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#include "rb_lapack.h"
static logical
rblapack_selctg(doublecomplex *arg0, doublecomplex *arg1){
VALUE rblapack_arg0, rblapack_arg1;
VALUE rblapack_ret;
logical ret;
rblapack_arg0 = rb_funcall(rb_gv_get("Complex"), rb_intern("new"), 2, rb_float_new((double)(arg0->r)), rb_float_new((double)(arg0->i)));
rblapack_arg1 = rb_funcall(rb_gv_get("Complex"), rb_intern("new"), 2, rb_float_new((double)(arg1->r)), rb_float_new((double)(arg1->i)));
rblapack_ret = rb_yield_values(2, rblapack_arg0, rblapack_arg1);
ret = (rblapack_ret == Qtrue);
return ret;
}
extern VOID zgges_(char* jobvsl, char* jobvsr, char* sort, L_fp selctg, integer* n, doublecomplex* a, integer* lda, doublecomplex* b, integer* ldb, integer* sdim, doublecomplex* alpha, doublecomplex* beta, doublecomplex* vsl, integer* ldvsl, doublecomplex* vsr, integer* ldvsr, doublecomplex* work, integer* lwork, doublereal* rwork, logical* bwork, integer* info);
static VALUE
rblapack_zgges(int argc, VALUE *argv, VALUE self){
VALUE rblapack_jobvsl;
char jobvsl;
VALUE rblapack_jobvsr;
char jobvsr;
VALUE rblapack_sort;
char sort;
VALUE rblapack_a;
doublecomplex *a;
VALUE rblapack_b;
doublecomplex *b;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_sdim;
integer sdim;
VALUE rblapack_alpha;
doublecomplex *alpha;
VALUE rblapack_beta;
doublecomplex *beta;
VALUE rblapack_vsl;
doublecomplex *vsl;
VALUE rblapack_vsr;
doublecomplex *vsr;
VALUE rblapack_work;
doublecomplex *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
doublecomplex *a_out__;
VALUE rblapack_b_out__;
doublecomplex *b_out__;
doublereal *rwork;
logical *bwork;
integer lda;
integer n;
integer ldb;
integer ldvsl;
integer ldvsr;
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 sdim, alpha, beta, vsl, vsr, work, info, a, b = NumRu::Lapack.zgges( jobvsl, jobvsr, sort, a, b, [:lwork => lwork, :usage => usage, :help => help]){|a,b| ... }\n\n\nFORTRAN MANUAL\n SUBROUTINE ZGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, BWORK, INFO )\n\n* Purpose\n* =======\n*\n* ZGGES computes for a pair of N-by-N complex nonsymmetric matrices\n* (A,B), the generalized eigenvalues, the generalized complex Schur\n* form (S, T), and optionally left and/or right Schur vectors (VSL\n* and VSR). This gives the generalized Schur factorization\n*\n* (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )\n*\n* where (VSR)**H is the conjugate-transpose of VSR.\n*\n* Optionally, it also orders the eigenvalues so that a selected cluster\n* of eigenvalues appears in the leading diagonal blocks of the upper\n* triangular matrix S and the upper triangular matrix T. The leading\n* columns of VSL and VSR then form an unitary basis for the\n* corresponding left and right eigenspaces (deflating subspaces).\n*\n* (If only the generalized eigenvalues are needed, use the driver\n* ZGGEV instead, which is faster.)\n*\n* A generalized eigenvalue for a pair of matrices (A,B) is a scalar w\n* or a ratio alpha/beta = w, such that A - w*B is singular. It is\n* usually represented as the pair (alpha,beta), as there is a\n* reasonable interpretation for beta=0, and even for both being zero.\n*\n* A pair of matrices (S,T) is in generalized complex Schur form if S\n* and T are upper triangular and, in addition, the diagonal elements\n* of T are non-negative real numbers.\n*\n\n* Arguments\n* =========\n*\n* JOBVSL (input) CHARACTER*1\n* = 'N': do not compute the left Schur vectors;\n* = 'V': compute the left Schur vectors.\n*\n* JOBVSR (input) CHARACTER*1\n* = 'N': do not compute the right Schur vectors;\n* = 'V': compute the right Schur vectors.\n*\n* SORT (input) CHARACTER*1\n* Specifies whether or not to order the eigenvalues on the\n* diagonal of the generalized Schur form.\n* = 'N': Eigenvalues are not ordered;\n* = 'S': Eigenvalues are ordered (see SELCTG).\n*\n* SELCTG (external procedure) LOGICAL FUNCTION of two COMPLEX*16 arguments\n* SELCTG must be declared EXTERNAL in the calling subroutine.\n* If SORT = 'N', SELCTG is not referenced.\n* If SORT = 'S', SELCTG is used to select eigenvalues to sort\n* to the top left of the Schur form.\n* An eigenvalue ALPHA(j)/BETA(j) is selected if\n* SELCTG(ALPHA(j),BETA(j)) is true.\n*\n* Note that a selected complex eigenvalue may no longer satisfy\n* SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since\n* ordering may change the value of complex eigenvalues\n* (especially if the eigenvalue is ill-conditioned), in this\n* case INFO is set to N+2 (See INFO below).\n*\n* N (input) INTEGER\n* The order of the matrices A, B, VSL, and VSR. N >= 0.\n*\n* A (input/output) COMPLEX*16 array, dimension (LDA, N)\n* On entry, the first of the pair of matrices.\n* On exit, A has been overwritten by its generalized Schur\n* form S.\n*\n* LDA (input) INTEGER\n* The leading dimension of A. LDA >= max(1,N).\n*\n* B (input/output) COMPLEX*16 array, dimension (LDB, N)\n* On entry, the second of the pair of matrices.\n* On exit, B has been overwritten by its generalized Schur\n* form T.\n*\n* LDB (input) INTEGER\n* The leading dimension of B. LDB >= max(1,N).\n*\n* SDIM (output) INTEGER\n* If SORT = 'N', SDIM = 0.\n* If SORT = 'S', SDIM = number of eigenvalues (after sorting)\n* for which SELCTG is true.\n*\n* ALPHA (output) COMPLEX*16 array, dimension (N)\n* BETA (output) COMPLEX*16 array, dimension (N)\n* On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the\n* generalized eigenvalues. ALPHA(j), j=1,...,N and BETA(j),\n* j=1,...,N are the diagonals of the complex Schur form (A,B)\n* output by ZGGES. The BETA(j) will be non-negative real.\n*\n* Note: the quotients ALPHA(j)/BETA(j) may easily over- or\n* underflow, and BETA(j) may even be zero. Thus, the user\n* should avoid naively computing the ratio alpha/beta.\n* However, ALPHA will be always less than and usually\n* comparable with norm(A) in magnitude, and BETA always less\n* than and usually comparable with norm(B).\n*\n* VSL (output) COMPLEX*16 array, dimension (LDVSL,N)\n* If JOBVSL = 'V', VSL will contain the left Schur vectors.\n* Not referenced if JOBVSL = 'N'.\n*\n* LDVSL (input) INTEGER\n* The leading dimension of the matrix VSL. LDVSL >= 1, and\n* if JOBVSL = 'V', LDVSL >= N.\n*\n* VSR (output) COMPLEX*16 array, dimension (LDVSR,N)\n* If JOBVSR = 'V', VSR will contain the right Schur vectors.\n* Not referenced if JOBVSR = 'N'.\n*\n* LDVSR (input) INTEGER\n* The leading dimension of the matrix VSR. LDVSR >= 1, and\n* if JOBVSR = 'V', LDVSR >= N.\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 dimension of the array WORK. LWORK >= max(1,2*N).\n* For good performance, LWORK must generally be larger.\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) DOUBLE PRECISION array, dimension (8*N)\n*\n* BWORK (workspace) LOGICAL array, dimension (N)\n* Not referenced if SORT = '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:\n* The QZ iteration failed. (A,B) are not in Schur\n* form, but ALPHA(j) and BETA(j) should be correct for\n* j=INFO+1,...,N.\n* > N: =N+1: other than QZ iteration failed in ZHGEQZ\n* =N+2: after reordering, roundoff changed values of\n* some complex eigenvalues so that leading\n* eigenvalues in the Generalized Schur form no\n* longer satisfy SELCTG=.TRUE. This could also\n* be caused due to scaling.\n* =N+3: reordering falied in ZTGSEN.\n*\n\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n sdim, alpha, beta, vsl, vsr, work, info, a, b = NumRu::Lapack.zgges( jobvsl, jobvsr, sort, a, b, [:lwork => lwork, :usage => usage, :help => help]){|a,b| ... }\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 5 && argc != 6)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 5)", argc);
rblapack_jobvsl = argv[0];
rblapack_jobvsr = argv[1];
rblapack_sort = argv[2];
rblapack_a = argv[3];
rblapack_b = argv[4];
if (argc == 6) {
rblapack_lwork = argv[5];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
jobvsl = StringValueCStr(rblapack_jobvsl)[0];
sort = StringValueCStr(rblapack_sort)[0];
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (5th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (5th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
n = NA_SHAPE1(rblapack_b);
if (NA_TYPE(rblapack_b) != NA_DCOMPLEX)
rblapack_b = na_change_type(rblapack_b, NA_DCOMPLEX);
b = NA_PTR_TYPE(rblapack_b, doublecomplex*);
jobvsr = StringValueCStr(rblapack_jobvsr)[0];
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);
if (NA_SHAPE1(rblapack_a) != n)
rb_raise(rb_eRuntimeError, "shape 1 of a must be the same as shape 1 of b");
if (NA_TYPE(rblapack_a) != NA_DCOMPLEX)
rblapack_a = na_change_type(rblapack_a, NA_DCOMPLEX);
a = NA_PTR_TYPE(rblapack_a, doublecomplex*);
ldvsl = lsame_(&jobvsl,"V") ? n : 1;
if (rblapack_lwork == Qnil)
lwork = 2*n;
else {
lwork = NUM2INT(rblapack_lwork);
}
ldvsr = lsame_(&jobvsr,"V") ? n : 1;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_alpha = na_make_object(NA_DCOMPLEX, 1, shape, cNArray);
}
alpha = NA_PTR_TYPE(rblapack_alpha, doublecomplex*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_beta = na_make_object(NA_DCOMPLEX, 1, shape, cNArray);
}
beta = NA_PTR_TYPE(rblapack_beta, doublecomplex*);
{
na_shape_t shape[2];
shape[0] = ldvsl;
shape[1] = n;
rblapack_vsl = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
vsl = NA_PTR_TYPE(rblapack_vsl, doublecomplex*);
{
na_shape_t shape[2];
shape[0] = ldvsr;
shape[1] = n;
rblapack_vsr = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
vsr = NA_PTR_TYPE(rblapack_vsr, doublecomplex*);
{
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[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__;
{
na_shape_t shape[2];
shape[0] = ldb;
shape[1] = n;
rblapack_b_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, doublecomplex*);
MEMCPY(b_out__, b, doublecomplex, NA_TOTAL(rblapack_b));
rblapack_b = rblapack_b_out__;
b = b_out__;
rwork = ALLOC_N(doublereal, (8*n));
bwork = ALLOC_N(logical, (lsame_(&sort,"N") ? 0 : n));
zgges_(&jobvsl, &jobvsr, &sort, rblapack_selctg, &n, a, &lda, b, &ldb, &sdim, alpha, beta, vsl, &ldvsl, vsr, &ldvsr, work, &lwork, rwork, bwork, &info);
free(rwork);
free(bwork);
rblapack_sdim = INT2NUM(sdim);
rblapack_info = INT2NUM(info);
return rb_ary_new3(9, rblapack_sdim, rblapack_alpha, rblapack_beta, rblapack_vsl, rblapack_vsr, rblapack_work, rblapack_info, rblapack_a, rblapack_b);
}
void
init_lapack_zgges(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zgges", rblapack_zgges, -1);
}
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