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#include "rb_lapack.h"
static logical
rblapack_select(real *arg0, real *arg1){
VALUE rblapack_arg0, rblapack_arg1;
VALUE rblapack_ret;
logical ret;
rblapack_arg0 = rb_float_new((double)(*arg0));
rblapack_arg1 = rb_float_new((double)(*arg1));
rblapack_ret = rb_yield_values(2, rblapack_arg0, rblapack_arg1);
ret = (rblapack_ret == Qtrue);
return ret;
}
extern VOID sgeesx_(char* jobvs, char* sort, L_fp select, char* sense, integer* n, real* a, integer* lda, integer* sdim, real* wr, real* wi, real* vs, integer* ldvs, real* rconde, real* rcondv, real* work, integer* lwork, integer* iwork, integer* liwork, logical* bwork, integer* info);
static VALUE
rblapack_sgeesx(int argc, VALUE *argv, VALUE self){
VALUE rblapack_jobvs;
char jobvs;
VALUE rblapack_sort;
char sort;
VALUE rblapack_sense;
char sense;
VALUE rblapack_a;
real *a;
VALUE rblapack_liwork;
integer liwork;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_sdim;
integer sdim;
VALUE rblapack_wr;
real *wr;
VALUE rblapack_wi;
real *wi;
VALUE rblapack_vs;
real *vs;
VALUE rblapack_rconde;
real rconde;
VALUE rblapack_rcondv;
real rcondv;
VALUE rblapack_work;
real *work;
VALUE rblapack_iwork;
integer *iwork;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
real *a_out__;
logical *bwork;
integer lda;
integer n;
integer ldvs;
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, wr, wi, vs, rconde, rcondv, work, iwork, info, a = NumRu::Lapack.sgeesx( jobvs, sort, sense, a, liwork, [:lwork => lwork, :usage => usage, :help => help]){|a,b| ... }\n\n\nFORTRAN MANUAL\n SUBROUTINE SGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, WR, WI, VS, LDVS, RCONDE, RCONDV, WORK, LWORK, IWORK, LIWORK, BWORK, INFO )\n\n* Purpose\n* =======\n*\n* SGEESX computes for an N-by-N real nonsymmetric matrix A, the\n* eigenvalues, the real Schur form T, and, optionally, the matrix of\n* Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).\n*\n* Optionally, it also orders the eigenvalues on the diagonal of the\n* real Schur form so that selected eigenvalues are at the top left;\n* computes a reciprocal condition number for the average of the\n* selected eigenvalues (RCONDE); and computes a reciprocal condition\n* number for the right invariant subspace corresponding to the\n* selected eigenvalues (RCONDV). The leading columns of Z form an\n* orthonormal basis for this invariant subspace.\n*\n* For further explanation of the reciprocal condition numbers RCONDE\n* and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where\n* these quantities are called s and sep respectively).\n*\n* A real matrix is in real Schur form if it is upper quasi-triangular\n* with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in\n* the form\n* [ a b ]\n* [ c a ]\n*\n* where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).\n*\n\n* Arguments\n* =========\n*\n* JOBVS (input) CHARACTER*1\n* = 'N': Schur vectors are not computed;\n* = 'V': Schur vectors are computed.\n*\n* SORT (input) CHARACTER*1\n* Specifies whether or not to order the eigenvalues on the\n* diagonal of the Schur form.\n* = 'N': Eigenvalues are not ordered;\n* = 'S': Eigenvalues are ordered (see SELECT).\n*\n* SELECT (external procedure) LOGICAL FUNCTION of two REAL arguments\n* SELECT must be declared EXTERNAL in the calling subroutine.\n* If SORT = 'S', SELECT is used to select eigenvalues to sort\n* to the top left of the Schur form.\n* If SORT = 'N', SELECT is not referenced.\n* An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if\n* SELECT(WR(j),WI(j)) is true; i.e., if either one of a\n* complex conjugate pair of eigenvalues is selected, then both\n* are. Note that a selected complex eigenvalue may no longer\n* satisfy SELECT(WR(j),WI(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 may be set to N+3 (see INFO below).\n*\n* SENSE (input) CHARACTER*1\n* Determines which reciprocal condition numbers are computed.\n* = 'N': None are computed;\n* = 'E': Computed for average of selected eigenvalues only;\n* = 'V': Computed for selected right invariant subspace only;\n* = 'B': Computed for both.\n* If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.\n*\n* N (input) INTEGER\n* The order of the matrix A. N >= 0.\n*\n* A (input/output) REAL array, dimension (LDA, N)\n* On entry, the N-by-N matrix A.\n* On exit, A is overwritten by its real Schur form T.\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= 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 SELECT is true. (Complex conjugate\n* pairs for which SELECT is true for either\n* eigenvalue count as 2.)\n*\n* WR (output) REAL array, dimension (N)\n* WI (output) REAL array, dimension (N)\n* WR and WI contain the real and imaginary parts, respectively,\n* of the computed eigenvalues, in the same order that they\n* appear on the diagonal of the output Schur form T. Complex\n* conjugate pairs of eigenvalues appear consecutively with the\n* eigenvalue having the positive imaginary part first.\n*\n* VS (output) REAL array, dimension (LDVS,N)\n* If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur\n* vectors.\n* If JOBVS = 'N', VS is not referenced.\n*\n* LDVS (input) INTEGER\n* The leading dimension of the array VS. LDVS >= 1, and if\n* JOBVS = 'V', LDVS >= N.\n*\n* RCONDE (output) REAL\n* If SENSE = 'E' or 'B', RCONDE contains the reciprocal\n* condition number for the average of the selected eigenvalues.\n* Not referenced if SENSE = 'N' or 'V'.\n*\n* RCONDV (output) REAL\n* If SENSE = 'V' or 'B', RCONDV contains the reciprocal\n* condition number for the selected right invariant subspace.\n* Not referenced if SENSE = 'N' or 'E'.\n*\n* WORK (workspace/output) REAL 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(1,3*N).\n* Also, if SENSE = 'E' or 'V' or 'B',\n* LWORK >= N+2*SDIM*(N-SDIM), where SDIM is the number of\n* selected eigenvalues computed by this routine. Note that\n* N+2*SDIM*(N-SDIM) <= N+N*N/2. Note also that an error is only\n* returned if LWORK < max(1,3*N), but if SENSE = 'E' or 'V' or\n* 'B' this may not be large enough.\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 upper bounds on the optimal sizes of the\n* arrays WORK and IWORK, returns these values as the first\n* entries of the WORK and IWORK arrays, and no error messages\n* related to LWORK or LIWORK are 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 LIWORK.\n*\n* LIWORK (input) INTEGER\n* The dimension of the array IWORK.\n* LIWORK >= 1; if SENSE = 'V' or 'B', LIWORK >= SDIM*(N-SDIM).\n* Note that SDIM*(N-SDIM) <= N*N/4. Note also that an error is\n* only returned if LIWORK < 1, but if SENSE = 'V' or 'B' this\n* may not be large enough.\n*\n* If LIWORK = -1, then a workspace query is assumed; the\n* routine only calculates upper bounds on the optimal sizes of\n* the arrays WORK and IWORK, returns these values as the first\n* entries of the WORK and IWORK arrays, and no error messages\n* related to LWORK or LIWORK are issued by XERBLA.\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* > 0: if INFO = i, and i is\n* <= N: the QR algorithm failed to compute all the\n* eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI\n* contain those eigenvalues which have converged; if\n* JOBVS = 'V', VS contains the transformation which\n* reduces A to its partially converged Schur form.\n* = N+1: the eigenvalues could not be reordered because some\n* eigenvalues were too close to separate (the problem\n* is very ill-conditioned);\n* = N+2: after reordering, roundoff changed values of some\n* complex eigenvalues so that leading eigenvalues in\n* the Schur form no longer satisfy SELECT=.TRUE. This\n* could also be caused by underflow due to scaling.\n*\n\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n sdim, wr, wi, vs, rconde, rcondv, work, iwork, info, a = NumRu::Lapack.sgeesx( jobvs, sort, sense, a, liwork, [: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_jobvs = argv[0];
rblapack_sort = argv[1];
rblapack_sense = argv[2];
rblapack_a = argv[3];
rblapack_liwork = 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;
}
jobvs = StringValueCStr(rblapack_jobvs)[0];
sense = StringValueCStr(rblapack_sense)[0];
liwork = NUM2INT(rblapack_liwork);
sort = StringValueCStr(rblapack_sort)[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);
n = NA_SHAPE1(rblapack_a);
if (NA_TYPE(rblapack_a) != NA_SFLOAT)
rblapack_a = na_change_type(rblapack_a, NA_SFLOAT);
a = NA_PTR_TYPE(rblapack_a, real*);
ldvs = lsame_(&jobvs,"V") ? n : 1;
if (rblapack_lwork == Qnil)
lwork = (lsame_(&sense,"E")||lsame_(&sense,"V")||lsame_(&sense,"B")) ? n+n*n/2 : 3*n;
else {
lwork = NUM2INT(rblapack_lwork);
}
{
na_shape_t shape[1];
shape[0] = n;
rblapack_wr = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
wr = NA_PTR_TYPE(rblapack_wr, real*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_wi = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
wi = NA_PTR_TYPE(rblapack_wi, real*);
{
na_shape_t shape[2];
shape[0] = ldvs;
shape[1] = n;
rblapack_vs = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
vs = NA_PTR_TYPE(rblapack_vs, real*);
{
na_shape_t shape[1];
shape[0] = MAX(1,lwork);
rblapack_work = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, real*);
{
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_SFLOAT, 2, shape, cNArray);
}
a_out__ = NA_PTR_TYPE(rblapack_a_out__, real*);
MEMCPY(a_out__, a, real, NA_TOTAL(rblapack_a));
rblapack_a = rblapack_a_out__;
a = a_out__;
bwork = ALLOC_N(logical, (lsame_(&sort,"N") ? 0 : n));
sgeesx_(&jobvs, &sort, rblapack_select, &sense, &n, a, &lda, &sdim, wr, wi, vs, &ldvs, &rconde, &rcondv, work, &lwork, iwork, &liwork, bwork, &info);
free(bwork);
rblapack_sdim = INT2NUM(sdim);
rblapack_rconde = rb_float_new((double)rconde);
rblapack_rcondv = rb_float_new((double)rcondv);
rblapack_info = INT2NUM(info);
return rb_ary_new3(10, rblapack_sdim, rblapack_wr, rblapack_wi, rblapack_vs, rblapack_rconde, rblapack_rcondv, rblapack_work, rblapack_iwork, rblapack_info, rblapack_a);
}
void
init_lapack_sgeesx(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "sgeesx", rblapack_sgeesx, -1);
}
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