void SolveEvolutionMatrix(
DataMatrix<double> & matM,
DataMatrix<double> & matB,
DataVector<double> & vecAlphaR,
DataVector<double> & vecAlphaI,
DataVector<double> & vecBeta,
DataMatrix<double> & matVR
) {
int iInfo = 0;
char jobvl = 'N';
char jobvr = 'V';
int n = matM.GetRows();
int lda = matM.GetRows();
int ldb = matM.GetRows();
int ldvl = 1;
int ldvr = matVR.GetRows();
DataVector<double> vecWork;
vecWork.Initialize(8 * n);
int lwork = vecWork.GetRows();
dggev_(
&jobvl,
&jobvr,
&n,
&(matM[0][0]),
&lda,
&(matB[0][0]),
&ldb,
&(vecAlphaR[0]),
&(vecAlphaI[0]),
&(vecBeta[0]),
NULL,
&ldvl,
&(matVR[0][0]),
&ldvr,
&(vecWork[0]),
&lwork,
&iInfo);
int nCount = 0;
for (int i = 0; i < n; i++) {
if (vecBeta[i] != 0.0) {
//printf("%i %1.5e %1.5e\n", i, vecAlphaR[i] / vecBeta[i], vecAlphaI[i] / vecBeta[i]);
nCount++;
}
}
/*
for (int i = 0; i < 40; i++) {
printf("%1.5e %1.5e\n", matVR[11][4*i+2], matVR[12][4*i+2]);
}
*/
Announce("%i total eigenvalues found", nCount);
}
/*! calculate generalized eigenvalues\n
All of the arguments don't need to be initialized.
wr and wi are overwitten and become
real and imaginary part of generalized eigenvalues, respectively.
This matrix and matB are also overwritten.
*/
inline long dgematrix::dggev(dgematrix& matB,
std::vector<double>& wr, std::vector<double>& wi)
{
#ifdef CPPL_VERBOSE
std::cerr << "# [MARK] dgematrix::dggev(dgematrix&, std::vector<double>&, std::vector<double>&)"
<< std::endl;
#endif//CPPL_VERBOSE
#ifdef CPPL_DEBUG
if(M!=N){
std::cerr << "[ERROR] dgematrix::dggev"
<< "(dgematrix&, vector<double>&, vector<double>&) " << std::endl
<< "This matrix is not a square matrix." << std::endl
<< "This matrix is (" << M << "x" << N << ")." << std::endl;
exit(1);
}
if(matB.M!=N || matB.N!=N){
std::cerr << "[ERROR] dgematrix::dggev"
<< "(dgematrix&, vector<double>&, vector<double>&) " << std::endl
<< "The matrix B is not a square matrix "
<< "having the same size as \"this\" matrix." << std::endl
<< "The B matrix is (" << matB.M << "x" << matB.N << ")."
<< std::endl;
exit(1);
}
#endif//CPPL_DEBUG
wr.resize(N); wi.resize(N);
char JOBVL('N'), JOBVR('N');
long LDA(N), LDB(N), LDVL(1), LDVR(1), LWORK(8*N), INFO(1);
double *BETA(new double[N]), *VL(NULL), *VR(NULL),
*WORK(new double[LWORK]);
dggev_(JOBVL, JOBVR, N, Array, LDA, matB.Array, LDB, &wr[0], &wi[0],
BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO);
delete [] WORK; delete [] VL; delete [] VR;
//// reforming ////
for(long i=0; i<N; i++){ wr[i]/=BETA[i]; wi[i]/=BETA[i]; }
delete [] BETA;
if(INFO!=0){
std::cerr << "[WARNING] dgematrix::dgeev"
<< "(dgematrix&, vector<double>&, vector<double>&)"
<< std::endl
<< "Serious trouble happend. INFO = " << INFO << "."
<< std::endl;
}
return INFO;
}
int FullGenEigenSolver::solve(int nEigen, bool generalized)
{
if (generalized == false) {
opserr << "FullGenEigenSolver::solve() - only solves generalized problem\n";
return -1;
}
if (theSOE == 0) {
opserr << "FullGenEigenSolver::solve()- "
<< " No EigenSOE object has been set yet\n";
return -1;
}
// check for quick return
if (nEigen < 1) {
numEigen = 0;
return 0;
}
// get the number of equations
int n = theSOE->size;
// set the number of eigenvalues
numEigen = nEigen;
if (numEigen > n)
numEigen = n;
// do not compute left eigenvalues and eigenvectors
char *jobvl = "N";
// compute right eigenvalues and eigenvectors
char *jobvr = "V";
// stiffness matrix data
double *Kptr = theSOE->A;
// leading dimension of K
int ldK = n;
// mass matrix data
double *Mptr = theSOE->M;
// leading dimension of M
int ldM = n;
// allocate memory for eigenvalues
double *alphaR = new double [n];
double *alphaI = new double [n];
double *beta = new double [n];
if (eigenvalue != 0)
delete [] eigenvalue;
eigenvalue = new double [n];
// allocate memory for sorting index array
if (sortingID != 0)
delete [] sortingID;
sortingID = new int [n];
// dummy left eigenvectors
double vl[1];
// leading dimension of dummy left eigenvectors
int ldvl = 1;
// allocate memory for right eigenvectors
if (eigenvector != 0)
delete [] eigenvector;
eigenvector = new double [n*n];
// leading dimension of right eigenvectors
int ldvr = n;
// dimension of the workspace array
int lwork = n*(8+64);
// allocate memory for workspace array
double *work = new double [lwork];
// output information
int info = 0;
// call the LAPACK eigenvalue subroutine
#ifdef _WIN32
DGGEV(jobvl, jobvr, &n, Kptr, &ldK, Mptr, &ldM, alphaR, alphaI, beta,
vl, &ldvl, eigenvector, &ldvr, work, &lwork, &info);
#else
dggev_(jobvl, jobvr, &n, Kptr, &ldK, Mptr, &ldM, alphaR, alphaI, beta,
vl, &ldvl, eigenvector, &ldvr, work, &lwork, &info);
#endif
if (info < 0) {
opserr << "FullGenEigenSolver::solve() - invalid argument number "
<< -info << " passed to LAPACK dggev routine\n";
return info;
}
if (info > 0) {
opserr << "FullGenEigenSolver::solve() - the LAPACK dggev routine "
<< "returned error code " << info << endln;
return -info;
}
theSOE->factored = true;
for (int i=0; i<n; i++) {
double mag = sqrt(alphaR[i]*alphaR[i]+alphaI[i]*alphaI[i]);
if (mag*DBL_EPSILON < fabs(beta[i])) {
if (alphaI[i] == 0.0) {
eigenvalue[i] = alphaR[i]/beta[i];
}
else {
eigenvalue[i] = -mag/beta[i];
opserr << "FullGenEigenSolver::solve() - the eigenvalue "
<< i+1 << " is complex with magnitude "
<< -eigenvalue[i] << endln;
}
}
else {
eigenvalue[i] = DBL_MAX;
}
sortingID[i] = i;
}
// sort eigenvalues in ascending order and return sorting ID
this->sort(n, eigenvalue, sortingID);
for (int i=0; i<numEigen; i++) {
if (eigenvalue[i] == DBL_MAX) {
opserr << "FullGenEigenSolver::solve() - the eigenvalue "
<< i+1 << " is numerically undetermined or infinite\n";
}
}
int lworkOpt = (int) work[0];
if (lwork < lworkOpt) {
opserr << "FullGenEigenSolver::solve() - optimal workspace size "
<< lworkOpt << " is larger than provided workspace size "
<< lwork << " consider increasing workspace\n";
}
// clean up the memory
delete [] alphaR;
delete [] alphaI;
delete [] beta;
delete [] work;
return 0;
}
void getParamsHelper(vector<double> &tofill, vector<double> &M, vector<double> &N, int numparams, bool recomputeErrors) {
double work[KINFITWORKSIZE];
double *Mtemp = new double[M.size()], *Ntemp = new double[N.size()];
for (size_t i = 0; i < M.size(); i++) { Mtemp[i] = M[i]; Ntemp[i] = N[i]; }
integer itype = 1;
char jobvl = 'N'; // skip the left eigenvectors
char jobvr = 'V'; // compute the right eigenvectors
integer n = numparams;
// A = Mtemp, will be overwritten
integer lda = n;
// B = Ntemp, will be overwritten
integer ldb = n;
double *alphar = new double[n], *alphai = new double[n], *beta = new double[n]; // real, imaginary and denom of eigs
double VL[1]; // dummy var, we don't want left eigvecs
integer ldvl = 1; // must be >= 1 even though we don't use VL
double *VR = new double[n*n]; // right eigvecs
integer ldvr = n;
integer lwork = KINFITWORKSIZE;
integer info;
dggev_(&jobvl, &jobvr, &n, Mtemp, &lda, Ntemp, &ldb,
alphar, alphai, beta, VL, &ldvl, VR, &ldvr,
work, &lwork, &info);
tofill.resize(n);
int mincol = -1;
if (recomputeErrors) {
double bestErr = -1;
for (int col = 0; col < n; col++) {
double merr = 0, nerr = 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
merr += M[i+n*j]*VR[i+n*col]*VR[j+n*col];
nerr += N[i+n*j]*VR[i+n*col]*VR[j+n*col];
}
}
double err = fabs(merr/nerr);
if (col == 0 || err < bestErr) {
bestErr = err;
mincol = col;
}
}
} else {
double mineig = -1;
for (int i = 0; i < n; i++) {
if (fabs(alphai[i]) < 0.00001 && beta[i] > 0) {
double eigval = fabs(alphar[i])/beta[i];
if (mincol == -1 || eigval < mineig) {
mincol = i;
mineig = eigval;
}
}
}
}
for (int i = 0; i < n; i++) {
tofill[i] = VR[i+n*mincol];
}
delete [] alphar;
delete [] alphai;
delete [] beta;
delete [] VR;
delete [] Mtemp;
delete [] Ntemp;
}
/* Subroutine */ int ddrgev_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, integer *nounit,
doublereal *a, integer *lda, doublereal *b, doublereal *s, doublereal
*t, doublereal *q, integer *ldq, doublereal *z__, doublereal *qe,
integer *ldqe, doublereal *alphar, doublereal *alphai, doublereal *
beta, doublereal *alphr1, doublereal *alphi1, doublereal *beta1,
doublereal *work, integer *lwork, doublereal *result, integer *info)
{
/* Initialized data */
static integer kclass[26] = { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,3 };
static integer kbmagn[26] = { 1,1,1,1,1,1,1,1,3,2,3,2,2,3,1,1,1,1,1,1,1,3,
2,3,2,1 };
static integer ktrian[26] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
1,1,1,1 };
static integer iasign[26] = { 0,0,0,0,0,0,2,0,2,2,0,0,2,2,2,0,2,0,0,0,2,2,
2,2,2,0 };
static integer ibsign[26] = { 0,0,0,0,0,0,0,2,0,0,2,2,0,0,2,0,2,0,0,0,0,0,
0,0,0,0 };
static integer kz1[6] = { 0,1,2,1,3,3 };
static integer kz2[6] = { 0,0,1,2,1,1 };
static integer kadd[6] = { 0,0,0,0,3,2 };
static integer katype[26] = { 0,1,0,1,2,3,4,1,4,4,1,1,4,4,4,2,4,5,8,7,9,4,
4,4,4,0 };
static integer kbtype[26] = { 0,0,1,1,2,-3,1,4,1,1,4,4,1,1,-4,2,-4,8,8,8,
8,8,8,8,8,0 };
static integer kazero[26] = { 1,1,1,1,1,1,2,1,2,2,1,1,2,2,3,1,3,5,5,5,5,3,
3,3,3,1 };
static integer kbzero[26] = { 1,1,1,1,1,1,1,2,1,1,2,2,1,1,4,1,4,6,6,6,6,4,
4,4,4,1 };
static integer kamagn[26] = { 1,1,1,1,1,1,1,1,2,3,2,3,2,3,1,1,1,1,1,1,1,2,
3,3,2,1 };
/* Format strings */
static char fmt_9999[] = "(\002 DDRGEV: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/3x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,4(i4,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 DDRGEV: \002,a,\002 Eigenvectors from"
" \002,a,\002 incorrectly \002,\002normalized.\002,/\002 Bits of "
"error=\002,0p,g10.3,\002,\002,3x,\002N=\002,i4,\002, JTYPE=\002,"
"i3,\002, ISEED=(\002,4(i4,\002,\002),i5,\002)\002)";
static char fmt_9997[] = "(/1x,a3,\002 -- Real Generalized eigenvalue pr"
"oblem driver\002)";
static char fmt_9996[] = "(\002 Matrix types (see DDRGEV for details):"
" \002)";
static char fmt_9995[] = "(\002 Special Matrices:\002,23x,\002(J'=transp"
"osed Jordan block)\002,/\002 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I"
") 5=(J',J') \002,\0026=(diag(J',I), diag(I,J'))\002,/\002 Diag"
"onal Matrices: ( \002,\002D=diag(0,1,2,...) )\002,/\002 7=(D,"
"I) 9=(large*D, small*I\002,\002) 11=(large*I, small*D) 13=(l"
"arge*D, large*I)\002,/\002 8=(I,D) 10=(small*D, large*I) 12="
"(small*I, large*D) \002,\002 14=(small*D, small*I)\002,/\002 15"
"=(D, reversed D)\002)";
static char fmt_9994[] = "(\002 Matrices Rotated by Random \002,a,\002 M"
"atrices U, V:\002,/\002 16=Transposed Jordan Blocks "
" 19=geometric \002,\002alpha, beta=0,1\002,/\002 17=arithm. alp"
"ha&beta \002,\002 20=arithmetic alpha, beta=0,"
"1\002,/\002 18=clustered \002,\002alpha, beta=0,1 21"
"=random alpha, beta=0,1\002,/\002 Large & Small Matrices:\002,"
"/\002 22=(large, small) \002,\00223=(small,large) 24=(smal"
"l,small) 25=(large,large)\002,/\002 26=random O(1) matrices"
".\002)";
static char fmt_9993[] = "(/\002 Tests performed: \002,/\002 1 = max "
"| ( b A - a B )'*l | / const.,\002,/\002 2 = | |VR(i)| - 1 | / u"
"lp,\002,/\002 3 = max | ( b A - a B )*r | / const.\002,/\002 4 ="
" | |VL(i)| - 1 | / ulp,\002,/\002 5 = 0 if W same no matter if r"
" or l computed,\002,/\002 6 = 0 if l same no matter if l compute"
"d,\002,/\002 7 = 0 if r same no matter if r computed,\002,/1x)";
static char fmt_9992[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
",0p,f8.2)";
static char fmt_9991[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
",1p,d10.3)";
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, qe_dim1,
qe_offset, s_dim1, s_offset, t_dim1, t_offset, z_dim1, z_offset,
i__1, i__2, i__3, i__4;
doublereal d__1;
/* Local variables */
integer i__, j, n, n1, jc, in, jr;
doublereal ulp;
integer iadd, ierr, nmax;
logical badnn;
extern /* Subroutine */ int dget52_(logical *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *), dggev_(char *, char *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, integer *);
doublereal rmagn[4];
integer nmats, jsize, nerrs, jtype;
extern /* Subroutine */ int dlatm4_(integer *, integer *, integer *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
integer *, integer *, doublereal *, integer *), dorm2r_(char *,
char *, integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *), dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int dlarfg_(integer *, doublereal *, doublereal *,
integer *, doublereal *);
extern doublereal dlarnd_(integer *, integer *);
doublereal safmin;
integer ioldsd[4];
doublereal safmax;
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
alasvm_(char *, integer *, integer *, integer *, integer *), dlaset_(char *, integer *, integer *, doublereal *,
doublereal *, doublereal *, integer *), xerbla_(char *,
integer *);
integer minwrk, maxwrk;
doublereal ulpinv;
integer mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___38 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___48 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9991, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DDRGEV checks the nonsymmetric generalized eigenvalue problem driver */
/* routine DGGEV. */
/* DGGEV computes for a pair of n-by-n nonsymmetric matrices (A,B) the */
/* generalized eigenvalues and, optionally, the left and right */
/* eigenvectors. */
/* A generalized eigenvalue for a pair of matrices (A,B) is a scalar w */
/* or a ratio alpha/beta = w, such that A - w*B is singular. It is */
/* usually represented as the pair (alpha,beta), as there is reasonalbe */
/* interpretation for beta=0, and even for both being zero. */
/* A right generalized eigenvector corresponding to a generalized */
/* eigenvalue w for a pair of matrices (A,B) is a vector r such that */
/* (A - wB) * r = 0. A left generalized eigenvector is a vector l such */
/* that l**H * (A - wB) = 0, where l**H is the conjugate-transpose of l. */
/* When DDRGEV is called, a number of matrix "sizes" ("n's") and a */
/* number of matrix "types" are specified. For each size ("n") */
/* and each type of matrix, a pair of matrices (A, B) will be generated */
/* and used for testing. For each matrix pair, the following tests */
/* will be performed and compared with the threshhold THRESH. */
/* Results from DGGEV: */
/* (1) max over all left eigenvalue/-vector pairs (alpha/beta,l) of */
/* | VL**H * (beta A - alpha B) |/( ulp max(|beta A|, |alpha B|) ) */
/* where VL**H is the conjugate-transpose of VL. */
/* (2) | |VL(i)| - 1 | / ulp and whether largest component real */
/* VL(i) denotes the i-th column of VL. */
/* (3) max over all left eigenvalue/-vector pairs (alpha/beta,r) of */
/* | (beta A - alpha B) * VR | / ( ulp max(|beta A|, |alpha B|) ) */
/* (4) | |VR(i)| - 1 | / ulp and whether largest component real */
/* VR(i) denotes the i-th column of VR. */
/* (5) W(full) = W(partial) */
/* W(full) denotes the eigenvalues computed when both l and r */
/* are also computed, and W(partial) denotes the eigenvalues */
/* computed when only W, only W and r, or only W and l are */
/* computed. */
/* (6) VL(full) = VL(partial) */
/* VL(full) denotes the left eigenvectors computed when both l */
/* and r are computed, and VL(partial) denotes the result */
/* when only l is computed. */
/* (7) VR(full) = VR(partial) */
/* VR(full) denotes the right eigenvectors computed when both l */
/* and r are also computed, and VR(partial) denotes the result */
/* when only l is computed. */
/* Test Matrices */
/* ---- -------- */
/* The sizes of the test matrices are specified by an array */
/* NN(1:NSIZES); the value of each element NN(j) specifies one size. */
/* The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if */
/* DOTYPE(j) is .TRUE., then matrix type "j" will be generated. */
/* Currently, the list of possible types is: */
/* (1) ( 0, 0 ) (a pair of zero matrices) */
/* (2) ( I, 0 ) (an identity and a zero matrix) */
/* (3) ( 0, I ) (an identity and a zero matrix) */
/* (4) ( I, I ) (a pair of identity matrices) */
/* t t */
/* (5) ( J , J ) (a pair of transposed Jordan blocks) */
/* t ( I 0 ) */
/* (6) ( X, Y ) where X = ( J 0 ) and Y = ( t ) */
/* ( 0 I ) ( 0 J ) */
/* and I is a k x k identity and J a (k+1)x(k+1) */
/* Jordan block; k=(N-1)/2 */
/* (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal */
/* matrix with those diagonal entries.) */
/* (8) ( I, D ) */
/* (9) ( big*D, small*I ) where "big" is near overflow and small=1/big */
/* (10) ( small*D, big*I ) */
/* (11) ( big*I, small*D ) */
/* (12) ( small*I, big*D ) */
/* (13) ( big*D, big*I ) */
/* (14) ( small*D, small*I ) */
/* (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and */
/* D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) */
/* t t */
/* (16) Q ( J , J ) Z where Q and Z are random orthogonal matrices. */
/* (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices */
/* with random O(1) entries above the diagonal */
/* and diagonal entries diag(T1) = */
/* ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = */
/* ( 0, N-3, N-4,..., 1, 0, 0 ) */
/* (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) */
/* s = machine precision. */
/* (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) */
/* N-5 */
/* (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/* (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/* where r1,..., r(N-4) are random. */
/* (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular */
/* matrices. */
/* Arguments */
/* ========= */
/* NSIZES (input) INTEGER */
/* The number of sizes of matrices to use. If it is zero, */
/* DDRGES does nothing. NSIZES >= 0. */
/* NN (input) INTEGER array, dimension (NSIZES) */
/* An array containing the sizes to be used for the matrices. */
/* Zero values will be skipped. NN >= 0. */
/* NTYPES (input) INTEGER */
/* The number of elements in DOTYPE. If it is zero, DDRGES */
/* does nothing. It must be at least zero. If it is MAXTYP+1 */
/* and NSIZES is 1, then an additional type, MAXTYP+1 is */
/* defined, which is to use whatever matrix is in A. This */
/* is only useful if DOTYPE(1:MAXTYP) is .FALSE. and */
/* DOTYPE(MAXTYP+1) is .TRUE. . */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* If DOTYPE(j) is .TRUE., then for each size in NN a */
/* matrix of that size and of type j will be generated. */
/* If NTYPES is smaller than the maximum number of types */
/* defined (PARAMETER MAXTYP), then types NTYPES+1 through */
/* MAXTYP will not be generated. If NTYPES is larger */
/* than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) */
/* will be ignored. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry ISEED specifies the seed of the random number */
/* generator. The array elements should be between 0 and 4095; */
/* if not they will be reduced mod 4096. Also, ISEED(4) must */
/* be odd. The random number generator uses a linear */
/* congruential sequence limited to small integers, and so */
/* should produce machine independent random numbers. The */
/* values of ISEED are changed on exit, and can be used in the */
/* next call to DDRGES to continue the same random number */
/* sequence. */
/* THRESH (input) DOUBLE PRECISION */
/* A test will count as "failed" if the "error", computed as */
/* described above, exceeds THRESH. Note that the error is */
/* scaled to be O(1), so THRESH should be a reasonably small */
/* multiple of 1, e.g., 10 or 100. In particular, it should */
/* not depend on the precision (single vs. double) or the size */
/* of the matrix. It must be at least zero. */
/* NOUNIT (input) INTEGER */
/* The FORTRAN unit number for printing out error messages */
/* (e.g., if a routine returns IERR not equal to 0.) */
/* A (input/workspace) DOUBLE PRECISION array, */
/* dimension(LDA, max(NN)) */
/* Used to hold the original A matrix. Used as input only */
/* if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/* DOTYPE(MAXTYP+1)=.TRUE. */
/* LDA (input) INTEGER */
/* The leading dimension of A, B, S, and T. */
/* It must be at least 1 and at least max( NN ). */
/* B (input/workspace) DOUBLE PRECISION array, */
/* dimension(LDA, max(NN)) */
/* Used to hold the original B matrix. Used as input only */
/* if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/* DOTYPE(MAXTYP+1)=.TRUE. */
/* S (workspace) DOUBLE PRECISION array, */
/* dimension (LDA, max(NN)) */
/* The Schur form matrix computed from A by DGGES. On exit, S */
/* contains the Schur form matrix corresponding to the matrix */
/* in A. */
/* T (workspace) DOUBLE PRECISION array, */
/* dimension (LDA, max(NN)) */
/* The upper triangular matrix computed from B by DGGES. */
/* Q (workspace) DOUBLE PRECISION array, */
/* dimension (LDQ, max(NN)) */
/* The (left) eigenvectors matrix computed by DGGEV. */
/* LDQ (input) INTEGER */
/* The leading dimension of Q and Z. It must */
/* be at least 1 and at least max( NN ). */
/* Z (workspace) DOUBLE PRECISION array, dimension( LDQ, max(NN) ) */
/* The (right) orthogonal matrix computed by DGGES. */
/* QE (workspace) DOUBLE PRECISION array, dimension( LDQ, max(NN) ) */
/* QE holds the computed right or left eigenvectors. */
/* LDQE (input) INTEGER */
/* The leading dimension of QE. LDQE >= max(1,max(NN)). */
/* ALPHAR (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* ALPHAI (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* BETA (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* The generalized eigenvalues of (A,B) computed by DGGEV. */
/* ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th */
/* generalized eigenvalue of A and B. */
/* ALPHR1 (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* ALPHI1 (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* BETA1 (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* Like ALPHAR, ALPHAI, BETA, these arrays contain the */
/* eigenvalues of A and B, but those computed when DGGEV only */
/* computes a partial eigendecomposition, i.e. not the */
/* eigenvalues and left and right eigenvectors. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The number of entries in WORK. LWORK >= MAX( 8*N, N*(N+1) ). */
/* RESULT (output) DOUBLE PRECISION array, dimension (2) */
/* The values computed by the tests described above. */
/* The values are currently limited to 1/ulp, to avoid overflow. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: A routine returned an error code. INFO is the */
/* absolute value of the INFO value returned. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nn;
--dotype;
--iseed;
t_dim1 = *lda;
t_offset = 1 + t_dim1;
t -= t_offset;
s_dim1 = *lda;
s_offset = 1 + s_dim1;
s -= s_offset;
b_dim1 = *lda;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
z_dim1 = *ldq;
z_offset = 1 + z_dim1;
z__ -= z_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
qe_dim1 = *ldqe;
qe_offset = 1 + qe_dim1;
qe -= qe_offset;
--alphar;
--alphai;
--beta;
--alphr1;
--alphi1;
--beta1;
--work;
--result;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
*info = 0;
badnn = FALSE_;
nmax = 1;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = nmax, i__3 = nn[j];
nmax = max(i__2,i__3);
if (nn[j] < 0) {
badnn = TRUE_;
}
/* L10: */
}
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.) {
*info = -6;
} else if (*lda <= 1 || *lda < nmax) {
*info = -9;
} else if (*ldq <= 1 || *ldq < nmax) {
*info = -14;
} else if (*ldqe <= 1 || *ldqe < nmax) {
*info = -17;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
/* Computing MAX */
i__1 = 1, i__2 = nmax << 3, i__1 = max(i__1,i__2), i__2 = nmax * (
nmax + 1);
minwrk = max(i__1,i__2);
maxwrk = nmax * 7 + nmax * ilaenv_(&c__1, "DGEQRF", " ", &nmax, &c__1,
&nmax, &c__0);
/* Computing MAX */
i__1 = maxwrk, i__2 = nmax * (nmax + 1);
maxwrk = max(i__1,i__2);
work[1] = (doublereal) maxwrk;
}
if (*lwork < minwrk) {
*info = -25;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DDRGEV", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
safmin = dlamch_("Safe minimum");
ulp = dlamch_("Epsilon") * dlamch_("Base");
safmin /= ulp;
safmax = 1. / safmin;
dlabad_(&safmin, &safmax);
ulpinv = 1. / ulp;
/* The values RMAGN(2:3) depend on N, see below. */
rmagn[0] = 0.;
rmagn[1] = 1.;
/* Loop over sizes, types */
ntestt = 0;
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
n1 = max(1,n);
rmagn[2] = safmax * ulp / (doublereal) n1;
rmagn[3] = safmin * ulpinv * n1;
if (*nsizes != 1) {
mtypes = min(26,*ntypes);
} else {
mtypes = min(27,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L210;
}
++nmats;
/* Save ISEED in case of an error. */
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Generate test matrices A and B */
/* Description of control parameters: */
/* KZLASS: =1 means w/o rotation, =2 means w/ rotation, */
/* =3 means random. */
/* KATYPE: the "type" to be passed to DLATM4 for computing A. */
/* KAZERO: the pattern of zeros on the diagonal for A: */
/* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ), */
/* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ), */
/* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of */
/* non-zero entries.) */
/* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1), */
/* =2: large, =3: small. */
/* IASIGN: 1 if the diagonal elements of A are to be */
/* multiplied by a random magnitude 1 number, =2 if */
/* randomly chosen diagonal blocks are to be rotated */
/* to form 2x2 blocks. */
/* KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B. */
/* KTRIAN: =0: don't fill in the upper triangle, =1: do. */
/* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO. */
/* RMAGN: used to implement KAMAGN and KBMAGN. */
if (mtypes > 26) {
goto L100;
}
ierr = 0;
if (kclass[jtype - 1] < 3) {
/* Generate A (w/o rotation) */
if ((i__3 = katype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
dlaset_("Full", &n, &n, &c_b17, &c_b17, &a[a_offset],
lda);
}
} else {
in = n;
}
dlatm4_(&katype[jtype - 1], &in, &kz1[kazero[jtype - 1] - 1],
&kz2[kazero[jtype - 1] - 1], &iasign[jtype - 1], &
rmagn[kamagn[jtype - 1]], &ulp, &rmagn[ktrian[jtype -
1] * kamagn[jtype - 1]], &c__2, &iseed[1], &a[
a_offset], lda);
iadd = kadd[kazero[jtype - 1] - 1];
if (iadd > 0 && iadd <= n) {
a[iadd + iadd * a_dim1] = 1.;
}
/* Generate B (w/o rotation) */
if ((i__3 = kbtype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
dlaset_("Full", &n, &n, &c_b17, &c_b17, &b[b_offset],
lda);
}
} else {
in = n;
}
dlatm4_(&kbtype[jtype - 1], &in, &kz1[kbzero[jtype - 1] - 1],
&kz2[kbzero[jtype - 1] - 1], &ibsign[jtype - 1], &
rmagn[kbmagn[jtype - 1]], &c_b23, &rmagn[ktrian[jtype
- 1] * kbmagn[jtype - 1]], &c__2, &iseed[1], &b[
b_offset], lda);
iadd = kadd[kbzero[jtype - 1] - 1];
if (iadd != 0 && iadd <= n) {
b[iadd + iadd * b_dim1] = 1.;
}
if (kclass[jtype - 1] == 2 && n > 0) {
/* Include rotations */
/* Generate Q, Z as Householder transformations times */
/* a diagonal matrix. */
i__3 = n - 1;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = jc; jr <= i__4; ++jr) {
q[jr + jc * q_dim1] = dlarnd_(&c__3, &iseed[1]);
z__[jr + jc * z_dim1] = dlarnd_(&c__3, &iseed[1]);
/* L30: */
}
i__4 = n + 1 - jc;
dlarfg_(&i__4, &q[jc + jc * q_dim1], &q[jc + 1 + jc *
q_dim1], &c__1, &work[jc]);
work[(n << 1) + jc] = d_sign(&c_b23, &q[jc + jc *
q_dim1]);
q[jc + jc * q_dim1] = 1.;
i__4 = n + 1 - jc;
dlarfg_(&i__4, &z__[jc + jc * z_dim1], &z__[jc + 1 +
jc * z_dim1], &c__1, &work[n + jc]);
work[n * 3 + jc] = d_sign(&c_b23, &z__[jc + jc *
z_dim1]);
z__[jc + jc * z_dim1] = 1.;
/* L40: */
}
q[n + n * q_dim1] = 1.;
work[n] = 0.;
d__1 = dlarnd_(&c__2, &iseed[1]);
work[n * 3] = d_sign(&c_b23, &d__1);
z__[n + n * z_dim1] = 1.;
work[n * 2] = 0.;
d__1 = dlarnd_(&c__2, &iseed[1]);
work[n * 4] = d_sign(&c_b23, &d__1);
/* Apply the diagonal matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
a[jr + jc * a_dim1] = work[(n << 1) + jr] * work[
n * 3 + jc] * a[jr + jc * a_dim1];
b[jr + jc * b_dim1] = work[(n << 1) + jr] * work[
n * 3 + jc] * b[jr + jc * b_dim1];
/* L50: */
}
/* L60: */
}
i__3 = n - 1;
dorm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &a[a_offset], lda, &work[(n << 1) + 1], &ierr);
if (ierr != 0) {
goto L90;
}
i__3 = n - 1;
dorm2r_("R", "T", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &a[a_offset], lda, &work[(n << 1) +
1], &ierr);
if (ierr != 0) {
goto L90;
}
i__3 = n - 1;
dorm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &b[b_offset], lda, &work[(n << 1) + 1], &ierr);
if (ierr != 0) {
goto L90;
}
i__3 = n - 1;
dorm2r_("R", "T", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &b[b_offset], lda, &work[(n << 1) +
1], &ierr);
if (ierr != 0) {
goto L90;
}
}
} else {
/* Random matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
a[jr + jc * a_dim1] = rmagn[kamagn[jtype - 1]] *
dlarnd_(&c__2, &iseed[1]);
b[jr + jc * b_dim1] = rmagn[kbmagn[jtype - 1]] *
dlarnd_(&c__2, &iseed[1]);
/* L70: */
}
/* L80: */
}
}
L90:
if (ierr != 0) {
io___38.ciunit = *nounit;
s_wsfe(&io___38);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(ierr);
return 0;
}
L100:
for (i__ = 1; i__ <= 7; ++i__) {
result[i__] = -1.;
/* L110: */
}
/* Call DGGEV to compute eigenvalues and eigenvectors. */
dlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
dlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
dggev_("V", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &
alphar[1], &alphai[1], &beta[1], &q[q_offset], ldq, &z__[
z_offset], ldq, &work[1], lwork, &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___40.ciunit = *nounit;
s_wsfe(&io___40);
do_fio(&c__1, "DGGEV1", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(ierr);
goto L190;
}
/* Do the tests (1) and (2) */
dget52_(&c_true, &n, &a[a_offset], lda, &b[b_offset], lda, &q[
q_offset], ldq, &alphar[1], &alphai[1], &beta[1], &work[1]
, &result[1]);
if (result[2] > *thresh) {
io___41.ciunit = *nounit;
s_wsfe(&io___41);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "DGGEV1", (ftnlen)6);
do_fio(&c__1, (char *)&result[2], (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Do the tests (3) and (4) */
dget52_(&c_false, &n, &a[a_offset], lda, &b[b_offset], lda, &z__[
z_offset], ldq, &alphar[1], &alphai[1], &beta[1], &work[1]
, &result[3]);
if (result[4] > *thresh) {
io___42.ciunit = *nounit;
s_wsfe(&io___42);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "DGGEV1", (ftnlen)6);
do_fio(&c__1, (char *)&result[4], (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Do the test (5) */
dlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
dlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
dggev_("N", "N", &n, &s[s_offset], lda, &t[t_offset], lda, &
alphr1[1], &alphi1[1], &beta1[1], &q[q_offset], ldq, &z__[
z_offset], ldq, &work[1], lwork, &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___43.ciunit = *nounit;
s_wsfe(&io___43);
do_fio(&c__1, "DGGEV2", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(ierr);
goto L190;
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
if (alphar[j] != alphr1[j] || alphai[j] != alphi1[j] || beta[
j] != beta1[j]) {
result[5] = ulpinv;
}
/* L120: */
}
/* Do the test (6): Compute eigenvalues and left eigenvectors, */
/* and test them */
dlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
dlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
dggev_("V", "N", &n, &s[s_offset], lda, &t[t_offset], lda, &
alphr1[1], &alphi1[1], &beta1[1], &qe[qe_offset], ldqe, &
z__[z_offset], ldq, &work[1], lwork, &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, "DGGEV3", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(ierr);
goto L190;
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
if (alphar[j] != alphr1[j] || alphai[j] != alphi1[j] || beta[
j] != beta1[j]) {
result[6] = ulpinv;
}
/* L130: */
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (jc = 1; jc <= i__4; ++jc) {
if (q[j + jc * q_dim1] != qe[j + jc * qe_dim1]) {
result[6] = ulpinv;
}
/* L140: */
}
/* L150: */
}
/* DO the test (7): Compute eigenvalues and right eigenvectors, */
/* and test them */
dlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
dlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
dggev_("N", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &
alphr1[1], &alphi1[1], &beta1[1], &q[q_offset], ldq, &qe[
qe_offset], ldqe, &work[1], lwork, &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___45.ciunit = *nounit;
s_wsfe(&io___45);
do_fio(&c__1, "DGGEV4", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(ierr);
goto L190;
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
if (alphar[j] != alphr1[j] || alphai[j] != alphi1[j] || beta[
j] != beta1[j]) {
result[7] = ulpinv;
}
/* L160: */
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (jc = 1; jc <= i__4; ++jc) {
if (z__[j + jc * z_dim1] != qe[j + jc * qe_dim1]) {
result[7] = ulpinv;
}
/* L170: */
}
/* L180: */
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L190:
ntestt += 7;
/* Print out tests which fail. */
for (jr = 1; jr <= 7; ++jr) {
if (result[jr] >= *thresh) {
/* If this is the first test to fail, */
/* print a header to the data file. */
if (nerrs == 0) {
io___46.ciunit = *nounit;
s_wsfe(&io___46);
do_fio(&c__1, "DGV", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___47.ciunit = *nounit;
s_wsfe(&io___47);
e_wsfe();
io___48.ciunit = *nounit;
s_wsfe(&io___48);
e_wsfe();
io___49.ciunit = *nounit;
s_wsfe(&io___49);
do_fio(&c__1, "Orthogonal", (ftnlen)10);
e_wsfe();
/* Tests performed */
io___50.ciunit = *nounit;
s_wsfe(&io___50);
e_wsfe();
}
++nerrs;
if (result[jr] < 1e4) {
io___51.ciunit = *nounit;
s_wsfe(&io___51);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
} else {
io___52.ciunit = *nounit;
s_wsfe(&io___52);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
}
/* L200: */
}
L210:
;
}
/* L220: */
}
/* Summary */
alasvm_("DGV", nounit, &nerrs, &ntestt, &c__0);
work[1] = (doublereal) maxwrk;
return 0;
/* End of DDRGEV */
} /* ddrgev_ */
//Attention: A,B are overwritten !!
void LaEigNSSolve(int hn, double * A, double * B, std::complex<double> * lami, int evecs_bool, double * evecs_re, double * evecs_im, char balance_type )
{
integer n = hn;
char jobvr , jobvl= 'N';
bool balancing = 0;
if ( balance_type == 'B' || balance_type == 'S' || balance_type == 'P' )
balancing =1;
integer info;
double * wi= new double[n], * wr = new double[n];
double * beta = new double[n];
double vl=0;
integer nvl = 1;
integer nvr ;
if (evecs_bool)
{
jobvr = 'V';
nvr = n;
}
else
{
nvr=1;
jobvr = 'N';
}
double *vr = new double[nvr*nvr];
double* work = new double[16*n];
integer lwork = 16*n;
int i,j;
char job=balance_type; // Permute and Scale in Balancing
integer ihi,ilo;
double * lscale, *rscale;
lscale = new double[n];
rscale = new double[n];
char side = 'R';
if(balancing)
dggbal_(&job,&n, A,&n , B, &n, &ilo, &ihi, lscale, rscale, work, &info) ;
else info =0;
if(info ==0 )
{
dggev_(&jobvl, &jobvr, &n, A, &n, B, &n, wr, wi, beta, &vl, &nvl, vr, &nvr,
work , &lwork, &info);
if(info==0)
{
if(jobvr == 'V' && balancing)
{
dggbak_(&job, &side, &n, &ilo, &ihi, lscale, rscale, &n, vr, &n,&info) ;
if(info!=0)
{
cout << " Error in dggbak_ :: info " << info << endl;
return;
}
}
}
else
{
cout << " Error in dggev_ :: info " << info << endl;
return;
}
}
else
{
cout << " Error in dggbal_ :: info " << info << endl;
return;
}
delete[] lscale;
delete[] rscale;
for(i=0;i<n;i++)
{
if (fabs(beta[i])>1e-30) // not infinite eigenvalue
lami[i]=std::complex<double>(wr[i]/beta[i],wi[i]/beta[i]);
else
{
lami[i]=std::complex<double>(100.,100.);
}
}
if(evecs_bool)
{
for(i=0;i<n;i++)
{
if( imag(lami[i])== 0. || beta[i] == 0.) //real eigenvalue -> real eigenvector in i-th line
{
for(j=0;j<n;j++)
{
// evecs[i*n+j]= std::complex<double>(vr[i*n + j],0.);
evecs_re[i*n+j]= vr[i*n+j];
evecs_im[i*n+j]= 0.;
}
}
else // conjugate complex eigenvectors
{
for(j=0;j<n;j++)
{
// evecs[i*n+j]= std::complex<double>(vr[i*n+j],vr[(i+1)*n+j]);
// evecs[(i+1)*n+j]=std::complex<double>(vr[i*n+j],-vr[(i+1)*n+j]);
evecs_re[i*n+j]= vr[i*n+j];
evecs_re[(i+1)*n+j]=vr[i*n+j];
evecs_im[i*n+j]= vr[(i+1)*n+j];
evecs_im[(i+1)*n+j]=-vr[(i+1)*n+j];
}
i++;
}
}
}
delete[] wi;
delete[] wr;
delete[] beta;
delete[] work;
delete[] vr;
}
void
MAST::LAPACK_DGGEV::compute(const RealMatrixX &A,
const RealMatrixX &B,
bool computeEigenvectors) {
libmesh_assert(A.cols() == A.rows() &&
B.cols() == A.rows() &&
B.cols() == B.rows());
_A = A;
_B = B;
RealMatrixX
Amat = A,
Bmat = B;
int n = (int)A.cols();
char L='N',R='N';
if (computeEigenvectors) {
L = 'V'; R = 'V';
VL.setZero(n, n);
VR.setZero(n, n);
}
int
lwork=16*n;
info_val=-1;
alpha.setZero(n);
beta.setZero(n);
RealVectorX
work,
aval_r,
aval_i,
bval;
RealMatrixX
vecl,
vecr;
work.setZero(lwork);
aval_r.setZero(n);
aval_i.setZero(n);
bval.setZero(n);
vecl.setZero(n,n);
vecr.setZero(n,n);
Real
*a_vals = Amat.data(),
*b_vals = Bmat.data(),
*alpha_r_v = aval_r.data(),
*alpha_i_v = aval_i.data(),
*beta_v = bval.data(),
*vecl_v = vecl.data(),
*vecr_v = vecr.data(),
*work_v = work.data();
dggev_(&L, &R, &n,
&(a_vals[0]), &n,
&(b_vals[0]), &n,
&(alpha_r_v[0]), &(alpha_i_v[0]), &(beta_v[0]),
&(vecl_v[0]), &n, &(vecr_v[0]), &n,
&(work_v[0]), &lwork,
&info_val);
// now sort the eigenvalues for complex conjugates
unsigned int n_located = 0;
while (n_located < n) {
// if the imaginary part of the eigenvalue is non-zero, it is a
// complex conjugate
if (aval_i(n_located) != 0.) { // complex conjugate
alpha( n_located) = std::complex<double>(aval_r(n_located), aval_i(n_located));
alpha(1+n_located) = std::complex<double>(aval_r(n_located), -aval_i(n_located));
beta ( n_located) = bval(n_located);
beta (1+n_located) = bval(n_located);
// copy the eigenvectors if they were requested
if (computeEigenvectors) {
std::complex<double> iota = std::complex<double>(0, 1.);
VL.col( n_located) = (vecl.col( n_located).cast<Complex>() +
vecl.col(1+n_located).cast<Complex>() * iota);
VL.col(1+n_located) = (vecl.col( n_located).cast<Complex>() -
vecl.col(1+n_located).cast<Complex>() * iota);
VR.col( n_located) = (vecr.col( n_located).cast<Complex>() +
vecr.col(1+n_located).cast<Complex>() * iota);
VR.col(1+n_located) = (vecr.col( n_located).cast<Complex>() -
vecr.col(1+n_located).cast<Complex>() * iota);
}
// two complex conjugate roots were found
n_located +=2;
}
else {
alpha( n_located) = std::complex<double>(aval_r(n_located), 0.);
beta ( n_located) = bval(n_located);
// copy the eigenvectors if they were requested
if (computeEigenvectors) {
VL.col(n_located) = vecl.col(n_located).cast<Complex>();
VR.col(n_located) = vecr.col(n_located).cast<Complex>();
}
// only one real root was found
n_located++;
}
}
if (info_val != 0)
libMesh::out
<< "Warning!! DGGEV returned with nonzero info = "
<< info_val << std::endl;
}
