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#include "rb_lapack.h"
extern VOID ztgsna_(char* job, char* howmny, logical* select, integer* n, doublecomplex* a, integer* lda, doublecomplex* b, integer* ldb, doublecomplex* vl, integer* ldvl, doublecomplex* vr, integer* ldvr, doublereal* s, doublereal* dif, integer* mm, integer* m, doublecomplex* work, integer* lwork, integer* iwork, integer* info);
static VALUE
rblapack_ztgsna(int argc, VALUE *argv, VALUE self){
VALUE rblapack_job;
char job;
VALUE rblapack_howmny;
char howmny;
VALUE rblapack_select;
logical *select;
VALUE rblapack_a;
doublecomplex *a;
VALUE rblapack_b;
doublecomplex *b;
VALUE rblapack_vl;
doublecomplex *vl;
VALUE rblapack_vr;
doublecomplex *vr;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_s;
doublereal *s;
VALUE rblapack_dif;
doublereal *dif;
VALUE rblapack_m;
integer m;
VALUE rblapack_work;
doublecomplex *work;
VALUE rblapack_info;
integer info;
integer *iwork;
integer n;
integer lda;
integer ldb;
integer ldvl;
integer ldvr;
integer mm;
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, dif, m, work, info = NumRu::Lapack.ztgsna( job, howmny, select, a, b, vl, vr, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZTGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* ZTGSNA estimates reciprocal condition numbers for specified\n* eigenvalues and/or eigenvectors of a matrix pair (A, B).\n*\n* (A, B) must be in generalized Schur canonical form, that is, A and\n* B are both upper triangular.\n*\n\n* Arguments\n* =========\n*\n* JOB (input) CHARACTER*1\n* Specifies whether condition numbers are required for\n* eigenvalues (S) or eigenvectors (DIF):\n* = 'E': for eigenvalues only (S);\n* = 'V': for eigenvectors only (DIF);\n* = 'B': for both eigenvalues and eigenvectors (S and DIF).\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 corresponding j-th eigenvalue and/or eigenvector,\n* SELECT(j) must be set to .TRUE..\n* If HOWMNY = 'A', SELECT is not referenced.\n*\n* N (input) INTEGER\n* The order of the square matrix pair (A, B). N >= 0.\n*\n* A (input) COMPLEX*16 array, dimension (LDA,N)\n* The upper triangular matrix A in the pair (A,B).\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,N).\n*\n* B (input) COMPLEX*16 array, dimension (LDB,N)\n* The upper triangular matrix B in the pair (A, B).\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,N).\n*\n* VL (input) COMPLEX*16 array, dimension (LDVL,M)\n* IF JOB = 'E' or 'B', VL must contain left eigenvectors of\n* (A, B), corresponding to the eigenpairs specified by HOWMNY\n* and SELECT. The eigenvectors must be stored in consecutive\n* columns of VL, as returned by ZTGEVC.\n* If JOB = 'V', VL is not referenced.\n*\n* LDVL (input) INTEGER\n* The leading dimension of the array VL. LDVL >= 1; and\n* If JOB = 'E' or 'B', LDVL >= N.\n*\n* VR (input) COMPLEX*16 array, dimension (LDVR,M)\n* IF JOB = 'E' or 'B', VR must contain right eigenvectors of\n* (A, B), corresponding to the eigenpairs specified by HOWMNY\n* and SELECT. The eigenvectors must be stored in consecutive\n* columns of VR, as returned by ZTGEVC.\n* If JOB = 'V', VR is not referenced.\n*\n* LDVR (input) INTEGER\n* The leading dimension of the array VR. LDVR >= 1;\n* If JOB = 'E' or 'B', LDVR >= N.\n*\n* S (output) DOUBLE PRECISION 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.\n* If JOB = 'V', S is not referenced.\n*\n* DIF (output) DOUBLE PRECISION 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.\n* If the eigenvalues cannot be reordered to compute DIF(j),\n* DIF(j) is set to 0; this can only occur when the true value\n* would be very small anyway.\n* For each eigenvalue/vector specified by SELECT, DIF stores\n* a Frobenius norm-based estimate of Difl.\n* If JOB = 'E', DIF is not referenced.\n*\n* MM (input) INTEGER\n* The number of elements in the arrays S and DIF. MM >= M.\n*\n* M (output) INTEGER\n* The number of elements of the arrays S and DIF used to store\n* the specified condition numbers; for each selected eigenvalue\n* one element is used. If HOWMNY = 'A', M is set to 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,N).\n* If JOB = 'V' or 'B', LWORK >= max(1,2*N*N).\n*\n* IWORK (workspace) INTEGER array, dimension (N+2)\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 the i-th generalized\n* eigenvalue w = (a, b) is defined as\n*\n* S(I) = (|v'Au|**2 + |v'Bu|**2)**(1/2) / (norm(u)*norm(v))\n*\n* where u and v are the right and left eigenvectors of (A, B)\n* corresponding to w; |z| denotes the absolute value of the complex\n* number, and norm(u) denotes the 2-norm of the vector u. The pair\n* (a, b) corresponds to an eigenvalue w = a/b (= v'Au/v'Bu) of the\n* matrix pair (A, B). If both a and b equal zero, then (A,B) is\n* singular and S(I) = -1 is returned.\n*\n* An approximate error bound on the chordal distance between the i-th\n* computed generalized eigenvalue w and the corresponding exact\n* eigenvalue lambda is\n*\n* chord(w, lambda) <= EPS * norm(A, B) / S(I),\n*\n* where EPS is the machine precision.\n*\n* The reciprocal of the condition number of the right eigenvector u\n* and left eigenvector v corresponding to the generalized eigenvalue w\n* is defined as follows. Suppose\n*\n* (A, B) = ( a * ) ( b * ) 1\n* ( 0 A22 ),( 0 B22 ) n-1\n* 1 n-1 1 n-1\n*\n* Then the reciprocal condition number DIF(I) is\n*\n* Difl[(a, b), (A22, B22)] = sigma-min( Zl )\n*\n* where sigma-min(Zl) denotes the smallest singular value of\n*\n* Zl = [ kron(a, In-1) -kron(1, A22) ]\n* [ kron(b, In-1) -kron(1, B22) ].\n*\n* Here In-1 is the identity matrix of size n-1 and X' is the conjugate\n* transpose of X. kron(X, Y) is the Kronecker product between the\n* matrices X and Y.\n*\n* We approximate the smallest singular value of Zl with an upper\n* bound. This is done by ZLATDF.\n*\n* An approximate error bound for a computed eigenvector VL(i) or\n* VR(i) is given by\n*\n* EPS * norm(A, B) / DIF(i).\n*\n* See ref. [2-3] for more details and further references.\n*\n* Based on contributions by\n* Bo Kagstrom and Peter Poromaa, Department of Computing Science,\n* Umea University, S-901 87 Umea, Sweden.\n*\n* References\n* ==========\n*\n* [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the\n* Generalized Real Schur Form of a Regular Matrix Pair (A, B), in\n* M.S. Moonen et al (eds), Linear Algebra for Large Scale and\n* Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.\n*\n* [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified\n* Eigenvalues of a Regular Matrix Pair (A, B) and Condition\n* Estimation: Theory, Algorithms and Software, Report\n* UMINF - 94.04, Department of Computing Science, Umea University,\n* S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.\n* To appear in Numerical Algorithms, 1996.\n*\n* [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software\n* for Solving the Generalized Sylvester Equation and Estimating the\n* Separation between Regular Matrix Pairs, Report UMINF - 93.23,\n* Department of Computing Science, Umea University, S-901 87 Umea,\n* Sweden, December 1993, Revised April 1994, Also as LAPACK Working\n* Note 75.\n* To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n s, dif, m, work, info = NumRu::Lapack.ztgsna( job, howmny, select, a, b, vl, vr, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 7 && argc != 8)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 7)", argc);
rblapack_job = argv[0];
rblapack_howmny = argv[1];
rblapack_select = argv[2];
rblapack_a = argv[3];
rblapack_b = argv[4];
rblapack_vl = argv[5];
rblapack_vr = argv[6];
if (argc == 8) {
rblapack_lwork = argv[7];
} 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_b))
rb_raise(rb_eArgError, "b (5th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (5th 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 0 of select");
if (NA_TYPE(rblapack_b) != NA_DCOMPLEX)
rblapack_b = na_change_type(rblapack_b, NA_DCOMPLEX);
b = NA_PTR_TYPE(rblapack_b, doublecomplex*);
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);
m = NA_SHAPE1(rblapack_vr);
if (NA_TYPE(rblapack_vr) != NA_DCOMPLEX)
rblapack_vr = na_change_type(rblapack_vr, NA_DCOMPLEX);
vr = NA_PTR_TYPE(rblapack_vr, doublecomplex*);
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) != m)
rb_raise(rb_eRuntimeError, "shape 1 of vl must be the same as shape 1 of vr");
if (NA_TYPE(rblapack_vl) != NA_DCOMPLEX)
rblapack_vl = na_change_type(rblapack_vl, NA_DCOMPLEX);
vl = NA_PTR_TYPE(rblapack_vl, doublecomplex*);
mm = m;
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);
if (NA_SHAPE1(rblapack_a) != n)
rb_raise(rb_eRuntimeError, "shape 1 of a must be the same as shape 0 of select");
if (NA_TYPE(rblapack_a) != NA_DCOMPLEX)
rblapack_a = na_change_type(rblapack_a, NA_DCOMPLEX);
a = NA_PTR_TYPE(rblapack_a, doublecomplex*);
if (rblapack_lwork == Qnil)
lwork = (lsame_(&job,"V")||lsame_(&job,"B")) ? 2*n*n : n;
else {
lwork = NUM2INT(rblapack_lwork);
}
{
na_shape_t shape[1];
shape[0] = mm;
rblapack_s = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
s = NA_PTR_TYPE(rblapack_s, doublereal*);
{
na_shape_t shape[1];
shape[0] = mm;
rblapack_dif = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
dif = NA_PTR_TYPE(rblapack_dif, doublereal*);
{
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*);
iwork = ALLOC_N(integer, (lsame_(&job,"E") ? 0 : n+2));
ztgsna_(&job, &howmny, select, &n, a, &lda, b, &ldb, vl, &ldvl, vr, &ldvr, s, dif, &mm, &m, work, &lwork, iwork, &info);
free(iwork);
rblapack_m = INT2NUM(m);
rblapack_info = INT2NUM(info);
return rb_ary_new3(5, rblapack_s, rblapack_dif, rblapack_m, rblapack_work, rblapack_info);
}
void
init_lapack_ztgsna(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "ztgsna", rblapack_ztgsna, -1);
}
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