack_options, sHelp) == Qtrue) {
printf("%s\n", "USAGE:\n m, w, z, isuppz, work, rwork, iwork, info, a = NumRu::Lapack.zheevr( jobz, range, uplo, a, vl, vu, il, iu, abstol, [:lwork => lwork, :lrwork => lrwork, :liwork => liwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )\n\n* Purpose\n* =======\n*\n* ZHEEVR computes selected eigenvalues and, optionally, eigenvectors\n* of a complex Hermitian matrix A. Eigenvalues and eigenvectors can\n* be selected by specifying either a range of values or a range of\n* indices for the desired eigenvalues.\n*\n* ZHEEVR first reduces the matrix A to tridiagonal form T with a call\n* to ZHETRD. Then, whenever possible, ZHEEVR calls ZSTEMR to compute\n* eigenspectrum using Relatively Robust Representations. ZSTEMR\n* computes eigenvalues by the dqds algorithm, while orthogonal\n* eigenvectors are computed from various \"good\" L D L^T representations\n* (also known as Relatively Robust Representations). Gram-Schmidt\n* orthogonalization is avoided as far as possible. More specifically,\n* the various steps of the algorithm are as follows.\n*\n* For each unreduced block (submatrix) of T,\n* (a) Compute T - sigma I = L D L^T, so that L and D\n* define all the wanted eigenvalues to high relative accuracy.\n* This means that small relative changes in the entries of D and L\n* cause only small relative changes in the eigenvalues and\n* eigenvectors. The standard (unfactored) representation of the\n* tridiagonal matrix T does not have this property in general.\n* (b) Compute the eigenvalues to suitable accuracy.\n* If the eigenvectors are desired, the algorithm attains full\n* accuracy of the computed eigenvalues only right before\n* the corresponding vectors have to be computed, see steps c) and d).\n* (c) For each cluster of close eigenvalues, select a new\n* shift close to the cluster, find a new factorization, and refine\n* the shifted eigenvalues to suitable accuracy.\n* (d) For each eigenvalue with a large enough relative separation compute\n* the corresponding eigenvector by forming a rank revealing twisted\n* factorization. Go back to (c) for any clusters that remain.\n*\n* The desired accuracy of the output can be specified by the input\n* parameter ABSTOL.\n*\n* For more details, see DSTEMR's documentation and:\n* - Inderjit S. Dhillon and Beresford N. Parlett: \"Multiple representations\n* to compute orthogonal eigenvectors of symmetric tridiagonal matrices,\"\n* Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.\n* - Inderjit Dhillon and Beresford Parlett: \"Orthogonal Eigenvectors and\n* Relative Gaps,\" SIAM Journal on Matrix Analysis and Applications, Vol. 25,\n* 2004. Also LAPACK Working Note 154.\n* - Inderjit Dhillon: \"A new O(n^2) algorithm for the symmetric\n* tridiagonal eigenvalue/eigenvector problem\",\n* Computer Science Division Technical Report No. UCB/CSD-97-971,\n* UC Berkeley, May 1997.\n*\n*\n* Note 1 : ZHEEVR calls ZSTEMR when the full spectrum is requested\n* on machines which conform to the ieee-754 floating point standard.\n* ZHEEVR calls DSTEBZ and ZSTEIN on non-ieee machines and\n* when partial spectrum requests are made.\n*\n* Normal execution of ZSTEMR may create NaNs and infinities and\n* hence may abort due to a floating point exception in environments\n* which do not handle NaNs and infinities in the ieee standard default\n* manner.\n*\n\n* Arguments\n* =========\n*\n* JOBZ (input) CHARACTER*1\n* = 'N': Compute eigenvalues only;\n* = 'V': Compute eigenvalues and eigenvectors.\n*\n* RANGE (input) CHARACTER*1\n* = 'A': all eigenvalues will be found.\n* = 'V': all eigenvalues in the half-open interval (VL,VU]\n* will be found.\n* = 'I': the IL-th through IU-th eigenvalues will be found.\n********** For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and\n********** ZSTEIN are called\n*\n* UPLO (input) CHARACTER*1\n* = 'U': Upper triangle of A is stored;\n* = 'L': Lower triangle of A is stored.\n*\n* N (input) INTEGER\n* The order of the matrix A. N >= 0.\n*\n* A (input/output) COMPLEX*16 array, dimension (LDA, N)\n* On entry, the Hermitian matrix A. If UPLO = 'U', the\n* leading N-by-N upper triangular part of A contains the\n* upper triangular part of the matrix A. If UPLO = 'L',\n* the leading N-by-N lower triangular part of A contains\n* the lower triangular part of the matrix A.\n* On exit, the lower triangle (if UPLO='L') or the upper\n* triangle (if UPLO='U') of A, including the diagonal, is\n* destroyed.\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,N).\n*\n* VL (input) DOUBLE PRECISION\n* VU (input) DOUBLE PRECISION\n* If RANGE='V', the lower and upper bounds of the interval to\n* be searched for eigenvalues. VL < VU.\n* Not referenced if RANGE = 'A' or 'I'.\n*\n* IL (input) INTEGER\n* IU (input) INTEGER\n* If RANGE='I', the indices (in ascending order) of the\n* smallest and largest eigenvalues to be returned.\n* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.\n* Not referenced if RANGE = 'A' or 'V'.\n*\n* ABSTOL (input) DOUBLE PRECISION\n* The absolute error tolerance for the eigenvalues.\n* An approximate eigenvalue is accepted as converged\n* when it is determined to lie in an interval [a,b]\n* of width less than or equal to\n*\n* ABSTOL + EPS * max( |a|,|b| ) ,\n*\n* where EPS is the machine precision. If ABSTOL is less than\n* or equal to zero, then EPS*|T| will be used in its place,\n* where |T| is the 1-norm of the tridiagonal matrix obtained\n* by reducing A to tridiagonal form.\n*\n* See \"Computing Small Singular Values of Bidiagonal Matrices\n* with Guaranteed High Relative Accuracy,\" by Demmel and\n* Kahan, LAPACK Working Note #3.\n*\n* If high relative accuracy is important, set ABSTOL to\n* DLAMCH( 'Safe minimum' ). Doing so will guarantee that\n* eigenvalues are computed to high relative accuracy when\n* possible in future releases. The current code does not\n* make any guarantees about high relative accuracy, but\n* furutre releases will. See J. Barlow and J. Demmel,\n* \"Computing Accurate Eigensystems of Scaled Diagonally\n* Dominant Matrices\", LAPACK Working Note #7, for a discussion\n* of which matrices define their eigenvalues to high relative\n* accuracy.\n*\n* M (output) INTEGER\n* The total number of eigenvalues found. 0 <= M <= N.\n* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.\n*\n* W (output) DOUBLE PRECISION array, dimension (N)\n* The first M elements contain the selected eigenvalues in\n* ascending order.\n*\n* Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M))\n* If JOBZ = 'V', then if INFO = 0, the first M columns of Z\n* contain the orthonormal eigenvectors of the matrix A\n* corresponding to the selected eigenvalues, with the i-th\n* column of Z holding the eigenvector associated with W(i).\n* If JOBZ = 'N', then Z is not referenced.\n* Note: the user must ensure that at least max(1,M) columns are\n* supplied in the array Z; if RANGE = 'V', the exact value of M\n* is not known in advance and an upper bound must be used.\n*\n* LDZ (input) INTEGER\n* The leading dimension of the array Z. LDZ >= 1, and if\n* JOBZ = 'V', LDZ >= max(1,N).\n*\n* ISUPPZ (output) INTEGER array, dimension ( 2*max(1,M) )\n* The support of the eigenvectors in Z, i.e., the indices\n* indicating the nonzero elements in Z. The i-th eigenvector\n* is nonzero only in elements ISUPPZ( 2*i-1 ) through\n* ISUPPZ( 2*i ).\n********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1\n*\n* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))\n* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n*\n* LWORK (input) INTEGER\n* The length of the array WORK. LWORK >= max(1,2*N).\n* For optimal efficiency, LWORK >= (NB+1)*N,\n* where NB is the max of the blocksize for ZHETRD and for\n* ZUNMTR as returned by ILAENV.\n*\n* If LWORK = -1, then a workspace query is assumed; the routine\n* only calculates the optimal sizes of the WORK, RWORK and\n* IWORK arrays, returns these values as the first entries of\n* the WORK, RWORK and IWORK arrays, and no error message\n* related to LWORK or LRWORK or LIWORK is issued by XERBLA.\n*\n* RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))\n* On exit, if INFO = 0, RWORK(1) returns the optimal\n* (and minimal) LRWORK.\n*\n* LRWORK (input) INTEGER\n* The length of the array RWORK. LRWORK >= max(1,24*N).\n*\n* If LRWORK = -1, then a workspace query is assumed; the\n* routine only calculates the optimal sizes of the WORK, RWORK\n* and IWORK arrays, returns these values as the first entries\n* of the WORK, RWORK and IWORK arrays, and no error message\n* related to LWORK or LRWORK or LIWORK is issued by XERBLA.\n*\n* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))\n* On exit, if INFO = 0, IWORK(1) returns the optimal\n* (and minimal) LIWORK.\n*\n* LIWORK (input) INTEGER\n* The dimension of the array IWORK. LIWORK >= max(1,10*N).\n*\n* If LIWORK = -1, then a workspace query is assumed; the\n* routine only calculates the optimal sizes of the WORK, RWORK\n* and IWORK arrays, returns these values as the first entries\n* of the WORK, RWORK and IWORK arrays, and no error message\n* related to LWORK or LRWORK or LIWORK is issued by XERBLA.\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value\n* > 0: Internal error\n*\n\n* Further Details\n* ===============\n*\n* Based on contributions by\n* Inderjit Dhillon, IBM Almaden, USA\n* Osni Marques, LBNL/NERSC, USA\n* Ken Stanley, Computer Science Division, University of\n* California at Berkeley, USA\n* Jason Riedy, Computer Science Division, University of\n* California at Berkeley, USA\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n m, w, z, isuppz, work, rwork, iwork, info, a = NumRu::Lapack.zheevr( jobz, range, uplo, a, vl, vu, il, iu, abstol, [:lwork => lwork, :lrwork => lrwork, :liwork => liwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 9 && argc != 12)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 9)", argc);
rblapack_jobz = argv[0];
rblapack_range = argv[1];
rblapack_uplo = argv[2];
rblapack_a = argv[3];
rblapack_vl = argv[4];
rblapack_vu = argv[5];
rblapack_il = argv[6];
rblapack_iu = argv[7];
rblapack_abstol = argv[8];
if (argc == 12) {
rblapack_lwork = argv[9];
rblapack_lrwork = argv[10];
rblapack_liwork = argv[11];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
rblapack_lrwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lrwork")));
rblapack_liwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("liwork")));
} else {
rblapack_lwork = Qnil;
rblapack_lrwork = Qnil;
rblapack_liwork = Qnil;
}
jobz = StringValueCStr(rblapack_jobz)[0];
uplo = StringValueCStr(rblapack_uplo)[0];
vl = NUM2DBL(rblapack_vl);
il = NUM2INT(rblapack_il);
abstol = NUM2DBL(rblapack_abstol);
range = StringValueCStr(rblapack_range)[0];
vu = NUM2DBL(rblapack_vu);
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (4th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (4th argument) must be %d", 2);
lda = NA_SHAPE0(rblapack_a);
n = NA_SHAPE1(rblapack_a);
if (NA_TYPE(rblapack_a) != NA_DCOMPLEX)
rblapack_a = na_change_type(rblapack_a, NA_DCOMPLEX);
a = NA_PTR_TYPE(rblapack_a, doublecomplex*);
if (rblapack_lwork == Qnil)
lwork = 2*n;
else {
lwork = NUM2INT(rblapack_lwork);
}
if (rblapack_liwork == Qnil)
liwork = 10*n;
else {
liwork = NUM2INT(rblapack_liwork);
}
iu = NUM2INT(rblapack_iu);
ldz = lsame_(&jobz,"V") ? MAX(1,n) : 1;
if (rblapack_lrwork == Qnil)
lrwork = 24*n;
else {
lrwork = NUM2INT(rblapack_lrwork);
}
m = lsame_(&range,"A") ? n : lsame_(&range,"I") ? iu-il+1 : 0;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_w = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
w = NA_PTR_TYPE(rblapack_w, doublereal*);
{
na_shape_t shape[2];
shape[0] = ldz;
shape[1] = MAX(1,m);
rblapack_z = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
z = NA_PTR_TYPE(rblapack_z, doublecomplex*);
{
na_shape_t shape[1];
shape[0] = 2*MAX(1,m);
rblapack_isuppz = na_make_object(NA_LINT, 1, shape, cNArray);
}
isuppz = NA_PTR_TYPE(rblapack_isuppz, integer*);
{
na_shape_t shape[1];
shape[0] = MAX(1,lwork);
rblapack_work = na_make_object(NA_DCOMPLEX, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, doublecomplex*);
{
na_shape_t shape[1];
shape[0] = MAX(1,lrwork);
rblapack_rwork = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
rwork = NA_PTR_TYPE(rblapack_rwork, doublereal*);
{
na_shape_t shape[1];
shape[0] = MAX(1,liwork);
rblapack_iwork = na_make_object(NA_LINT, 1, shape, cNArray);
}
iwork = NA_PTR_TYPE(rblapack_iwork, integer*);
{
na_shape_t shape[2];
shape[0] = lda;
shape[1] = n;
rblapack_a_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
a_out__ = NA_PTR_TYPE(rblapack_a_out__, doublecomplex*);
MEMCPY(a_out__, a, doublecomplex, NA_TOTAL(rblapack_a));
rblapack_a = rblapack_a_out__;
a = a_out__;
zheevr_(&jobz, &range, &uplo, &n, a, &lda, &vl, &vu, &il, &iu, &abstol, &m, w, z, &ldz, isuppz, work, &lwork, rwork, &lrwork, iwork, &liwork, &info);
rblapack_m = INT2NUM(m);
rblapack_info = INT2NUM(info);
return rb_ary_new3(9, rblapack_m, rblapack_w, rblapack_z, rblapack_isuppz, rblapack_work, rblapack_rwork, rblapack_iwork, rblapack_info, rblapack_a);
}
void
init_lapack_zheevr(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zheevr", rblapack_zheevr, -1);
}
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