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#include "rb_lapack.h"
extern VOID strsen_(char* job, char* compq, logical* select, integer* n, real* t, integer* ldt, real* q, integer* ldq, real* wr, real* wi, integer* m, real* s, real* sep, real* work, integer* lwork, integer* iwork, integer* liwork, integer* info);
static VALUE
rblapack_strsen(int argc, VALUE *argv, VALUE self){
VALUE rblapack_job;
char job;
VALUE rblapack_compq;
char compq;
VALUE rblapack_select;
logical *select;
VALUE rblapack_t;
real *t;
VALUE rblapack_q;
real *q;
VALUE rblapack_liwork;
integer liwork;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_wr;
real *wr;
VALUE rblapack_wi;
real *wi;
VALUE rblapack_m;
integer m;
VALUE rblapack_s;
real s;
VALUE rblapack_sep;
real sep;
VALUE rblapack_work;
real *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_t_out__;
real *t_out__;
VALUE rblapack_q_out__;
real *q_out__;
integer *iwork;
integer n;
integer ldt;
integer ldq;
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 wr, wi, m, s, sep, work, info, t, q = NumRu::Lapack.strsen( job, compq, select, t, q, liwork, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE STRSEN( JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, WR, WI, M, S, SEP, WORK, LWORK, IWORK, LIWORK, INFO )\n\n* Purpose\n* =======\n*\n* STRSEN reorders the real Schur factorization of a real matrix\n* A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in\n* the leading diagonal blocks of the upper quasi-triangular matrix T,\n* and the leading columns of Q form an orthonormal basis of the\n* corresponding right invariant subspace.\n*\n* Optionally the routine computes the reciprocal condition numbers of\n* the cluster of eigenvalues and/or the invariant subspace.\n*\n* T must be in Schur canonical form (as returned by SHSEQR), that is,\n* block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each\n* 2-by-2 diagonal block has its diagonal elemnts equal and its\n* off-diagonal elements of opposite sign.\n*\n\n* Arguments\n* =========\n*\n* JOB (input) CHARACTER*1\n* Specifies whether condition numbers are required for the\n* cluster of eigenvalues (S) or the invariant subspace (SEP):\n* = 'N': none;\n* = 'E': for eigenvalues only (S);\n* = 'V': for invariant subspace only (SEP);\n* = 'B': for both eigenvalues and invariant subspace (S and\n* SEP).\n*\n* COMPQ (input) CHARACTER*1\n* = 'V': update the matrix Q of Schur vectors;\n* = 'N': do not update Q.\n*\n* SELECT (input) LOGICAL array, dimension (N)\n* SELECT specifies the eigenvalues in the selected cluster. To\n* select a real eigenvalue w(j), SELECT(j) must be set to\n* .TRUE.. To select a complex conjugate pair of eigenvalues\n* w(j) and w(j+1), corresponding to a 2-by-2 diagonal block,\n* either SELECT(j) or SELECT(j+1) or both must be set to\n* .TRUE.; a complex conjugate pair of eigenvalues must be\n* either both included in the cluster or both excluded.\n*\n* N (input) INTEGER\n* The order of the matrix T. N >= 0.\n*\n* T (input/output) REAL array, dimension (LDT,N)\n* On entry, the upper quasi-triangular matrix T, in Schur\n* canonical form.\n* On exit, T is overwritten by the reordered matrix T, again in\n* Schur canonical form, with the selected eigenvalues in the\n* leading diagonal blocks.\n*\n* LDT (input) INTEGER\n* The leading dimension of the array T. LDT >= max(1,N).\n*\n* Q (input/output) REAL array, dimension (LDQ,N)\n* On entry, if COMPQ = 'V', the matrix Q of Schur vectors.\n* On exit, if COMPQ = 'V', Q has been postmultiplied by the\n* orthogonal transformation matrix which reorders T; the\n* leading M columns of Q form an orthonormal basis for the\n* specified invariant subspace.\n* If COMPQ = 'N', Q is not referenced.\n*\n* LDQ (input) INTEGER\n* The leading dimension of the array Q.\n* LDQ >= 1; and if COMPQ = 'V', LDQ >= N.\n*\n* WR (output) REAL array, dimension (N)\n* WI (output) REAL array, dimension (N)\n* The real and imaginary parts, respectively, of the reordered\n* eigenvalues of T. The eigenvalues are stored in the same\n* order as on the diagonal of T, with WR(i) = T(i,i) and, if\n* T(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) > 0 and\n* WI(i+1) = -WI(i). Note that if a complex eigenvalue is\n* sufficiently ill-conditioned, then its value may differ\n* significantly from its value before reordering.\n*\n* M (output) INTEGER\n* The dimension of the specified invariant subspace.\n* 0 < = M <= N.\n*\n* S (output) REAL\n* If JOB = 'E' or 'B', S is a lower bound on the reciprocal\n* condition number for the selected cluster of eigenvalues.\n* S cannot underestimate the true reciprocal condition number\n* by more than a factor of sqrt(N). If M = 0 or N, S = 1.\n* If JOB = 'N' or 'V', S is not referenced.\n*\n* SEP (output) REAL\n* If JOB = 'V' or 'B', SEP is the estimated reciprocal\n* condition number of the specified invariant subspace. If\n* M = 0 or N, SEP = norm(T).\n* If JOB = 'N' or 'E', SEP is not referenced.\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.\n* If JOB = 'N', LWORK >= max(1,N);\n* if JOB = 'E', LWORK >= max(1,M*(N-M));\n* if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)).\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* IWORK (workspace) 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* If JOB = 'N' or 'E', LIWORK >= 1;\n* if JOB = 'V' or 'B', LIWORK >= max(1,M*(N-M)).\n*\n* If LIWORK = -1, then a workspace query is assumed; the\n* routine only calculates the optimal size of the IWORK array,\n* returns this value as the first entry of the IWORK array, and\n* no error message related to LIWORK is issued by XERBLA.\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value\n* = 1: reordering of T failed because some eigenvalues are too\n* close to separate (the problem is very ill-conditioned);\n* T may have been partially reordered, and WR and WI\n* contain the eigenvalues in the same order as in T; S and\n* SEP (if requested) are set to zero.\n*\n\n* Further Details\n* ===============\n*\n* STRSEN first collects the selected eigenvalues by computing an\n* orthogonal transformation Z to move them to the top left corner of T.\n* In other words, the selected eigenvalues are the eigenvalues of T11\n* in:\n*\n* Z'*T*Z = ( T11 T12 ) n1\n* ( 0 T22 ) n2\n* n1 n2\n*\n* where N = n1+n2 and Z' means the transpose of Z. The first n1 columns\n* of Z span the specified invariant subspace of T.\n*\n* If T has been obtained from the real Schur factorization of a matrix\n* A = Q*T*Q', then the reordered real Schur factorization of A is given\n* by A = (Q*Z)*(Z'*T*Z)*(Q*Z)', and the first n1 columns of Q*Z span\n* the corresponding invariant subspace of A.\n*\n* The reciprocal condition number of the average of the eigenvalues of\n* T11 may be returned in S. S lies between 0 (very badly conditioned)\n* and 1 (very well conditioned). It is computed as follows. First we\n* compute R so that\n*\n* P = ( I R ) n1\n* ( 0 0 ) n2\n* n1 n2\n*\n* is the projector on the invariant subspace associated with T11.\n* R is the solution of the Sylvester equation:\n*\n* T11*R - R*T22 = T12.\n*\n* Let F-norm(M) denote the Frobenius-norm of M and 2-norm(M) denote\n* the two-norm of M. Then S is computed as the lower bound\n*\n* (1 + F-norm(R)**2)**(-1/2)\n*\n* on the reciprocal of 2-norm(P), the true reciprocal condition number.\n* S cannot underestimate 1 / 2-norm(P) by more than a factor of\n* sqrt(N).\n*\n* An approximate error bound for the computed average of the\n* eigenvalues of T11 is\n*\n* EPS * norm(T) / S\n*\n* where EPS is the machine precision.\n*\n* The reciprocal condition number of the right invariant subspace\n* spanned by the first n1 columns of Z (or of Q*Z) is returned in SEP.\n* SEP is defined as the separation of T11 and T22:\n*\n* sep( T11, T22 ) = sigma-min( C )\n*\n* where sigma-min(C) is the smallest singular value of the\n* n1*n2-by-n1*n2 matrix\n*\n* C = kprod( I(n2), T11 ) - kprod( transpose(T22), I(n1) )\n*\n* I(m) is an m by m identity matrix, and kprod denotes the Kronecker\n* product. We estimate sigma-min(C) by the reciprocal of an estimate of\n* the 1-norm of inverse(C). The true reciprocal 1-norm of inverse(C)\n* cannot differ from sigma-min(C) by more than a factor of sqrt(n1*n2).\n*\n* When SEP is small, small changes in T can cause large changes in\n* the invariant subspace. An approximate bound on the maximum angular\n* error in the computed right invariant subspace is\n*\n* EPS * norm(T) / SEP\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n wr, wi, m, s, sep, work, info, t, q = NumRu::Lapack.strsen( job, compq, select, t, q, liwork, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 6 && argc != 7)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 6)", argc);
rblapack_job = argv[0];
rblapack_compq = argv[1];
rblapack_select = argv[2];
rblapack_t = argv[3];
rblapack_q = argv[4];
rblapack_liwork = argv[5];
if (argc == 7) {
rblapack_lwork = argv[6];
} 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];
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_q))
rb_raise(rb_eArgError, "q (5th argument) must be NArray");
if (NA_RANK(rblapack_q) != 2)
rb_raise(rb_eArgError, "rank of q (5th 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 0 of select");
if (NA_TYPE(rblapack_q) != NA_SFLOAT)
rblapack_q = na_change_type(rblapack_q, NA_SFLOAT);
q = NA_PTR_TYPE(rblapack_q, real*);
compq = StringValueCStr(rblapack_compq)[0];
liwork = NUM2INT(rblapack_liwork);
if (!NA_IsNArray(rblapack_t))
rb_raise(rb_eArgError, "t (4th argument) must be NArray");
if (NA_RANK(rblapack_t) != 2)
rb_raise(rb_eArgError, "rank of t (4th argument) must be %d", 2);
ldt = NA_SHAPE0(rblapack_t);
if (NA_SHAPE1(rblapack_t) != n)
rb_raise(rb_eRuntimeError, "shape 1 of t must be the same as shape 0 of select");
if (NA_TYPE(rblapack_t) != NA_SFLOAT)
rblapack_t = na_change_type(rblapack_t, NA_SFLOAT);
t = NA_PTR_TYPE(rblapack_t, real*);
if (rblapack_lwork == Qnil)
lwork = lsame_(&job,"N") ? n : lsame_(&job,"E") ? m*(n-m) : (lsame_(&job,"V")||lsame_(&job,"B")) ? 2*m*(n-m) : 0;
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[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[2];
shape[0] = ldt;
shape[1] = n;
rblapack_t_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
t_out__ = NA_PTR_TYPE(rblapack_t_out__, real*);
MEMCPY(t_out__, t, real, 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_SFLOAT, 2, shape, cNArray);
}
q_out__ = NA_PTR_TYPE(rblapack_q_out__, real*);
MEMCPY(q_out__, q, real, NA_TOTAL(rblapack_q));
rblapack_q = rblapack_q_out__;
q = q_out__;
iwork = ALLOC_N(integer, (MAX(1,liwork)));
strsen_(&job, &compq, select, &n, t, &ldt, q, &ldq, wr, wi, &m, &s, &sep, work, &lwork, iwork, &liwork, &info);
free(iwork);
rblapack_m = INT2NUM(m);
rblapack_s = rb_float_new((double)s);
rblapack_sep = rb_float_new((double)sep);
rblapack_info = INT2NUM(info);
return rb_ary_new3(9, rblapack_wr, rblapack_wi, rblapack_m, rblapack_s, rblapack_sep, rblapack_work, rblapack_info, rblapack_t, rblapack_q);
}
void
init_lapack_strsen(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "strsen", rblapack_strsen, -1);
}
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