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#include "rb_lapack.h"
extern VOID sgegv_(char* jobvl, char* jobvr, integer* n, real* a, integer* lda, real* b, integer* ldb, real* alphar, real* alphai, real* beta, real* vl, integer* ldvl, real* vr, integer* ldvr, real* work, integer* lwork, integer* info);
static VALUE
rblapack_sgegv(int argc, VALUE *argv, VALUE self){
VALUE rblapack_jobvl;
char jobvl;
VALUE rblapack_jobvr;
char jobvr;
VALUE rblapack_a;
real *a;
VALUE rblapack_b;
real *b;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_alphar;
real *alphar;
VALUE rblapack_alphai;
real *alphai;
VALUE rblapack_beta;
real *beta;
VALUE rblapack_vl;
real *vl;
VALUE rblapack_vr;
real *vr;
VALUE rblapack_work;
real *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
real *a_out__;
VALUE rblapack_b_out__;
real *b_out__;
integer lda;
integer n;
integer ldb;
integer ldvl;
integer ldvr;
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 alphar, alphai, beta, vl, vr, work, info, a, b = NumRu::Lapack.sgegv( jobvl, jobvr, a, b, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE SGEGV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO )\n\n* Purpose\n* =======\n*\n* This routine is deprecated and has been replaced by routine SGGEV.\n*\n* SGEGV computes the eigenvalues and, optionally, the left and/or right\n* eigenvectors of a real matrix pair (A,B).\n* Given two square matrices A and B,\n* the generalized nonsymmetric eigenvalue problem (GNEP) is to find the\n* eigenvalues lambda and corresponding (non-zero) eigenvectors x such\n* that\n*\n* A*x = lambda*B*x.\n*\n* An alternate form is to find the eigenvalues mu and corresponding\n* eigenvectors y such that\n*\n* mu*A*y = B*y.\n*\n* These two forms are equivalent with mu = 1/lambda and x = y if\n* neither lambda nor mu is zero. In order to deal with the case that\n* lambda or mu is zero or small, two values alpha and beta are returned\n* for each eigenvalue, such that lambda = alpha/beta and\n* mu = beta/alpha.\n*\n* The vectors x and y in the above equations are right eigenvectors of\n* the matrix pair (A,B). Vectors u and v satisfying\n*\n* u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B\n*\n* are left eigenvectors of (A,B).\n*\n* Note: this routine performs \"full balancing\" on A and B -- see\n* \"Further Details\", below.\n*\n\n* Arguments\n* =========\n*\n* JOBVL (input) CHARACTER*1\n* = 'N': do not compute the left generalized eigenvectors;\n* = 'V': compute the left generalized eigenvectors (returned\n* in VL).\n*\n* JOBVR (input) CHARACTER*1\n* = 'N': do not compute the right generalized eigenvectors;\n* = 'V': compute the right generalized eigenvectors (returned\n* in VR).\n*\n* N (input) INTEGER\n* The order of the matrices A, B, VL, and VR. N >= 0.\n*\n* A (input/output) REAL array, dimension (LDA, N)\n* On entry, the matrix A.\n* If JOBVL = 'V' or JOBVR = 'V', then on exit A\n* contains the real Schur form of A from the generalized Schur\n* factorization of the pair (A,B) after balancing.\n* If no eigenvectors were computed, then only the diagonal\n* blocks from the Schur form will be correct. See SGGHRD and\n* SHGEQZ for details.\n*\n* LDA (input) INTEGER\n* The leading dimension of A. LDA >= max(1,N).\n*\n* B (input/output) REAL array, dimension (LDB, N)\n* On entry, the matrix B.\n* If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the\n* upper triangular matrix obtained from B in the generalized\n* Schur factorization of the pair (A,B) after balancing.\n* If no eigenvectors were computed, then only those elements of\n* B corresponding to the diagonal blocks from the Schur form of\n* A will be correct. See SGGHRD and SHGEQZ for details.\n*\n* LDB (input) INTEGER\n* The leading dimension of B. LDB >= max(1,N).\n*\n* ALPHAR (output) REAL array, dimension (N)\n* The real parts of each scalar alpha defining an eigenvalue of\n* GNEP.\n*\n* ALPHAI (output) REAL array, dimension (N)\n* The imaginary parts of each scalar alpha defining an\n* eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th\n* eigenvalue is real; if positive, then the j-th and\n* (j+1)-st eigenvalues are a complex conjugate pair, with\n* ALPHAI(j+1) = -ALPHAI(j).\n*\n* BETA (output) REAL array, dimension (N)\n* The scalars beta that define the eigenvalues of GNEP.\n* \n* Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and\n* beta = BETA(j) represent the j-th eigenvalue of the matrix\n* pair (A,B), in one of the forms lambda = alpha/beta or\n* mu = beta/alpha. Since either lambda or mu may overflow,\n* they should not, in general, be computed.\n*\n* VL (output) REAL array, dimension (LDVL,N)\n* If JOBVL = 'V', the left eigenvectors u(j) are stored\n* in the columns of VL, in the same order as their eigenvalues.\n* If the j-th eigenvalue is real, then u(j) = VL(:,j).\n* If the j-th and (j+1)-st eigenvalues form a complex conjugate\n* pair, then\n* u(j) = VL(:,j) + i*VL(:,j+1)\n* and\n* u(j+1) = VL(:,j) - i*VL(:,j+1).\n*\n* Each eigenvector is scaled so that its largest component has\n* abs(real part) + abs(imag. part) = 1, except for eigenvectors\n* corresponding to an eigenvalue with alpha = beta = 0, which\n* are set to zero.\n* Not referenced if JOBVL = 'N'.\n*\n* LDVL (input) INTEGER\n* The leading dimension of the matrix VL. LDVL >= 1, and\n* if JOBVL = 'V', LDVL >= N.\n*\n* VR (output) REAL array, dimension (LDVR,N)\n* If JOBVR = 'V', the right eigenvectors x(j) are stored\n* in the columns of VR, in the same order as their eigenvalues.\n* If the j-th eigenvalue is real, then x(j) = VR(:,j).\n* If the j-th and (j+1)-st eigenvalues form a complex conjugate\n* pair, then\n* x(j) = VR(:,j) + i*VR(:,j+1)\n* and\n* x(j+1) = VR(:,j) - i*VR(:,j+1).\n*\n* Each eigenvector is scaled so that its largest component has\n* abs(real part) + abs(imag. part) = 1, except for eigenvalues\n* corresponding to an eigenvalue with alpha = beta = 0, which\n* are set to zero.\n* Not referenced if JOBVR = 'N'.\n*\n* LDVR (input) INTEGER\n* The leading dimension of the matrix VR. LDVR >= 1, and\n* if JOBVR = 'V', LDVR >= N.\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. LWORK >= max(1,8*N).\n* For good performance, LWORK must generally be larger.\n* To compute the optimal value of LWORK, call ILAENV to get\n* blocksizes (for SGEQRF, SORMQR, and SORGQR.) Then compute:\n* NB -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR;\n* The optimal LWORK is:\n* 2*N + MAX( 6*N, N*(NB+1) ).\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* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value.\n* = 1,...,N:\n* The QZ iteration failed. No eigenvectors have been\n* calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)\n* should be correct for j=INFO+1,...,N.\n* > N: errors that usually indicate LAPACK problems:\n* =N+1: error return from SGGBAL\n* =N+2: error return from SGEQRF\n* =N+3: error return from SORMQR\n* =N+4: error return from SORGQR\n* =N+5: error return from SGGHRD\n* =N+6: error return from SHGEQZ (other than failed\n* iteration)\n* =N+7: error return from STGEVC\n* =N+8: error return from SGGBAK (computing VL)\n* =N+9: error return from SGGBAK (computing VR)\n* =N+10: error return from SLASCL (various calls)\n*\n\n* Further Details\n* ===============\n*\n* Balancing\n* ---------\n*\n* This driver calls SGGBAL to both permute and scale rows and columns\n* of A and B. The permutations PL and PR are chosen so that PL*A*PR\n* and PL*B*R will be upper triangular except for the diagonal blocks\n* A(i:j,i:j) and B(i:j,i:j), with i and j as close together as\n* possible. The diagonal scaling matrices DL and DR are chosen so\n* that the pair DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to\n* one (except for the elements that start out zero.)\n*\n* After the eigenvalues and eigenvectors of the balanced matrices\n* have been computed, SGGBAK transforms the eigenvectors back to what\n* they would have been (in perfect arithmetic) if they had not been\n* balanced.\n*\n* Contents of A and B on Exit\n* -------- -- - --- - -- ----\n*\n* If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or\n* both), then on exit the arrays A and B will contain the real Schur\n* form[*] of the \"balanced\" versions of A and B. If no eigenvectors\n* are computed, then only the diagonal blocks will be correct.\n*\n* [*] See SHGEQZ, SGEGS, or read the book \"Matrix Computations\",\n* by Golub & van Loan, pub. by Johns Hopkins U. Press.\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n alphar, alphai, beta, vl, vr, work, info, a, b = NumRu::Lapack.sgegv( jobvl, jobvr, a, b, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 4 && argc != 5)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 4)", argc);
rblapack_jobvl = argv[0];
rblapack_jobvr = argv[1];
rblapack_a = argv[2];
rblapack_b = argv[3];
if (argc == 5) {
rblapack_lwork = argv[4];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
jobvl = StringValueCStr(rblapack_jobvl)[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);
n = NA_SHAPE1(rblapack_a);
if (NA_TYPE(rblapack_a) != NA_SFLOAT)
rblapack_a = na_change_type(rblapack_a, NA_SFLOAT);
a = NA_PTR_TYPE(rblapack_a, real*);
jobvr = StringValueCStr(rblapack_jobvr)[0];
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 a");
if (NA_TYPE(rblapack_b) != NA_SFLOAT)
rblapack_b = na_change_type(rblapack_b, NA_SFLOAT);
b = NA_PTR_TYPE(rblapack_b, real*);
ldvr = lsame_(&jobvr,"V") ? n : 1;
if (rblapack_lwork == Qnil)
lwork = 8*n;
else {
lwork = NUM2INT(rblapack_lwork);
}
ldvl = lsame_(&jobvl,"V") ? n : 1;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_alphar = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
alphar = NA_PTR_TYPE(rblapack_alphar, real*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_alphai = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
alphai = NA_PTR_TYPE(rblapack_alphai, real*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_beta = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
beta = NA_PTR_TYPE(rblapack_beta, real*);
{
na_shape_t shape[2];
shape[0] = ldvl;
shape[1] = n;
rblapack_vl = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
vl = NA_PTR_TYPE(rblapack_vl, real*);
{
na_shape_t shape[2];
shape[0] = ldvr;
shape[1] = n;
rblapack_vr = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
vr = NA_PTR_TYPE(rblapack_vr, 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] = lda;
shape[1] = n;
rblapack_a_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
a_out__ = NA_PTR_TYPE(rblapack_a_out__, real*);
MEMCPY(a_out__, a, real, NA_TOTAL(rblapack_a));
rblapack_a = rblapack_a_out__;
a = a_out__;
{
na_shape_t shape[2];
shape[0] = ldb;
shape[1] = n;
rblapack_b_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, real*);
MEMCPY(b_out__, b, real, NA_TOTAL(rblapack_b));
rblapack_b = rblapack_b_out__;
b = b_out__;
sgegv_(&jobvl, &jobvr, &n, a, &lda, b, &ldb, alphar, alphai, beta, vl, &ldvl, vr, &ldvr, work, &lwork, &info);
rblapack_info = INT2NUM(info);
return rb_ary_new3(9, rblapack_alphar, rblapack_alphai, rblapack_beta, rblapack_vl, rblapack_vr, rblapack_work, rblapack_info, rblapack_a, rblapack_b);
}
void
init_lapack_sgegv(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "sgegv", rblapack_sgegv, -1);
}
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