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#include "rb_lapack.h"
extern VOID dtgsyl_(char* trans, integer* ijob, integer* m, integer* n, doublereal* a, integer* lda, doublereal* b, integer* ldb, doublereal* c, integer* ldc, doublereal* d, integer* ldd, doublereal* e, integer* lde, doublereal* f, integer* ldf, doublereal* scale, doublereal* dif, doublereal* work, integer* lwork, integer* iwork, integer* info);
static VALUE
rblapack_dtgsyl(int argc, VALUE *argv, VALUE self){
VALUE rblapack_trans;
char trans;
VALUE rblapack_ijob;
integer ijob;
VALUE rblapack_a;
doublereal *a;
VALUE rblapack_b;
doublereal *b;
VALUE rblapack_c;
doublereal *c;
VALUE rblapack_d;
doublereal *d;
VALUE rblapack_e;
doublereal *e;
VALUE rblapack_f;
doublereal *f;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_scale;
doublereal scale;
VALUE rblapack_dif;
doublereal dif;
VALUE rblapack_work;
doublereal *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_c_out__;
doublereal *c_out__;
VALUE rblapack_f_out__;
doublereal *f_out__;
integer *iwork;
integer lda;
integer m;
integer ldb;
integer n;
integer ldc;
integer ldd;
integer lde;
integer ldf;
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 scale, dif, work, info, c, f = NumRu::Lapack.dtgsyl( trans, ijob, a, b, c, d, e, f, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE DTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* DTGSYL solves the generalized Sylvester equation:\n*\n* A * R - L * B = scale * C (1)\n* D * R - L * E = scale * F\n*\n* where R and L are unknown m-by-n matrices, (A, D), (B, E) and\n* (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n,\n* respectively, with real entries. (A, D) and (B, E) must be in\n* generalized (real) Schur canonical form, i.e. A, B are upper quasi\n* triangular and D, E are upper triangular.\n*\n* The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output\n* scaling factor chosen to avoid overflow.\n*\n* In matrix notation (1) is equivalent to solve Zx = scale b, where\n* Z is defined as\n*\n* Z = [ kron(In, A) -kron(B', Im) ] (2)\n* [ kron(In, D) -kron(E', Im) ].\n*\n* Here Ik is the identity matrix of size k and X' is the transpose of\n* X. kron(X, Y) is the Kronecker product between the matrices X and Y.\n*\n* If TRANS = 'T', DTGSYL solves the transposed system Z'*y = scale*b,\n* which is equivalent to solve for R and L in\n*\n* A' * R + D' * L = scale * C (3)\n* R * B' + L * E' = scale * (-F)\n*\n* This case (TRANS = 'T') is used to compute an one-norm-based estimate\n* of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)\n* and (B,E), using DLACON.\n*\n* If IJOB >= 1, DTGSYL computes a Frobenius norm-based estimate\n* of Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the\n* reciprocal of the smallest singular value of Z. See [1-2] for more\n* information.\n*\n* This is a level 3 BLAS algorithm.\n*\n\n* Arguments\n* =========\n*\n* TRANS (input) CHARACTER*1\n* = 'N', solve the generalized Sylvester equation (1).\n* = 'T', solve the 'transposed' system (3).\n*\n* IJOB (input) INTEGER\n* Specifies what kind of functionality to be performed.\n* =0: solve (1) only.\n* =1: The functionality of 0 and 3.\n* =2: The functionality of 0 and 4.\n* =3: Only an estimate of Dif[(A,D), (B,E)] is computed.\n* (look ahead strategy IJOB = 1 is used).\n* =4: Only an estimate of Dif[(A,D), (B,E)] is computed.\n* ( DGECON on sub-systems is used ).\n* Not referenced if TRANS = 'T'.\n*\n* M (input) INTEGER\n* The order of the matrices A and D, and the row dimension of\n* the matrices C, F, R and L.\n*\n* N (input) INTEGER\n* The order of the matrices B and E, and the column dimension\n* of the matrices C, F, R and L.\n*\n* A (input) DOUBLE PRECISION array, dimension (LDA, M)\n* The upper quasi triangular matrix A.\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1, M).\n*\n* B (input) DOUBLE PRECISION array, dimension (LDB, N)\n* The upper quasi triangular matrix B.\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1, N).\n*\n* C (input/output) DOUBLE PRECISION array, dimension (LDC, N)\n* On entry, C contains the right-hand-side of the first matrix\n* equation in (1) or (3).\n* On exit, if IJOB = 0, 1 or 2, C has been overwritten by\n* the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,\n* the solution achieved during the computation of the\n* Dif-estimate.\n*\n* LDC (input) INTEGER\n* The leading dimension of the array C. LDC >= max(1, M).\n*\n* D (input) DOUBLE PRECISION array, dimension (LDD, M)\n* The upper triangular matrix D.\n*\n* LDD (input) INTEGER\n* The leading dimension of the array D. LDD >= max(1, M).\n*\n* E (input) DOUBLE PRECISION array, dimension (LDE, N)\n* The upper triangular matrix E.\n*\n* LDE (input) INTEGER\n* The leading dimension of the array E. LDE >= max(1, N).\n*\n* F (input/output) DOUBLE PRECISION array, dimension (LDF, N)\n* On entry, F contains the right-hand-side of the second matrix\n* equation in (1) or (3).\n* On exit, if IJOB = 0, 1 or 2, F has been overwritten by\n* the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,\n* the solution achieved during the computation of the\n* Dif-estimate.\n*\n* LDF (input) INTEGER\n* The leading dimension of the array F. LDF >= max(1, M).\n*\n* DIF (output) DOUBLE PRECISION\n* On exit DIF is the reciprocal of a lower bound of the\n* reciprocal of the Dif-function, i.e. DIF is an upper bound of\n* Dif[(A,D), (B,E)] = sigma_min(Z), where Z as in (2).\n* IF IJOB = 0 or TRANS = 'T', DIF is not touched.\n*\n* SCALE (output) DOUBLE PRECISION\n* On exit SCALE is the scaling factor in (1) or (3).\n* If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,\n* to a slightly perturbed system but the input matrices A, B, D\n* and E have not been changed. If SCALE = 0, C and F hold the\n* solutions R and L, respectively, to the homogeneous system\n* with C = F = 0. Normally, SCALE = 1.\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 > = 1.\n* If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N).\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 (M+N+6)\n*\n* INFO (output) INTEGER\n* =0: successful exit\n* <0: If INFO = -i, the i-th argument had an illegal value.\n* >0: (A, D) and (B, E) have common or close eigenvalues.\n*\n\n* Further Details\n* ===============\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* [1] 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* [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester\n* Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal.\n* Appl., 15(4):1045-1060, 1994\n*\n* [3] B. Kagstrom and L. Westin, Generalized Schur Methods with\n* Condition Estimators for Solving the Generalized Sylvester\n* Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,\n* July 1989, pp 745-751.\n*\n* =====================================================================\n* Replaced various illegal calls to DCOPY by calls to DLASET.\n* Sven Hammarling, 1/5/02.\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n scale, dif, work, info, c, f = NumRu::Lapack.dtgsyl( trans, ijob, a, b, c, d, e, f, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 8 && argc != 9)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 8)", argc);
rblapack_trans = argv[0];
rblapack_ijob = argv[1];
rblapack_a = argv[2];
rblapack_b = argv[3];
rblapack_c = argv[4];
rblapack_d = argv[5];
rblapack_e = argv[6];
rblapack_f = argv[7];
if (argc == 9) {
rblapack_lwork = argv[8];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
trans = StringValueCStr(rblapack_trans)[0];
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (3th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (3th argument) must be %d", 2);
lda = NA_SHAPE0(rblapack_a);
m = NA_SHAPE1(rblapack_a);
if (NA_TYPE(rblapack_a) != NA_DFLOAT)
rblapack_a = na_change_type(rblapack_a, NA_DFLOAT);
a = NA_PTR_TYPE(rblapack_a, doublereal*);
if (!NA_IsNArray(rblapack_c))
rb_raise(rb_eArgError, "c (5th argument) must be NArray");
if (NA_RANK(rblapack_c) != 2)
rb_raise(rb_eArgError, "rank of c (5th argument) must be %d", 2);
ldc = NA_SHAPE0(rblapack_c);
n = NA_SHAPE1(rblapack_c);
if (NA_TYPE(rblapack_c) != NA_DFLOAT)
rblapack_c = na_change_type(rblapack_c, NA_DFLOAT);
c = NA_PTR_TYPE(rblapack_c, doublereal*);
if (!NA_IsNArray(rblapack_e))
rb_raise(rb_eArgError, "e (7th argument) must be NArray");
if (NA_RANK(rblapack_e) != 2)
rb_raise(rb_eArgError, "rank of e (7th argument) must be %d", 2);
lde = NA_SHAPE0(rblapack_e);
if (NA_SHAPE1(rblapack_e) != n)
rb_raise(rb_eRuntimeError, "shape 1 of e must be the same as shape 1 of c");
if (NA_TYPE(rblapack_e) != NA_DFLOAT)
rblapack_e = na_change_type(rblapack_e, NA_DFLOAT);
e = NA_PTR_TYPE(rblapack_e, doublereal*);
ijob = NUM2INT(rblapack_ijob);
if (!NA_IsNArray(rblapack_d))
rb_raise(rb_eArgError, "d (6th argument) must be NArray");
if (NA_RANK(rblapack_d) != 2)
rb_raise(rb_eArgError, "rank of d (6th argument) must be %d", 2);
ldd = NA_SHAPE0(rblapack_d);
if (NA_SHAPE1(rblapack_d) != m)
rb_raise(rb_eRuntimeError, "shape 1 of d must be the same as shape 1 of a");
if (NA_TYPE(rblapack_d) != NA_DFLOAT)
rblapack_d = na_change_type(rblapack_d, NA_DFLOAT);
d = NA_PTR_TYPE(rblapack_d, doublereal*);
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (4th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (4th 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 1 of c");
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_f))
rb_raise(rb_eArgError, "f (8th argument) must be NArray");
if (NA_RANK(rblapack_f) != 2)
rb_raise(rb_eArgError, "rank of f (8th argument) must be %d", 2);
ldf = NA_SHAPE0(rblapack_f);
if (NA_SHAPE1(rblapack_f) != n)
rb_raise(rb_eRuntimeError, "shape 1 of f must be the same as shape 1 of c");
if (NA_TYPE(rblapack_f) != NA_DFLOAT)
rblapack_f = na_change_type(rblapack_f, NA_DFLOAT);
f = NA_PTR_TYPE(rblapack_f, doublereal*);
if (rblapack_lwork == Qnil)
lwork = ((ijob==1||ijob==2)&&lsame_(&trans,"N")) ? 2*m*n : 1;
else {
lwork = NUM2INT(rblapack_lwork);
}
{
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*);
{
na_shape_t shape[2];
shape[0] = ldc;
shape[1] = n;
rblapack_c_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
c_out__ = NA_PTR_TYPE(rblapack_c_out__, doublereal*);
MEMCPY(c_out__, c, doublereal, NA_TOTAL(rblapack_c));
rblapack_c = rblapack_c_out__;
c = c_out__;
{
na_shape_t shape[2];
shape[0] = ldf;
shape[1] = n;
rblapack_f_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
f_out__ = NA_PTR_TYPE(rblapack_f_out__, doublereal*);
MEMCPY(f_out__, f, doublereal, NA_TOTAL(rblapack_f));
rblapack_f = rblapack_f_out__;
f = f_out__;
iwork = ALLOC_N(integer, (m+n+6));
dtgsyl_(&trans, &ijob, &m, &n, a, &lda, b, &ldb, c, &ldc, d, &ldd, e, &lde, f, &ldf, &scale, &dif, work, &lwork, iwork, &info);
free(iwork);
rblapack_scale = rb_float_new((double)scale);
rblapack_dif = rb_float_new((double)dif);
rblapack_info = INT2NUM(info);
return rb_ary_new3(6, rblapack_scale, rblapack_dif, rblapack_work, rblapack_info, rblapack_c, rblapack_f);
}
void
init_lapack_dtgsyl(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "dtgsyl", rblapack_dtgsyl, -1);
}
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