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#include "rb_lapack.h"
extern VOID chgeqz_(char* job, char* compq, char* compz, integer* n, integer* ilo, integer* ihi, complex* h, integer* ldh, complex* t, integer* ldt, complex* alpha, complex* beta, complex* q, integer* ldq, complex* z, integer* ldz, complex* work, integer* lwork, real* rwork, integer* info);
static VALUE
rblapack_chgeqz(int argc, VALUE *argv, VALUE self){
VALUE rblapack_job;
char job;
VALUE rblapack_compq;
char compq;
VALUE rblapack_compz;
char compz;
VALUE rblapack_ilo;
integer ilo;
VALUE rblapack_ihi;
integer ihi;
VALUE rblapack_h;
complex *h;
VALUE rblapack_t;
complex *t;
VALUE rblapack_q;
complex *q;
VALUE rblapack_z;
complex *z;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_alpha;
complex *alpha;
VALUE rblapack_beta;
complex *beta;
VALUE rblapack_work;
complex *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_h_out__;
complex *h_out__;
VALUE rblapack_t_out__;
complex *t_out__;
VALUE rblapack_q_out__;
complex *q_out__;
VALUE rblapack_z_out__;
complex *z_out__;
real *rwork;
integer ldh;
integer n;
integer ldt;
integer ldq;
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 alpha, beta, work, info, h, t, q, z = NumRu::Lapack.chgeqz( job, compq, compz, ilo, ihi, h, t, q, z, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, RWORK, INFO )\n\n* Purpose\n* =======\n*\n* CHGEQZ computes the eigenvalues of a complex matrix pair (H,T),\n* where H is an upper Hessenberg matrix and T is upper triangular,\n* using the single-shift QZ method.\n* Matrix pairs of this type are produced by the reduction to\n* generalized upper Hessenberg form of a complex matrix pair (A,B):\n* \n* A = Q1*H*Z1**H, B = Q1*T*Z1**H,\n* \n* as computed by CGGHRD.\n* \n* If JOB='S', then the Hessenberg-triangular pair (H,T) is\n* also reduced to generalized Schur form,\n* \n* H = Q*S*Z**H, T = Q*P*Z**H,\n* \n* where Q and Z are unitary matrices and S and P are upper triangular.\n* \n* Optionally, the unitary matrix Q from the generalized Schur\n* factorization may be postmultiplied into an input matrix Q1, and the\n* unitary matrix Z may be postmultiplied into an input matrix Z1.\n* If Q1 and Z1 are the unitary matrices from CGGHRD that reduced\n* the matrix pair (A,B) to generalized Hessenberg form, then the output\n* matrices Q1*Q and Z1*Z are the unitary factors from the generalized\n* Schur factorization of (A,B):\n* \n* A = (Q1*Q)*S*(Z1*Z)**H, B = (Q1*Q)*P*(Z1*Z)**H.\n* \n* To avoid overflow, eigenvalues of the matrix pair (H,T)\n* (equivalently, of (A,B)) are computed as a pair of complex values\n* (alpha,beta). If beta is nonzero, lambda = alpha / beta is an\n* eigenvalue of the generalized nonsymmetric eigenvalue problem (GNEP)\n* A*x = lambda*B*x\n* and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the\n* alternate form of the GNEP\n* mu*A*y = B*y.\n* The values of alpha and beta for the i-th eigenvalue can be read\n* directly from the generalized Schur form: alpha = S(i,i),\n* beta = P(i,i).\n*\n* Ref: C.B. Moler & G.W. Stewart, \"An Algorithm for Generalized Matrix\n* Eigenvalue Problems\", SIAM J. Numer. Anal., 10(1973),\n* pp. 241--256.\n*\n\n* Arguments\n* =========\n*\n* JOB (input) CHARACTER*1\n* = 'E': Compute eigenvalues only;\n* = 'S': Computer eigenvalues and the Schur form.\n*\n* COMPQ (input) CHARACTER*1\n* = 'N': Left Schur vectors (Q) are not computed;\n* = 'I': Q is initialized to the unit matrix and the matrix Q\n* of left Schur vectors of (H,T) is returned;\n* = 'V': Q must contain a unitary matrix Q1 on entry and\n* the product Q1*Q is returned.\n*\n* COMPZ (input) CHARACTER*1\n* = 'N': Right Schur vectors (Z) are not computed;\n* = 'I': Q is initialized to the unit matrix and the matrix Z\n* of right Schur vectors of (H,T) is returned;\n* = 'V': Z must contain a unitary matrix Z1 on entry and\n* the product Z1*Z is returned.\n*\n* N (input) INTEGER\n* The order of the matrices H, T, Q, and Z. N >= 0.\n*\n* ILO (input) INTEGER\n* IHI (input) INTEGER\n* ILO and IHI mark the rows and columns of H which are in\n* Hessenberg form. It is assumed that A is already upper\n* triangular in rows and columns 1:ILO-1 and IHI+1:N.\n* If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0.\n*\n* H (input/output) COMPLEX array, dimension (LDH, N)\n* On entry, the N-by-N upper Hessenberg matrix H.\n* On exit, if JOB = 'S', H contains the upper triangular\n* matrix S from the generalized Schur factorization.\n* If JOB = 'E', the diagonal of H matches that of S, but\n* the rest of H is unspecified.\n*\n* LDH (input) INTEGER\n* The leading dimension of the array H. LDH >= max( 1, N ).\n*\n* T (input/output) COMPLEX array, dimension (LDT, N)\n* On entry, the N-by-N upper triangular matrix T.\n* On exit, if JOB = 'S', T contains the upper triangular\n* matrix P from the generalized Schur factorization.\n* If JOB = 'E', the diagonal of T matches that of P, but\n* the rest of T is unspecified.\n*\n* LDT (input) INTEGER\n* The leading dimension of the array T. LDT >= max( 1, N ).\n*\n* ALPHA (output) COMPLEX array, dimension (N)\n* The complex scalars alpha that define the eigenvalues of\n* GNEP. ALPHA(i) = S(i,i) in the generalized Schur\n* factorization.\n*\n* BETA (output) COMPLEX array, dimension (N)\n* The real non-negative scalars beta that define the\n* eigenvalues of GNEP. BETA(i) = P(i,i) in the generalized\n* Schur factorization.\n*\n* Together, the quantities alpha = ALPHA(j) and beta = BETA(j)\n* represent the j-th eigenvalue of the matrix pair (A,B), in\n* one of the forms lambda = alpha/beta or mu = beta/alpha.\n* Since either lambda or mu may overflow, they should not,\n* in general, be computed.\n*\n* Q (input/output) COMPLEX array, dimension (LDQ, N)\n* On entry, if COMPZ = 'V', the unitary matrix Q1 used in the\n* reduction of (A,B) to generalized Hessenberg form.\n* On exit, if COMPZ = 'I', the unitary matrix of left Schur\n* vectors of (H,T), and if COMPZ = 'V', the unitary matrix of\n* left Schur vectors of (A,B).\n* Not referenced if COMPZ = 'N'.\n*\n* LDQ (input) INTEGER\n* The leading dimension of the array Q. LDQ >= 1.\n* If COMPQ='V' or 'I', then LDQ >= N.\n*\n* Z (input/output) COMPLEX array, dimension (LDZ, N)\n* On entry, if COMPZ = 'V', the unitary matrix Z1 used in the\n* reduction of (A,B) to generalized Hessenberg form.\n* On exit, if COMPZ = 'I', the unitary matrix of right Schur\n* vectors of (H,T), and if COMPZ = 'V', the unitary matrix of\n* right Schur vectors of (A,B).\n* Not referenced if COMPZ = 'N'.\n*\n* LDZ (input) INTEGER\n* The leading dimension of the array Z. LDZ >= 1.\n* If COMPZ='V' or 'I', then LDZ >= N.\n*\n* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))\n* On exit, if INFO >= 0, WORK(1) returns the optimal LWORK.\n*\n* LWORK (input) INTEGER\n* The dimension of the array WORK. LWORK >= max(1,N).\n*\n* If LWORK = -1, then a workspace query is assumed; the routine\n* only calculates the optimal size of the WORK array, returns\n* this value as the first entry of the WORK array, and no error\n* message related to LWORK is issued by XERBLA.\n*\n* RWORK (workspace) REAL array, dimension (N)\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value\n* = 1,...,N: the QZ iteration did not converge. (H,T) is not\n* in Schur form, but ALPHA(i) and BETA(i),\n* i=INFO+1,...,N should be correct.\n* = N+1,...,2*N: the shift calculation failed. (H,T) is not\n* in Schur form, but ALPHA(i) and BETA(i),\n* i=INFO-N+1,...,N should be correct.\n*\n\n* Further Details\n* ===============\n*\n* We assume that complex ABS works as long as its value is less than\n* overflow.\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n alpha, beta, work, info, h, t, q, z = NumRu::Lapack.chgeqz( job, compq, compz, ilo, ihi, h, t, q, z, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 9 && argc != 10)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 9)", argc);
rblapack_job = argv[0];
rblapack_compq = argv[1];
rblapack_compz = argv[2];
rblapack_ilo = argv[3];
rblapack_ihi = argv[4];
rblapack_h = argv[5];
rblapack_t = argv[6];
rblapack_q = argv[7];
rblapack_z = argv[8];
if (argc == 10) {
rblapack_lwork = argv[9];
} 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];
compz = StringValueCStr(rblapack_compz)[0];
ihi = NUM2INT(rblapack_ihi);
if (!NA_IsNArray(rblapack_t))
rb_raise(rb_eArgError, "t (7th argument) must be NArray");
if (NA_RANK(rblapack_t) != 2)
rb_raise(rb_eArgError, "rank of t (7th argument) must be %d", 2);
ldt = NA_SHAPE0(rblapack_t);
n = NA_SHAPE1(rblapack_t);
if (NA_TYPE(rblapack_t) != NA_SCOMPLEX)
rblapack_t = na_change_type(rblapack_t, NA_SCOMPLEX);
t = NA_PTR_TYPE(rblapack_t, complex*);
if (!NA_IsNArray(rblapack_z))
rb_raise(rb_eArgError, "z (9th argument) must be NArray");
if (NA_RANK(rblapack_z) != 2)
rb_raise(rb_eArgError, "rank of z (9th argument) must be %d", 2);
ldz = NA_SHAPE0(rblapack_z);
if (NA_SHAPE1(rblapack_z) != n)
rb_raise(rb_eRuntimeError, "shape 1 of z must be the same as shape 1 of t");
if (NA_TYPE(rblapack_z) != NA_SCOMPLEX)
rblapack_z = na_change_type(rblapack_z, NA_SCOMPLEX);
z = NA_PTR_TYPE(rblapack_z, complex*);
compq = StringValueCStr(rblapack_compq)[0];
if (!NA_IsNArray(rblapack_h))
rb_raise(rb_eArgError, "h (6th argument) must be NArray");
if (NA_RANK(rblapack_h) != 2)
rb_raise(rb_eArgError, "rank of h (6th argument) must be %d", 2);
ldh = NA_SHAPE0(rblapack_h);
if (NA_SHAPE1(rblapack_h) != n)
rb_raise(rb_eRuntimeError, "shape 1 of h must be the same as shape 1 of t");
if (NA_TYPE(rblapack_h) != NA_SCOMPLEX)
rblapack_h = na_change_type(rblapack_h, NA_SCOMPLEX);
h = NA_PTR_TYPE(rblapack_h, complex*);
ilo = NUM2INT(rblapack_ilo);
if (!NA_IsNArray(rblapack_q))
rb_raise(rb_eArgError, "q (8th argument) must be NArray");
if (NA_RANK(rblapack_q) != 2)
rb_raise(rb_eArgError, "rank of q (8th argument) must be %d", 2);
ldq = NA_SHAPE0(rblapack_q);
if (NA_SHAPE1(rblapack_q) != n)
rb_raise(rb_eRuntimeError, "shape 1 of q must be the same as shape 1 of t");
if (NA_TYPE(rblapack_q) != NA_SCOMPLEX)
rblapack_q = na_change_type(rblapack_q, NA_SCOMPLEX);
q = NA_PTR_TYPE(rblapack_q, complex*);
if (rblapack_lwork == Qnil)
lwork = n;
else {
lwork = NUM2INT(rblapack_lwork);
}
{
na_shape_t shape[1];
shape[0] = n;
rblapack_alpha = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
alpha = NA_PTR_TYPE(rblapack_alpha, complex*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_beta = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
beta = NA_PTR_TYPE(rblapack_beta, complex*);
{
na_shape_t shape[1];
shape[0] = MAX(1,lwork);
rblapack_work = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, complex*);
{
na_shape_t shape[2];
shape[0] = ldh;
shape[1] = n;
rblapack_h_out__ = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
}
h_out__ = NA_PTR_TYPE(rblapack_h_out__, complex*);
MEMCPY(h_out__, h, complex, NA_TOTAL(rblapack_h));
rblapack_h = rblapack_h_out__;
h = h_out__;
{
na_shape_t shape[2];
shape[0] = ldt;
shape[1] = n;
rblapack_t_out__ = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
}
t_out__ = NA_PTR_TYPE(rblapack_t_out__, complex*);
MEMCPY(t_out__, t, complex, NA_TOTAL(rblapack_t));
rblapack_t = rblapack_t_out__;
t = t_out__;
{
na_shape_t shape[2];
shape[0] = ldq;
shape[1] = n;
rblapack_q_out__ = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
}
q_out__ = NA_PTR_TYPE(rblapack_q_out__, complex*);
MEMCPY(q_out__, q, complex, NA_TOTAL(rblapack_q));
rblapack_q = rblapack_q_out__;
q = q_out__;
{
na_shape_t shape[2];
shape[0] = ldz;
shape[1] = n;
rblapack_z_out__ = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
}
z_out__ = NA_PTR_TYPE(rblapack_z_out__, complex*);
MEMCPY(z_out__, z, complex, NA_TOTAL(rblapack_z));
rblapack_z = rblapack_z_out__;
z = z_out__;
rwork = ALLOC_N(real, (n));
chgeqz_(&job, &compq, &compz, &n, &ilo, &ihi, h, &ldh, t, &ldt, alpha, beta, q, &ldq, z, &ldz, work, &lwork, rwork, &info);
free(rwork);
rblapack_info = INT2NUM(info);
return rb_ary_new3(8, rblapack_alpha, rblapack_beta, rblapack_work, rblapack_info, rblapack_h, rblapack_t, rblapack_q, rblapack_z);
}
void
init_lapack_chgeqz(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "chgeqz", rblapack_chgeqz, -1);
}
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