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#include "rb_lapack.h"
extern VOID zgegs_(char* jobvsl, char* jobvsr, integer* n, doublecomplex* a, integer* lda, doublecomplex* b, integer* ldb, doublecomplex* alpha, doublecomplex* beta, doublecomplex* vsl, integer* ldvsl, doublecomplex* vsr, integer* ldvsr, doublecomplex* work, integer* lwork, doublereal* rwork, integer* info);
static VALUE
rblapack_zgegs(int argc, VALUE *argv, VALUE self){
VALUE rblapack_jobvsl;
char jobvsl;
VALUE rblapack_jobvsr;
char jobvsr;
VALUE rblapack_a;
doublecomplex *a;
VALUE rblapack_b;
doublecomplex *b;
VALUE rblapack_lwork;
integer lwork;
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;
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 alpha, beta, vsl, vsr, work, info, a, b = NumRu::Lapack.zgegs( jobvsl, jobvsr, a, b, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, INFO )\n\n* Purpose\n* =======\n*\n* This routine is deprecated and has been replaced by routine ZGGES.\n*\n* ZGEGS computes the eigenvalues, Schur form, and, optionally, the\n* left and or/right Schur vectors of a complex matrix pair (A,B).\n* Given two square matrices A and B, the generalized Schur\n* factorization has the form\n* \n* A = Q*S*Z**H, B = Q*T*Z**H\n* \n* where Q and Z are unitary matrices and S and T are upper triangular.\n* The columns of Q are the left Schur vectors\n* and the columns of Z are the right Schur vectors.\n* \n* If only the eigenvalues of (A,B) are needed, the driver routine\n* ZGEGV should be used instead. See ZGEGV for a description of the\n* eigenvalues of the generalized nonsymmetric eigenvalue problem\n* (GNEP).\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 (returned in VSL).\n*\n* JOBVSR (input) CHARACTER*1\n* = 'N': do not compute the right Schur vectors;\n* = 'V': compute the right Schur vectors (returned in VSR).\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 matrix A.\n* On exit, the upper triangular matrix S from the generalized\n* Schur factorization.\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 matrix B.\n* On exit, the upper triangular matrix T from the generalized\n* Schur factorization.\n*\n* LDB (input) INTEGER\n* The leading dimension of B. LDB >= max(1,N).\n*\n* ALPHA (output) COMPLEX*16 array, dimension (N)\n* The complex scalars alpha that define the eigenvalues of\n* GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur\n* form of A.\n*\n* BETA (output) COMPLEX*16 array, dimension (N)\n* The non-negative real scalars beta that define the\n* eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element\n* of the triangular factor T.\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*\n* VSL (output) COMPLEX*16 array, dimension (LDVSL,N)\n* If JOBVSL = 'V', the matrix of left Schur vectors Q.\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', the matrix of right Schur vectors Z.\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* To compute the optimal value of LWORK, call ILAENV to get\n* blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.) Then compute:\n* NB -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;\n* the optimal LWORK is N*(NB+1).\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 (3*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: errors that usually indicate LAPACK problems:\n* =N+1: error return from ZGGBAL\n* =N+2: error return from ZGEQRF\n* =N+3: error return from ZUNMQR\n* =N+4: error return from ZUNGQR\n* =N+5: error return from ZGGHRD\n* =N+6: error return from ZHGEQZ (other than failed\n* iteration)\n* =N+7: error return from ZGGBAK (computing VSL)\n* =N+8: error return from ZGGBAK (computing VSR)\n* =N+9: error return from ZLASCL (various places)\n*\n\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n alpha, beta, vsl, vsr, work, info, a, b = NumRu::Lapack.zgegs( jobvsl, jobvsr, a, b, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 4 && argc != 5)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 4)", argc);
rblapack_jobvsl = argv[0];
rblapack_jobvsr = argv[1];
rblapack_a = argv[2];
rblapack_b = argv[3];
if (argc == 5) {
rblapack_lwork = argv[4];
} 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];
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (3th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (3th 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*);
jobvsr = StringValueCStr(rblapack_jobvsr)[0];
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (4th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (4th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
if (NA_SHAPE1(rblapack_b) != n)
rb_raise(rb_eRuntimeError, "shape 1 of b must be the same as shape 1 of a");
if (NA_TYPE(rblapack_b) != NA_DCOMPLEX)
rblapack_b = na_change_type(rblapack_b, NA_DCOMPLEX);
b = NA_PTR_TYPE(rblapack_b, 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, (3*n));
zgegs_(&jobvsl, &jobvsr, &n, a, &lda, b, &ldb, alpha, beta, vsl, &ldvsl, vsr, &ldvsr, work, &lwork, rwork, &info);
free(rwork);
rblapack_info = INT2NUM(info);
return rb_ary_new3(8, rblapack_alpha, rblapack_beta, rblapack_vsl, rblapack_vsr, rblapack_work, rblapack_info, rblapack_a, rblapack_b);
}
void
init_lapack_zgegs(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zgegs", rblapack_zgegs, -1);
}
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