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#include "rb_lapack.h"
extern VOID strsna_(char* job, char* howmny, logical* select, integer* n, real* t, integer* ldt, real* vl, integer* ldvl, real* vr, integer* ldvr, real* s, real* sep, integer* mm, integer* m, real* work, integer* ldwork, integer* iwork, integer* info);
static VALUE
rblapack_strsna(int argc, VALUE *argv, VALUE self){
VALUE rblapack_job;
char job;
VALUE rblapack_howmny;
char howmny;
VALUE rblapack_select;
logical *select;
VALUE rblapack_t;
real *t;
VALUE rblapack_vl;
real *vl;
VALUE rblapack_vr;
real *vr;
VALUE rblapack_s;
real *s;
VALUE rblapack_sep;
real *sep;
VALUE rblapack_m;
integer m;
VALUE rblapack_info;
integer info;
real *work;
integer *iwork;
integer n;
integer ldt;
integer ldvl;
integer ldvr;
integer mm;
integer ldwork;
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 s, sep, m, info = NumRu::Lapack.strsna( job, howmny, select, t, vl, vr, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE STRSNA( JOB, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, S, SEP, MM, M, WORK, LDWORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* STRSNA estimates reciprocal condition numbers for specified\n* eigenvalues and/or right eigenvectors of a real upper\n* quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q\n* orthogonal).\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 elements 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\n* eigenvalues (S) or eigenvectors (SEP):\n* = 'E': for eigenvalues only (S);\n* = 'V': for eigenvectors only (SEP);\n* = 'B': for both eigenvalues and eigenvectors (S and SEP).\n*\n* HOWMNY (input) CHARACTER*1\n* = 'A': compute condition numbers for all eigenpairs;\n* = 'S': compute condition numbers for selected eigenpairs\n* specified by the array SELECT.\n*\n* SELECT (input) LOGICAL array, dimension (N)\n* If HOWMNY = 'S', SELECT specifies the eigenpairs for which\n* condition numbers are required. To select condition numbers\n* for the eigenpair corresponding to a real eigenvalue w(j),\n* SELECT(j) must be set to .TRUE.. To select condition numbers\n* corresponding to a complex conjugate pair of eigenvalues w(j)\n* and w(j+1), either SELECT(j) or SELECT(j+1) or both, must be\n* set to .TRUE..\n* If HOWMNY = 'A', SELECT is not referenced.\n*\n* N (input) INTEGER\n* The order of the matrix T. N >= 0.\n*\n* T (input) REAL array, dimension (LDT,N)\n* The upper quasi-triangular matrix T, in Schur canonical form.\n*\n* LDT (input) INTEGER\n* The leading dimension of the array T. LDT >= max(1,N).\n*\n* VL (input) REAL array, dimension (LDVL,M)\n* If JOB = 'E' or 'B', VL must contain left eigenvectors of T\n* (or of any Q*T*Q**T with Q orthogonal), corresponding to the\n* eigenpairs specified by HOWMNY and SELECT. The eigenvectors\n* must be stored in consecutive columns of VL, as returned by\n* SHSEIN or STREVC.\n* If JOB = 'V', VL is not referenced.\n*\n* LDVL (input) INTEGER\n* The leading dimension of the array VL.\n* LDVL >= 1; and if JOB = 'E' or 'B', LDVL >= N.\n*\n* VR (input) REAL array, dimension (LDVR,M)\n* If JOB = 'E' or 'B', VR must contain right eigenvectors of T\n* (or of any Q*T*Q**T with Q orthogonal), corresponding to the\n* eigenpairs specified by HOWMNY and SELECT. The eigenvectors\n* must be stored in consecutive columns of VR, as returned by\n* SHSEIN or STREVC.\n* If JOB = 'V', VR is not referenced.\n*\n* LDVR (input) INTEGER\n* The leading dimension of the array VR.\n* LDVR >= 1; and if JOB = 'E' or 'B', LDVR >= N.\n*\n* S (output) REAL array, dimension (MM)\n* If JOB = 'E' or 'B', the reciprocal condition numbers of the\n* selected eigenvalues, stored in consecutive elements of the\n* array. For a complex conjugate pair of eigenvalues two\n* consecutive elements of S are set to the same value. Thus\n* S(j), SEP(j), and the j-th columns of VL and VR all\n* correspond to the same eigenpair (but not in general the\n* j-th eigenpair, unless all eigenpairs are selected).\n* If JOB = 'V', S is not referenced.\n*\n* SEP (output) REAL array, dimension (MM)\n* If JOB = 'V' or 'B', the estimated reciprocal condition\n* numbers of the selected eigenvectors, stored in consecutive\n* elements of the array. For a complex eigenvector two\n* consecutive elements of SEP are set to the same value. If\n* the eigenvalues cannot be reordered to compute SEP(j), SEP(j)\n* is set to 0; this can only occur when the true value would be\n* very small anyway.\n* If JOB = 'E', SEP is not referenced.\n*\n* MM (input) INTEGER\n* The number of elements in the arrays S (if JOB = 'E' or 'B')\n* and/or SEP (if JOB = 'V' or 'B'). MM >= M.\n*\n* M (output) INTEGER\n* The number of elements of the arrays S and/or SEP actually\n* used to store the estimated condition numbers.\n* If HOWMNY = 'A', M is set to N.\n*\n* WORK (workspace) REAL array, dimension (LDWORK,N+6)\n* If JOB = 'E', WORK is not referenced.\n*\n* LDWORK (input) INTEGER\n* The leading dimension of the array WORK.\n* LDWORK >= 1; and if JOB = 'V' or 'B', LDWORK >= N.\n*\n* IWORK (workspace) INTEGER array, dimension (2*(N-1))\n* If JOB = 'E', IWORK is not referenced.\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value\n*\n\n* Further Details\n* ===============\n*\n* The reciprocal of the condition number of an eigenvalue lambda is\n* defined as\n*\n* S(lambda) = |v'*u| / (norm(u)*norm(v))\n*\n* where u and v are the right and left eigenvectors of T corresponding\n* to lambda; v' denotes the conjugate-transpose of v, and norm(u)\n* denotes the Euclidean norm. These reciprocal condition numbers always\n* lie between zero (very badly conditioned) and one (very well\n* conditioned). If n = 1, S(lambda) is defined to be 1.\n*\n* An approximate error bound for a computed eigenvalue W(i) is given by\n*\n* EPS * norm(T) / S(i)\n*\n* where EPS is the machine precision.\n*\n* The reciprocal of the condition number of the right eigenvector u\n* corresponding to lambda is defined as follows. Suppose\n*\n* T = ( lambda c )\n* ( 0 T22 )\n*\n* Then the reciprocal condition number is\n*\n* SEP( lambda, T22 ) = sigma-min( T22 - lambda*I )\n*\n* where sigma-min denotes the smallest singular value. We approximate\n* the smallest singular value by the reciprocal of an estimate of the\n* one-norm of the inverse of T22 - lambda*I. If n = 1, SEP(1) is\n* defined to be abs(T(1,1)).\n*\n* An approximate error bound for a computed right eigenvector VR(i)\n* is given by\n*\n* EPS * norm(T) / SEP(i)\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n s, sep, m, info = NumRu::Lapack.strsna( job, howmny, select, t, vl, vr, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 6 && argc != 6)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 6)", argc);
rblapack_job = argv[0];
rblapack_howmny = argv[1];
rblapack_select = argv[2];
rblapack_t = argv[3];
rblapack_vl = argv[4];
rblapack_vr = argv[5];
if (argc == 6) {
} else if (rblapack_options != Qnil) {
} else {
}
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_vl))
rb_raise(rb_eArgError, "vl (5th argument) must be NArray");
if (NA_RANK(rblapack_vl) != 2)
rb_raise(rb_eArgError, "rank of vl (5th argument) must be %d", 2);
ldvl = NA_SHAPE0(rblapack_vl);
m = NA_SHAPE1(rblapack_vl);
if (NA_TYPE(rblapack_vl) != NA_SFLOAT)
rblapack_vl = na_change_type(rblapack_vl, NA_SFLOAT);
vl = NA_PTR_TYPE(rblapack_vl, real*);
howmny = StringValueCStr(rblapack_howmny)[0];
if (!NA_IsNArray(rblapack_vr))
rb_raise(rb_eArgError, "vr (6th argument) must be NArray");
if (NA_RANK(rblapack_vr) != 2)
rb_raise(rb_eArgError, "rank of vr (6th argument) must be %d", 2);
ldvr = NA_SHAPE0(rblapack_vr);
if (NA_SHAPE1(rblapack_vr) != m)
rb_raise(rb_eRuntimeError, "shape 1 of vr must be the same as shape 1 of vl");
if (NA_TYPE(rblapack_vr) != NA_SFLOAT)
rblapack_vr = na_change_type(rblapack_vr, NA_SFLOAT);
vr = NA_PTR_TYPE(rblapack_vr, real*);
mm = m;
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*);
ldwork = ((lsame_(&job,"V")) || (lsame_(&job,"B"))) ? n : 1;
{
na_shape_t shape[1];
shape[0] = mm;
rblapack_s = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
s = NA_PTR_TYPE(rblapack_s, real*);
{
na_shape_t shape[1];
shape[0] = mm;
rblapack_sep = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
sep = NA_PTR_TYPE(rblapack_sep, real*);
work = ALLOC_N(real, (lsame_(&job,"E") ? 0 : ldwork)*(lsame_(&job,"E") ? 0 : n+6));
iwork = ALLOC_N(integer, (lsame_(&job,"E") ? 0 : 2*(n-1)));
strsna_(&job, &howmny, select, &n, t, &ldt, vl, &ldvl, vr, &ldvr, s, sep, &mm, &m, work, &ldwork, iwork, &info);
free(work);
free(iwork);
rblapack_m = INT2NUM(m);
rblapack_info = INT2NUM(info);
return rb_ary_new3(4, rblapack_s, rblapack_sep, rblapack_m, rblapack_info);
}
void
init_lapack_strsna(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "strsna", rblapack_strsna, -1);
}
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