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#include "rb_lapack.h"
extern VOID dhseqr_(char* job, char* compz, integer* n, integer* ilo, integer* ihi, doublereal* h, integer* ldh, doublereal* wr, doublereal* wi, doublereal* z, integer* ldz, doublereal* work, integer* lwork, integer* info);
static VALUE
rblapack_dhseqr(int argc, VALUE *argv, VALUE self){
VALUE rblapack_job;
char job;
VALUE rblapack_compz;
char compz;
VALUE rblapack_ilo;
integer ilo;
VALUE rblapack_ihi;
integer ihi;
VALUE rblapack_h;
doublereal *h;
VALUE rblapack_z;
doublereal *z;
VALUE rblapack_ldz;
integer ldz;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_wr;
doublereal *wr;
VALUE rblapack_wi;
doublereal *wi;
VALUE rblapack_work;
doublereal *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_h_out__;
doublereal *h_out__;
VALUE rblapack_z_out__;
doublereal *z_out__;
integer ldh;
integer n;
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 wr, wi, work, info, h, z = NumRu::Lapack.dhseqr( job, compz, ilo, ihi, h, z, ldz, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE DHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z, LDZ, WORK, LWORK, INFO )\n\n* Purpose\n* =======\n*\n* DHSEQR computes the eigenvalues of a Hessenberg matrix H\n* and, optionally, the matrices T and Z from the Schur decomposition\n* H = Z T Z**T, where T is an upper quasi-triangular matrix (the\n* Schur form), and Z is the orthogonal matrix of Schur vectors.\n*\n* Optionally Z may be postmultiplied into an input orthogonal\n* matrix Q so that this routine can give the Schur factorization\n* of a matrix A which has been reduced to the Hessenberg form H\n* by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.\n*\n\n* Arguments\n* =========\n*\n* JOB (input) CHARACTER*1\n* = 'E': compute eigenvalues only;\n* = 'S': compute eigenvalues and the Schur form T.\n*\n* COMPZ (input) CHARACTER*1\n* = 'N': no Schur vectors are computed;\n* = 'I': Z is initialized to the unit matrix and the matrix Z\n* of Schur vectors of H is returned;\n* = 'V': Z must contain an orthogonal matrix Q on entry, and\n* the product Q*Z is returned.\n*\n* N (input) INTEGER\n* The order of the matrix H. N .GE. 0.\n*\n* ILO (input) INTEGER\n* IHI (input) INTEGER\n* It is assumed that H is already upper triangular in rows\n* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally\n* set by a previous call to DGEBAL, and then passed to DGEHRD\n* when the matrix output by DGEBAL is reduced to Hessenberg\n* form. Otherwise ILO and IHI should be set to 1 and N\n* respectively. If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N.\n* If N = 0, then ILO = 1 and IHI = 0.\n*\n* H (input/output) DOUBLE PRECISION array, dimension (LDH,N)\n* On entry, the upper Hessenberg matrix H.\n* On exit, if INFO = 0 and JOB = 'S', then H contains the\n* upper quasi-triangular matrix T from the Schur decomposition\n* (the Schur form); 2-by-2 diagonal blocks (corresponding to\n* complex conjugate pairs of eigenvalues) are returned in\n* standard form, with H(i,i) = H(i+1,i+1) and\n* H(i+1,i)*H(i,i+1).LT.0. If INFO = 0 and JOB = 'E', the\n* contents of H are unspecified on exit. (The output value of\n* H when INFO.GT.0 is given under the description of INFO\n* below.)\n*\n* Unlike earlier versions of DHSEQR, this subroutine may\n* explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1\n* or j = IHI+1, IHI+2, ... N.\n*\n* LDH (input) INTEGER\n* The leading dimension of the array H. LDH .GE. max(1,N).\n*\n* WR (output) DOUBLE PRECISION array, dimension (N)\n* WI (output) DOUBLE PRECISION array, dimension (N)\n* The real and imaginary parts, respectively, of the computed\n* eigenvalues. If two eigenvalues are computed as a complex\n* conjugate pair, they are stored in consecutive elements of\n* WR and WI, say the i-th and (i+1)th, with WI(i) .GT. 0 and\n* WI(i+1) .LT. 0. If JOB = 'S', the eigenvalues are stored in\n* the same order as on the diagonal of the Schur form returned\n* in H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2\n* diagonal block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and\n* WI(i+1) = -WI(i).\n*\n* Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N)\n* If COMPZ = 'N', Z is not referenced.\n* If COMPZ = 'I', on entry Z need not be set and on exit,\n* if INFO = 0, Z contains the orthogonal matrix Z of the Schur\n* vectors of H. If COMPZ = 'V', on entry Z must contain an\n* N-by-N matrix Q, which is assumed to be equal to the unit\n* matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On exit,\n* if INFO = 0, Z contains Q*Z.\n* Normally Q is the orthogonal matrix generated by DORGHR\n* after the call to DGEHRD which formed the Hessenberg matrix\n* H. (The output value of Z when INFO.GT.0 is given under\n* the description of INFO below.)\n*\n* LDZ (input) INTEGER\n* The leading dimension of the array Z. if COMPZ = 'I' or\n* COMPZ = 'V', then LDZ.GE.MAX(1,N). Otherwize, LDZ.GE.1.\n*\n* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)\n* On exit, if INFO = 0, WORK(1) returns an estimate of\n* the optimal value for LWORK.\n*\n* LWORK (input) INTEGER\n* The dimension of the array WORK. LWORK .GE. max(1,N)\n* is sufficient and delivers very good and sometimes\n* optimal performance. However, LWORK as large as 11*N\n* may be required for optimal performance. A workspace\n* query is recommended to determine the optimal workspace\n* size.\n*\n* If LWORK = -1, then DHSEQR does a workspace query.\n* In this case, DHSEQR checks the input parameters and\n* estimates the optimal workspace size for the given\n* values of N, ILO and IHI. The estimate is returned\n* in WORK(1). No error message related to LWORK is\n* issued by XERBLA. Neither H nor Z are accessed.\n*\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* .LT. 0: if INFO = -i, the i-th argument had an illegal\n* value\n* .GT. 0: if INFO = i, DHSEQR failed to compute all of\n* the eigenvalues. Elements 1:ilo-1 and i+1:n of WR\n* and WI contain those eigenvalues which have been\n* successfully computed. (Failures are rare.)\n*\n* If INFO .GT. 0 and JOB = 'E', then on exit, the\n* remaining unconverged eigenvalues are the eigen-\n* values of the upper Hessenberg matrix rows and\n* columns ILO through INFO of the final, output\n* value of H.\n*\n* If INFO .GT. 0 and JOB = 'S', then on exit\n*\n* (*) (initial value of H)*U = U*(final value of H)\n*\n* where U is an orthogonal matrix. The final\n* value of H is upper Hessenberg and quasi-triangular\n* in rows and columns INFO+1 through IHI.\n*\n* If INFO .GT. 0 and COMPZ = 'V', then on exit\n*\n* (final value of Z) = (initial value of Z)*U\n*\n* where U is the orthogonal matrix in (*) (regard-\n* less of the value of JOB.)\n*\n* If INFO .GT. 0 and COMPZ = 'I', then on exit\n* (final value of Z) = U\n* where U is the orthogonal matrix in (*) (regard-\n* less of the value of JOB.)\n*\n* If INFO .GT. 0 and COMPZ = 'N', then Z is not\n* accessed.\n*\n\n* ================================================================\n* Default values supplied by\n* ILAENV(ISPEC,'DHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK).\n* It is suggested that these defaults be adjusted in order\n* to attain best performance in each particular\n* computational environment.\n*\n* ISPEC=12: The DLAHQR vs DLAQR0 crossover point.\n* Default: 75. (Must be at least 11.)\n*\n* ISPEC=13: Recommended deflation window size.\n* This depends on ILO, IHI and NS. NS is the\n* number of simultaneous shifts returned\n* by ILAENV(ISPEC=15). (See ISPEC=15 below.)\n* The default for (IHI-ILO+1).LE.500 is NS.\n* The default for (IHI-ILO+1).GT.500 is 3*NS/2.\n*\n* ISPEC=14: Nibble crossover point. (See IPARMQ for\n* details.) Default: 14% of deflation window\n* size.\n*\n* ISPEC=15: Number of simultaneous shifts in a multishift\n* QR iteration.\n*\n* If IHI-ILO+1 is ...\n*\n* greater than ...but less ... the\n* or equal to ... than default is\n*\n* 1 30 NS = 2(+)\n* 30 60 NS = 4(+)\n* 60 150 NS = 10(+)\n* 150 590 NS = **\n* 590 3000 NS = 64\n* 3000 6000 NS = 128\n* 6000 infinity NS = 256\n*\n* (+) By default some or all matrices of this order\n* are passed to the implicit double shift routine\n* DLAHQR and this parameter is ignored. See\n* ISPEC=12 above and comments in IPARMQ for\n* details.\n*\n* (**) The asterisks (**) indicate an ad-hoc\n* function of N increasing from 10 to 64.\n*\n* ISPEC=16: Select structured matrix multiply.\n* If the number of simultaneous shifts (specified\n* by ISPEC=15) is less than 14, then the default\n* for ISPEC=16 is 0. Otherwise the default for\n* ISPEC=16 is 2.\n*\n* ================================================================\n* Based on contributions by\n* Karen Braman and Ralph Byers, Department of Mathematics,\n* University of Kansas, USA\n*\n* ================================================================\n* References:\n* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR\n* Algorithm Part I: Maintaining Well Focused Shifts, and Level 3\n* Performance, SIAM Journal of Matrix Analysis, volume 23, pages\n* 929--947, 2002.\n*\n* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR\n* Algorithm Part II: Aggressive Early Deflation, SIAM Journal\n* of Matrix Analysis, volume 23, pages 948--973, 2002.\n*\n* ================================================================\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n wr, wi, work, info, h, z = NumRu::Lapack.dhseqr( job, compz, ilo, ihi, h, z, ldz, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 7 && argc != 8)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 7)", argc);
rblapack_job = argv[0];
rblapack_compz = argv[1];
rblapack_ilo = argv[2];
rblapack_ihi = argv[3];
rblapack_h = argv[4];
rblapack_z = argv[5];
rblapack_ldz = argv[6];
if (argc == 8) {
rblapack_lwork = argv[7];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
job = StringValueCStr(rblapack_job)[0];
ilo = NUM2INT(rblapack_ilo);
if (!NA_IsNArray(rblapack_h))
rb_raise(rb_eArgError, "h (5th argument) must be NArray");
if (NA_RANK(rblapack_h) != 2)
rb_raise(rb_eArgError, "rank of h (5th argument) must be %d", 2);
ldh = NA_SHAPE0(rblapack_h);
n = NA_SHAPE1(rblapack_h);
if (NA_TYPE(rblapack_h) != NA_DFLOAT)
rblapack_h = na_change_type(rblapack_h, NA_DFLOAT);
h = NA_PTR_TYPE(rblapack_h, doublereal*);
ldz = NUM2INT(rblapack_ldz);
compz = StringValueCStr(rblapack_compz)[0];
if (!NA_IsNArray(rblapack_z))
rb_raise(rb_eArgError, "z (6th argument) must be NArray");
if (NA_RANK(rblapack_z) != 2)
rb_raise(rb_eArgError, "rank of z (6th argument) must be %d", 2);
if (NA_SHAPE0(rblapack_z) != (lsame_(&compz,"N") ? 0 : ldz))
rb_raise(rb_eRuntimeError, "shape 0 of z must be %d", lsame_(&compz,"N") ? 0 : ldz);
if (NA_SHAPE1(rblapack_z) != (lsame_(&compz,"N") ? 0 : n))
rb_raise(rb_eRuntimeError, "shape 1 of z must be %d", lsame_(&compz,"N") ? 0 : n);
if (NA_TYPE(rblapack_z) != NA_DFLOAT)
rblapack_z = na_change_type(rblapack_z, NA_DFLOAT);
z = NA_PTR_TYPE(rblapack_z, doublereal*);
ihi = NUM2INT(rblapack_ihi);
if (rblapack_lwork == Qnil)
lwork = n;
else {
lwork = NUM2INT(rblapack_lwork);
}
{
na_shape_t shape[1];
shape[0] = n;
rblapack_wr = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
wr = NA_PTR_TYPE(rblapack_wr, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_wi = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
wi = NA_PTR_TYPE(rblapack_wi, doublereal*);
{
na_shape_t shape[1];
shape[0] = MAX(1,lwork);
rblapack_work = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, doublereal*);
{
na_shape_t shape[2];
shape[0] = ldh;
shape[1] = n;
rblapack_h_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
h_out__ = NA_PTR_TYPE(rblapack_h_out__, doublereal*);
MEMCPY(h_out__, h, doublereal, NA_TOTAL(rblapack_h));
rblapack_h = rblapack_h_out__;
h = h_out__;
{
na_shape_t shape[2];
shape[0] = lsame_(&compz,"N") ? 0 : ldz;
shape[1] = lsame_(&compz,"N") ? 0 : n;
rblapack_z_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
z_out__ = NA_PTR_TYPE(rblapack_z_out__, doublereal*);
MEMCPY(z_out__, z, doublereal, NA_TOTAL(rblapack_z));
rblapack_z = rblapack_z_out__;
z = z_out__;
dhseqr_(&job, &compz, &n, &ilo, &ihi, h, &ldh, wr, wi, z, &ldz, work, &lwork, &info);
rblapack_info = INT2NUM(info);
return rb_ary_new3(6, rblapack_wr, rblapack_wi, rblapack_work, rblapack_info, rblapack_h, rblapack_z);
}
void
init_lapack_dhseqr(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "dhseqr", rblapack_dhseqr, -1);
}
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