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#include "rb_lapack.h"
extern VOID dtgsna_(char* job, char* howmny, logical* select, integer* n, doublereal* a, integer* lda, doublereal* b, integer* ldb, doublereal* vl, integer* ldvl, doublereal* vr, integer* ldvr, doublereal* s, doublereal* dif, integer* mm, integer* m, doublereal* work, integer* lwork, integer* iwork, integer* info);
static VALUE
rblapack_dtgsna(int argc, VALUE *argv, VALUE self){
VALUE rblapack_job;
char job;
VALUE rblapack_howmny;
char howmny;
VALUE rblapack_select;
logical *select;
VALUE rblapack_a;
doublereal *a;
VALUE rblapack_b;
doublereal *b;
VALUE rblapack_vl;
doublereal *vl;
VALUE rblapack_vr;
doublereal *vr;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_s;
doublereal *s;
VALUE rblapack_dif;
doublereal *dif;
VALUE rblapack_m;
integer m;
VALUE rblapack_work;
doublereal *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.dtgsna( job, howmny, select, a, b, vl, vr, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE DTGSNA( 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* DTGSNA estimates reciprocal condition numbers for specified\n* eigenvalues and/or eigenvectors of a matrix pair (A, B) in\n* generalized real Schur canonical form (or of any matrix pair\n* (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where\n* Z' denotes the transpose of Z.\n*\n* (A, B) must be in generalized real Schur form (as returned by DGGES),\n* i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal\n* blocks. B is upper triangular.\n*\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 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 square matrix pair (A, B). N >= 0.\n*\n* A (input) DOUBLE PRECISION array, dimension (LDA,N)\n* The upper quasi-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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 DTGEVC.\n* If JOB = 'V', VL is not referenced.\n*\n* LDVL (input) INTEGER\n* The leading dimension of the array VL. LDVL >= 1.\n* If JOB = 'E' or 'B', LDVL >= N.\n*\n* VR (input) DOUBLE PRECISION 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 ov VR, as returned by DTGEVC.\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. For a complex conjugate pair of eigenvalues two\n* consecutive elements of S are set to the same value. Thus\n* S(j), DIF(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* 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. For a complex eigenvector two\n* consecutive elements of DIF are set to the same value. If\n* the eigenvalues cannot be reordered to compute DIF(j), DIF(j)\n* is set to 0; this can only occur when the true value would be\n* very small anyway.\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 real\n* eigenvalue one element is used, and for each selected complex\n* conjugate pair of eigenvalues, two elements are used.\n* If HOWMNY = 'A', M is set to N.\n*\n* WORK (workspace/output) DOUBLE PRECISION 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 >= 2*N*(N+2)+16.\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 (N + 6)\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\n* Further Details\n* ===============\n*\n* The reciprocal of the condition number of a generalized eigenvalue\n* w = (a, b) is defined as\n*\n* S(w) = (|u'Av|**2 + |u'Bv|**2)**(1/2) / (norm(u)*norm(v))\n*\n* where u and v are the left and right 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.\n* The pair (a, b) corresponds to an eigenvalue w = a/b (= u'Av/u'Bv)\n* of the 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 DIF(i) of right eigenvector u\n* and left eigenvector v corresponding to the generalized eigenvalue w\n* is defined as follows:\n*\n* a) If the i-th eigenvalue w = (a,b) is real\n*\n* Suppose U and V are orthogonal transformations such that\n*\n* U'*(A, B)*V = (S, T) = ( a * ) ( b * ) 1\n* ( 0 S22 ),( 0 T22 ) n-1\n* 1 n-1 1 n-1\n*\n* Then the reciprocal condition number DIF(i) is\n*\n* Difl((a, b), (S22, T22)) = sigma-min( Zl ),\n*\n* where sigma-min(Zl) denotes the smallest singular value of the\n* 2(n-1)-by-2(n-1) matrix\n*\n* Zl = [ kron(a, In-1) -kron(1, S22) ]\n* [ kron(b, In-1) -kron(1, T22) ] .\n*\n* Here In-1 is the identity matrix of size n-1. kron(X, Y) is the\n* Kronecker product between the matrices X and Y.\n*\n* Note that if the default method for computing DIF(i) is wanted\n* (see DLATDF), then the parameter DIFDRI (see below) should be\n* changed from 3 to 4 (routine DLATDF(IJOB = 2 will be used)).\n* See DTGSYL for more details.\n*\n* b) If the i-th and (i+1)-th eigenvalues are complex conjugate pair,\n*\n* Suppose U and V are orthogonal transformations such that\n*\n* U'*(A, B)*V = (S, T) = ( S11 * ) ( T11 * ) 2\n* ( 0 S22 ),( 0 T22) n-2\n* 2 n-2 2 n-2\n*\n* and (S11, T11) corresponds to the complex conjugate eigenvalue\n* pair (w, conjg(w)). There exist unitary matrices U1 and V1 such\n* that\n*\n* U1'*S11*V1 = ( s11 s12 ) and U1'*T11*V1 = ( t11 t12 )\n* ( 0 s22 ) ( 0 t22 )\n*\n* where the generalized eigenvalues w = s11/t11 and\n* conjg(w) = s22/t22.\n*\n* Then the reciprocal condition number DIF(i) is bounded by\n*\n* min( d1, max( 1, |real(s11)/real(s22)| )*d2 )\n*\n* where, d1 = Difl((s11, t11), (s22, t22)) = sigma-min(Z1), where\n* Z1 is the complex 2-by-2 matrix\n*\n* Z1 = [ s11 -s22 ]\n* [ t11 -t22 ],\n*\n* This is done by computing (using real arithmetic) the\n* roots of the characteristical polynomial det(Z1' * Z1 - lambda I),\n* where Z1' denotes the conjugate transpose of Z1 and det(X) denotes\n* the determinant of X.\n*\n* and d2 is an upper bound on Difl((S11, T11), (S22, T22)), i.e. an\n* upper bound on sigma-min(Z2), where Z2 is (2n-2)-by-(2n-2)\n*\n* Z2 = [ kron(S11', In-2) -kron(I2, S22) ]\n* [ kron(T11', In-2) -kron(I2, T22) ]\n*\n* Note that if the default method for computing DIF is wanted (see\n* DLATDF), then the parameter DIFDRI (see below) should be changed\n* from 3 to 4 (routine DLATDF(IJOB = 2 will be used)). See DTGSYL\n* for more details.\n*\n* For each eigenvalue/vector specified by SELECT, DIF stores a\n* Frobenius norm-based estimate of Difl.\n*\n* An approximate error bound for the i-th 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,\n* Report UMINF - 94.04, Department of Computing Science, Umea\n* University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working\n* Note 87. 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. To appear in ACM Trans. on Math. Software, Vol 22,\n* 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.dtgsna( 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_DFLOAT)
rblapack_b = na_change_type(rblapack_b, NA_DFLOAT);
b = NA_PTR_TYPE(rblapack_b, 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);
m = 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) != m)
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*);
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_DFLOAT)
rblapack_a = na_change_type(rblapack_a, NA_DFLOAT);
a = NA_PTR_TYPE(rblapack_a, doublereal*);
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_DFLOAT, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, doublereal*);
iwork = ALLOC_N(integer, (lsame_(&job,"E") ? 0 : n + 6));
dtgsna_(&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_dtgsna(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "dtgsna", rblapack_dtgsna, -1);
}
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