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#include "rb_lapack.h"
extern VOID dtgevc_(char* side, char* howmny, logical* select, integer* n, doublereal* s, integer* lds, doublereal* p, integer* ldp, doublereal* vl, integer* ldvl, doublereal* vr, integer* ldvr, integer* mm, integer* m, doublereal* work, integer* info);
static VALUE
rblapack_dtgevc(int argc, VALUE *argv, VALUE self){
VALUE rblapack_side;
char side;
VALUE rblapack_howmny;
char howmny;
VALUE rblapack_select;
logical *select;
VALUE rblapack_s;
doublereal *s;
VALUE rblapack_p;
doublereal *p;
VALUE rblapack_vl;
doublereal *vl;
VALUE rblapack_vr;
doublereal *vr;
VALUE rblapack_m;
integer m;
VALUE rblapack_info;
integer info;
VALUE rblapack_vl_out__;
doublereal *vl_out__;
VALUE rblapack_vr_out__;
doublereal *vr_out__;
doublereal *work;
integer n;
integer lds;
integer ldp;
integer ldvl;
integer mm;
integer ldvr;
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 m, info, vl, vr = NumRu::Lapack.dtgevc( side, howmny, select, s, p, vl, vr, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE DTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL, VR, LDVR, MM, M, WORK, INFO )\n\n* Purpose\n* =======\n*\n* DTGEVC computes some or all of the right and/or left eigenvectors of\n* a pair of real matrices (S,P), where S is a quasi-triangular matrix\n* and P is upper triangular. Matrix pairs of this type are produced by\n* the generalized Schur factorization of a matrix pair (A,B):\n*\n* A = Q*S*Z**T, B = Q*P*Z**T\n*\n* as computed by DGGHRD + DHGEQZ.\n*\n* The right eigenvector x and the left eigenvector y of (S,P)\n* corresponding to an eigenvalue w are defined by:\n* \n* S*x = w*P*x, (y**H)*S = w*(y**H)*P,\n* \n* where y**H denotes the conjugate tranpose of y.\n* The eigenvalues are not input to this routine, but are computed\n* directly from the diagonal blocks of S and P.\n* \n* This routine returns the matrices X and/or Y of right and left\n* eigenvectors of (S,P), or the products Z*X and/or Q*Y,\n* where Z and Q are input matrices.\n* If Q and Z are the orthogonal factors from the generalized Schur\n* factorization of a matrix pair (A,B), then Z*X and Q*Y\n* are the matrices of right and left eigenvectors of (A,B).\n* \n\n* Arguments\n* =========\n*\n* SIDE (input) CHARACTER*1\n* = 'R': compute right eigenvectors only;\n* = 'L': compute left eigenvectors only;\n* = 'B': compute both right and left eigenvectors.\n*\n* HOWMNY (input) CHARACTER*1\n* = 'A': compute all right and/or left eigenvectors;\n* = 'B': compute all right and/or left eigenvectors,\n* backtransformed by the matrices in VR and/or VL;\n* = 'S': compute selected right and/or left eigenvectors,\n* specified by the logical array SELECT.\n*\n* SELECT (input) LOGICAL array, dimension (N)\n* If HOWMNY='S', SELECT specifies the eigenvectors to be\n* computed. If w(j) is a real eigenvalue, the corresponding\n* real eigenvector is computed if SELECT(j) is .TRUE..\n* If w(j) and w(j+1) are the real and imaginary parts of a\n* complex eigenvalue, the corresponding complex eigenvector\n* is computed if either SELECT(j) or SELECT(j+1) is .TRUE.,\n* and on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is\n* set to .FALSE..\n* Not referenced if HOWMNY = 'A' or 'B'.\n*\n* N (input) INTEGER\n* The order of the matrices S and P. N >= 0.\n*\n* S (input) DOUBLE PRECISION array, dimension (LDS,N)\n* The upper quasi-triangular matrix S from a generalized Schur\n* factorization, as computed by DHGEQZ.\n*\n* LDS (input) INTEGER\n* The leading dimension of array S. LDS >= max(1,N).\n*\n* P (input) DOUBLE PRECISION array, dimension (LDP,N)\n* The upper triangular matrix P from a generalized Schur\n* factorization, as computed by DHGEQZ.\n* 2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks\n* of S must be in positive diagonal form.\n*\n* LDP (input) INTEGER\n* The leading dimension of array P. LDP >= max(1,N).\n*\n* VL (input/output) DOUBLE PRECISION array, dimension (LDVL,MM)\n* On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must\n* contain an N-by-N matrix Q (usually the orthogonal matrix Q\n* of left Schur vectors returned by DHGEQZ).\n* On exit, if SIDE = 'L' or 'B', VL contains:\n* if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);\n* if HOWMNY = 'B', the matrix Q*Y;\n* if HOWMNY = 'S', the left eigenvectors of (S,P) specified by\n* SELECT, stored consecutively in the columns of\n* VL, in the same order as their eigenvalues.\n*\n* A complex eigenvector corresponding to a complex eigenvalue\n* is stored in two consecutive columns, the first holding the\n* real part, and the second the imaginary part.\n*\n* Not referenced if SIDE = 'R'.\n*\n* LDVL (input) INTEGER\n* The leading dimension of array VL. LDVL >= 1, and if\n* SIDE = 'L' or 'B', LDVL >= N.\n*\n* VR (input/output) DOUBLE PRECISION array, dimension (LDVR,MM)\n* On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must\n* contain an N-by-N matrix Z (usually the orthogonal matrix Z\n* of right Schur vectors returned by DHGEQZ).\n*\n* On exit, if SIDE = 'R' or 'B', VR contains:\n* if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);\n* if HOWMNY = 'B' or 'b', the matrix Z*X;\n* if HOWMNY = 'S' or 's', the right eigenvectors of (S,P)\n* specified by SELECT, stored consecutively in the\n* columns of VR, in the same order as their\n* eigenvalues.\n*\n* A complex eigenvector corresponding to a complex eigenvalue\n* is stored in two consecutive columns, the first holding the\n* real part and the second the imaginary part.\n* \n* Not referenced if SIDE = 'L'.\n*\n* LDVR (input) INTEGER\n* The leading dimension of the array VR. LDVR >= 1, and if\n* SIDE = 'R' or 'B', LDVR >= N.\n*\n* MM (input) INTEGER\n* The number of columns in the arrays VL and/or VR. MM >= M.\n*\n* M (output) INTEGER\n* The number of columns in the arrays VL and/or VR actually\n* used to store the eigenvectors. If HOWMNY = 'A' or 'B', M\n* is set to N. Each selected real eigenvector occupies one\n* column and each selected complex eigenvector occupies two\n* columns.\n*\n* WORK (workspace) DOUBLE PRECISION array, dimension (6*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: the 2-by-2 block (INFO:INFO+1) does not have a complex\n* eigenvalue.\n*\n\n* Further Details\n* ===============\n*\n* Allocation of workspace:\n* ---------- -- ---------\n*\n* WORK( j ) = 1-norm of j-th column of A, above the diagonal\n* WORK( N+j ) = 1-norm of j-th column of B, above the diagonal\n* WORK( 2*N+1:3*N ) = real part of eigenvector\n* WORK( 3*N+1:4*N ) = imaginary part of eigenvector\n* WORK( 4*N+1:5*N ) = real part of back-transformed eigenvector\n* WORK( 5*N+1:6*N ) = imaginary part of back-transformed eigenvector\n*\n* Rowwise vs. columnwise solution methods:\n* ------- -- ---------- -------- -------\n*\n* Finding a generalized eigenvector consists basically of solving the\n* singular triangular system\n*\n* (A - w B) x = 0 (for right) or: (A - w B)**H y = 0 (for left)\n*\n* Consider finding the i-th right eigenvector (assume all eigenvalues\n* are real). The equation to be solved is:\n* n i\n* 0 = sum C(j,k) v(k) = sum C(j,k) v(k) for j = i,. . .,1\n* k=j k=j\n*\n* where C = (A - w B) (The components v(i+1:n) are 0.)\n*\n* The \"rowwise\" method is:\n*\n* (1) v(i) := 1\n* for j = i-1,. . .,1:\n* i\n* (2) compute s = - sum C(j,k) v(k) and\n* k=j+1\n*\n* (3) v(j) := s / C(j,j)\n*\n* Step 2 is sometimes called the \"dot product\" step, since it is an\n* inner product between the j-th row and the portion of the eigenvector\n* that has been computed so far.\n*\n* The \"columnwise\" method consists basically in doing the sums\n* for all the rows in parallel. As each v(j) is computed, the\n* contribution of v(j) times the j-th column of C is added to the\n* partial sums. Since FORTRAN arrays are stored columnwise, this has\n* the advantage that at each step, the elements of C that are accessed\n* are adjacent to one another, whereas with the rowwise method, the\n* elements accessed at a step are spaced LDS (and LDP) words apart.\n*\n* When finding left eigenvectors, the matrix in question is the\n* transpose of the one in storage, so the rowwise method then\n* actually accesses columns of A and B at each step, and so is the\n* preferred method.\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n m, info, vl, vr = NumRu::Lapack.dtgevc( side, howmny, select, s, p, vl, vr, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 7 && argc != 7)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 7)", argc);
rblapack_side = argv[0];
rblapack_howmny = argv[1];
rblapack_select = argv[2];
rblapack_s = argv[3];
rblapack_p = argv[4];
rblapack_vl = argv[5];
rblapack_vr = argv[6];
if (argc == 7) {
} else if (rblapack_options != Qnil) {
} else {
}
side = StringValueCStr(rblapack_side)[0];
if (!NA_IsNArray(rblapack_select))
rb_raise(rb_eArgError, "select (3th argument) must be NArray");
if (NA_RANK(rblapack_select) != 1)
rb_raise(rb_eArgError, "rank of select (3th argument) must be %d", 1);
n = NA_SHAPE0(rblapack_select);
if (NA_TYPE(rblapack_select) != NA_LINT)
rblapack_select = na_change_type(rblapack_select, NA_LINT);
select = NA_PTR_TYPE(rblapack_select, logical*);
if (!NA_IsNArray(rblapack_p))
rb_raise(rb_eArgError, "p (5th argument) must be NArray");
if (NA_RANK(rblapack_p) != 2)
rb_raise(rb_eArgError, "rank of p (5th argument) must be %d", 2);
ldp = NA_SHAPE0(rblapack_p);
if (NA_SHAPE1(rblapack_p) != n)
rb_raise(rb_eRuntimeError, "shape 1 of p must be the same as shape 0 of select");
if (NA_TYPE(rblapack_p) != NA_DFLOAT)
rblapack_p = na_change_type(rblapack_p, NA_DFLOAT);
p = NA_PTR_TYPE(rblapack_p, doublereal*);
if (!NA_IsNArray(rblapack_vr))
rb_raise(rb_eArgError, "vr (7th argument) must be NArray");
if (NA_RANK(rblapack_vr) != 2)
rb_raise(rb_eArgError, "rank of vr (7th argument) must be %d", 2);
ldvr = NA_SHAPE0(rblapack_vr);
mm = NA_SHAPE1(rblapack_vr);
if (NA_TYPE(rblapack_vr) != NA_DFLOAT)
rblapack_vr = na_change_type(rblapack_vr, NA_DFLOAT);
vr = NA_PTR_TYPE(rblapack_vr, doublereal*);
howmny = StringValueCStr(rblapack_howmny)[0];
if (!NA_IsNArray(rblapack_vl))
rb_raise(rb_eArgError, "vl (6th argument) must be NArray");
if (NA_RANK(rblapack_vl) != 2)
rb_raise(rb_eArgError, "rank of vl (6th argument) must be %d", 2);
ldvl = NA_SHAPE0(rblapack_vl);
if (NA_SHAPE1(rblapack_vl) != mm)
rb_raise(rb_eRuntimeError, "shape 1 of vl must be the same as shape 1 of vr");
if (NA_TYPE(rblapack_vl) != NA_DFLOAT)
rblapack_vl = na_change_type(rblapack_vl, NA_DFLOAT);
vl = NA_PTR_TYPE(rblapack_vl, doublereal*);
if (!NA_IsNArray(rblapack_s))
rb_raise(rb_eArgError, "s (4th argument) must be NArray");
if (NA_RANK(rblapack_s) != 2)
rb_raise(rb_eArgError, "rank of s (4th argument) must be %d", 2);
lds = NA_SHAPE0(rblapack_s);
if (NA_SHAPE1(rblapack_s) != n)
rb_raise(rb_eRuntimeError, "shape 1 of s must be the same as shape 0 of select");
if (NA_TYPE(rblapack_s) != NA_DFLOAT)
rblapack_s = na_change_type(rblapack_s, NA_DFLOAT);
s = NA_PTR_TYPE(rblapack_s, doublereal*);
{
na_shape_t shape[2];
shape[0] = ldvl;
shape[1] = mm;
rblapack_vl_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
vl_out__ = NA_PTR_TYPE(rblapack_vl_out__, doublereal*);
MEMCPY(vl_out__, vl, doublereal, NA_TOTAL(rblapack_vl));
rblapack_vl = rblapack_vl_out__;
vl = vl_out__;
{
na_shape_t shape[2];
shape[0] = ldvr;
shape[1] = mm;
rblapack_vr_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
vr_out__ = NA_PTR_TYPE(rblapack_vr_out__, doublereal*);
MEMCPY(vr_out__, vr, doublereal, NA_TOTAL(rblapack_vr));
rblapack_vr = rblapack_vr_out__;
vr = vr_out__;
work = ALLOC_N(doublereal, (6*n));
dtgevc_(&side, &howmny, select, &n, s, &lds, p, &ldp, vl, &ldvl, vr, &ldvr, &mm, &m, work, &info);
free(work);
rblapack_m = INT2NUM(m);
rblapack_info = INT2NUM(info);
return rb_ary_new3(4, rblapack_m, rblapack_info, rblapack_vl, rblapack_vr);
}
void
init_lapack_dtgevc(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "dtgevc", rblapack_dtgevc, -1);
}
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