double MC_Condition_Number(double **X, int dim, int expl)
{
int i = 0, j = 0, row = 0, column = 0;
double xn = 0;
DenseVector *x = new DenseVector [dim];
for (i = 0; i < expl; i++)
x[i].absorb(X[i], dim, false);
for (i = 0; i < expl; i++) {
xn = x[i].norm();
for (j = 0; j < dim; j++) {
x[i].setAt(j, x[i].getValue(j) / sqrt(xn));
}
}
// use CLAPACK to compute the largest and the smallest eigenvalues
// use dspev_
char jobz = 'N', uplo = 'U';
long int n = expl;
long int ldz = expl, lwork = 3 * expl, info = 0;
double *a = new double [expl * (expl + 1) / 2];
double *s = new double [expl];
double *z = NULL;
double *work = new double [lwork];
for (row = 0; row < expl; row++) {
for (column = row + 1; column < expl; column++)
a[row + column * (column + 1) / 2] = x[row].product(x[column]);
a[row + row * (row + 1) / 2] = x[row].norm();
}
// use __WXMAC__ to call vecLib
//#ifdef WORDS_BIGENDIAN
#ifdef __WXMAC__MMM
dspev_(&jobz, &uplo, &n, a, s, z, &ldz, work, &info);
#else
dspev_(&jobz, &uplo, (integer*)&n, (doublereal*)a, (doublereal*)s, (doublereal*)z, (integer*)&ldz, (doublereal*)work, (integer*)&info);
#endif
if (!info) {
double max = s[expl - 1], min = s[0];
return sqrt(max / min);
} else {
// cerr << "error in computing eigenvalues" << endl;
wxMessageBox("error in computing eigenvalues");
return -999;
}
}
int local_dspev(const int* n, double* A, double* W, double* Z, const int *ldz, double* work){
//extern void dspev_(const char* jobz, const char* uplo,
// const int* n, double * A, double* W, double* Z, const int* ldz, double* work, long* info);
int info;
dspev_(&V, &Upper, n, A, W, Z, ldz, work, &info);
return info;
}
void
dspev(char jobz, char uplo, int n, double *dap, double *w,
double *dz, int ldz, int *info)
{
double *work ;
allot ( double *, work, 3*n ) ;
dspev_ ( &jobz, &uplo, &n, dap, w, dz, &ldz, work, info );
free(work) ;
}
/// Solve symmetric eigenvalue problem using CLAPACK routines.
void quantfin::interfaceCLAPACK::SymmetricEigenvalueProblem(
const Array<double,2>& A, ///< Symmetric Array to be decomposed.
Array<double,1>& eigval, ///< Array (vector) containing all non-zero eigenvalues.
Array<double,2>& eigvec, ///< Array of eigenvectors (Array, each column is an eigenvector)
double eps ///< Threshold for comparison to zero, default 1e-12
)
{
int i,j;
long int n = A.rows();
if (n!=A.columns()) throw(std::logic_error("Array must be square"));
double* ap = new double[(n*(n+1))/2];
double* pos = ap;
for (i=0;i<n;i++) {
for (j=0;j<=i;j++) *pos++ = A(j,i); }
double* w = new double[n];
double* z = new double[n*n];
double* work = new double[3*n];
long int ldz = n;
long int info = 0;
char jobz = 'V';
char uplo = 'U';
dspev_(&jobz,&uplo,&n,ap,w,z,&ldz,work,&info);
if (!info) {
int k = n;
for (i=0;i<n;i++) {
if (my_abs(w[i])<=eps) k--; }
Array<double,1> val(k);
Array<double,2> vec(n,k);
int l = 0;
pos = z;
for (i=0;i<n;i++) {
if (my_abs(w[i])>eps) {
val(l) = w[i];
for (j=0;j<n;j++) vec(j,l) = *pos++;
l++; }
else pos += n; }
eigval.resize(k);
eigvec.resize(n,k);
eigval = val;
eigvec = vec; }
delete[] ap;
delete[] w;
delete[] z;
delete[] work;
if (info) throw(std::logic_error("Eigenvalue decomposition failed"));
}
void Eigensystem( char* jobz, char* uplo, int* n, double* ap, double* w, int* ldz)
{
if( *jobz =='V' ) { printf( "Sorry sucka! I'm too lazy to do this.\n" ); exit(1); }
/* Query and allocate the optimal workspace */
int info=0;
double* work = (double*)malloc( 3 * (*n) * sizeof(double) );
/* Solve eigenproblem */
double* z; // Dummy
dspev_( jobz, uplo, n, ap, w, z, ldz, work, &info );
/* Check for convergence */
if( info != 0 ) { printf( "The algorithm failed to compute eigenvalues.\n" ); exit( 1 ); }
/* Free workspace */
free( (void*)work );
}
/* Subroutine */ int dspgv_(integer *itype, char *jobz, char *uplo, integer *
n, doublereal *ap, doublereal *bp, doublereal *w, doublereal *z__,
integer *ldz, doublereal *work, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
DSPGV computes all the eigenvalues and, optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be symmetric, stored in packed format,
and B is also positive definite.
Arguments
=========
ITYPE (input) INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
AP (input/output) DOUBLE PRECISION array, dimension
(N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, the contents of AP are destroyed.
BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
B, packed columnwise in a linear array. The j-th column of B
is stored in the array BP as follows:
if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
On exit, the triangular factor U or L from the Cholesky
factorization B = U**T*U or B = L*L**T, in the same storage
format as B.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
eigenvectors. The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
If JOBZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: DPPTRF or DSPEV returned an error code:
<= N: if INFO = i, DSPEV failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero.
> N: if INFO = n + i, for 1 <= i <= n, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer z_dim1, z_offset, i__1;
/* Local variables */
static integer neig, j;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int dspev_(char *, char *, integer *, doublereal *
, doublereal *, doublereal *, integer *, doublereal *, integer *);
static char trans[1];
static logical upper;
extern /* Subroutine */ int dtpmv_(char *, char *, char *, integer *,
doublereal *, doublereal *, integer *),
dtpsv_(char *, char *, char *, integer *, doublereal *,
doublereal *, integer *);
static logical wantz;
extern /* Subroutine */ int xerbla_(char *, integer *), dpptrf_(
char *, integer *, doublereal *, integer *), dspgst_(
integer *, char *, integer *, doublereal *, doublereal *, integer
*);
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
--ap;
--bp;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--work;
/* Function Body */
wantz = lsame_(jobz, "V");
upper = lsame_(uplo, "U");
*info = 0;
if (*itype < 0 || *itype > 3) {
*info = -1;
} else if (! (wantz || lsame_(jobz, "N"))) {
*info = -2;
} else if (! (upper || lsame_(uplo, "L"))) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*ldz < 1 || wantz && *ldz < *n) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSPGV ", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a Cholesky factorization of B. */
dpptrf_(uplo, n, &bp[1], info);
if (*info != 0) {
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem and solve. */
dspgst_(itype, uplo, n, &ap[1], &bp[1], info);
dspev_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], info);
if (wantz) {
/* Backtransform eigenvectors to the original problem. */
neig = *n;
if (*info > 0) {
neig = *info - 1;
}
if (*itype == 1 || *itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (upper) {
*(unsigned char *)trans = 'N';
} else {
*(unsigned char *)trans = 'T';
}
i__1 = neig;
for (j = 1; j <= i__1; ++j) {
dtpsv_(uplo, trans, "Non-unit", n, &bp[1], &z___ref(1, j), &
c__1);
/* L10: */
}
} else if (*itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (upper) {
*(unsigned char *)trans = 'T';
} else {
*(unsigned char *)trans = 'N';
}
i__1 = neig;
for (j = 1; j <= i__1; ++j) {
dtpmv_(uplo, trans, "Non-unit", n, &bp[1], &z___ref(1, j), &
c__1);
/* L20: */
}
}
}
return 0;
/* End of DSPGV */
} /* dspgv_ */
/** Get eigenvectors and eigenvalues. They will be stored in descending
* order (largest eigenvalue first).
*/
int DataSet_Modes::CalcEigen(DataSet_2D const& mIn, int n_to_calc) {
#ifdef NO_MATHLIB
mprinterr("Error: modes: Compiled without ARPACK/LAPACK/BLAS routines.\n");
return 1;
#else
bool eigenvaluesOnly = false;
int info = 0;
if (mIn.MatrixKind() != DataSet_2D::HALF) {
mprinterr("Error: DataSet_Modes: Eigenvector/value calc only for symmetric matrices.\n");
return 1;
}
// If number to calc is 0, assume we want eigenvalues only
if (n_to_calc < 1) {
if (n_to_calc == 0) eigenvaluesOnly = true;
nmodes_ = (int)mIn.Ncols();
} else
nmodes_ = n_to_calc;
if (nmodes_ > (int)mIn.Ncols()) {
mprintf("Warning: Specified # of eigenvalues to calc (%i) > matrix dimension (%i).\n",
nmodes_, mIn.Ncols());
nmodes_ = mIn.Ncols();
mprintf("Warning: Only calculating %i eigenvalues.\n", nmodes_);
}
if (eigenvaluesOnly)
mprintf("\tCalculating %i eigenvalues only.\n", nmodes_);
else
mprintf("\tCalculating %i eigenvectors and eigenvalues.\n", nmodes_);
// -----------------------------------------------------------------
if (nmodes_ == (int)mIn.Ncols()) {
// Calculate all eigenvalues (and optionally eigenvectors).
char jobz = 'V'; // Default: Calc both eigenvectors and eigenvalues
vecsize_ = mIn.Ncols();
// Check if only calculating eigenvalues
if (eigenvaluesOnly) {
jobz = 'N';
vecsize_ = 1;
}
// Set up space to hold eigenvectors
if (evectors_ != 0) delete[] evectors_;
if (!eigenvaluesOnly)
evectors_ = new double[ nmodes_ * vecsize_ ];
else
evectors_ = 0;
// Set up space to hold eigenvalues
if (evalues_ != 0) delete[] evalues_;
evalues_ = new double[ nmodes_ ];
// Create copy of matrix since call to dspev destroys it
double* mat = mIn.MatrixArray();
// Lower triangle; not upper since fortran array layout is inverted w.r.t. C/C++
char uplo = 'L';
// Allocate temporary workspace
double* work = new double[ 3 * nmodes_ ];
// NOTE: The call to dspev is supposed to store eigenvectors in columns.
// However as mentioned above fortran array layout is inverted
// w.r.t. C/C++ so eigenvectors end up in rows.
// NOTE: Eigenvalues/vectors are returned in ascending order.
dspev_(jobz, uplo, nmodes_, mat, evalues_, evectors_, vecsize_, work, info);
// If no eigenvectors calcd set vecsize to 0
if (evectors_==0)
vecsize_ = 0;
delete[] work;
delete[] mat;
if (info != 0) {
if (info < 0) {
mprinterr("Internal Error: from dspev: Argument %i had illegal value.\n", -info);
mprinterr("Args: %c %c %i matrix %x %x %i work %i\n", jobz, uplo, nmodes_,
evalues_, evectors_, vecsize_, info);
} else { // info > 0
mprinterr("Internal Error: from dspev: The algorithm failed to converge.\n");
mprinterr("%i off-diagonal elements of an intermediate tridiagonal form\n", info);
mprinterr("did not converge to zero.\n");
}
return 1;
}
// -----------------------------------------------------------------
} else {
// Calculate up to n-1 eigenvalues/vectors using the Implicitly Restarted
// Arnoldi iteration.
// FIXME: Eigenvectors obtained with this method appear to have signs
// flipped compared to full method - is dot product wrong?
int nelem = mIn.Ncols(); // Dimension of input matrix (N)
// Allocate memory to store eigenvectors
vecsize_ = mIn.Ncols();
int ncv; // # of columns of the matrix V (evectors_), <= N (mIn.Ncols())
if (evectors_!=0) delete[] evectors_;
if (nmodes_*2 <= nelem)
ncv = nmodes_*2;
else
ncv = nelem;
evectors_ = new double[ ncv * nelem ];
// Temporary storage for eigenvectors to avoid memory overlap in dseupd
double* eigenvectors = new double[ ncv * nelem ];
// Allocate memory to store eigenvalues
if ( evalues_ != 0) delete[] evalues_;
evalues_ = new double[ nelem ] ; // NOTE: Should this be nmodes?
// Allocate workspace
double* workd = new double[ 3 * nelem ];
int lworkl = ncv * (ncv+8); // NOTE: should this be ncv^2 * (ncv+8)
double* workl = new double[ lworkl ];
double* resid = new double[ nelem ];
// Set parameters for dsaupd (Arnolid)
int ido = 0; // Reverse comm. flag; 0 = first call
// The iparam array is used to set parameters for the calc.
int iparam[11];
std::fill( iparam, iparam + 11, 0 );
iparam[0] = 1; // Method for selecting implicit shifts; 1 = exact
iparam[2] = 300; // Max # of iterations allowed
iparam[3] = 1; // blocksize to be used in the recurrence (code works with only 1).
iparam[6] = 1; // Type of eigenproblem being solved; 1: A*x = lambda*x
double tol = 0; // Stopping criterion (tolerance); 0 = arpack default
char bmat = 'I'; // Type of matrix B that defines semi-inner product; I = identity
char which[2]; // Which of the Ritz values of OP to compute;
which[0] = 'L'; // 'LA' = compute the NEV largest eigenvalues
which[1] = 'A';
// The ipntr array will hold starting locations in workd and workl arrays
// for matrices/vectors used by the Lanczos iteration.
int ipntr[11];
std::fill( ipntr, ipntr + 11, 0 );
// Create copy of matrix since it will be modified
double* mat = mIn.MatrixArray();
// LOOP
bool loop = false;
do {
if (loop) {
// Dot products
double* target = workd + (ipntr[1] - 1); // -1 since fortran indexing starts at 1
double* vec = workd + (ipntr[0] - 1);
std::fill( target, target + nelem, 0 );
for(int i = 0; i < nelem; i++) {
for(int j = i; j < nelem; j++) {
int ind = nelem * i + j - (i * (i + 1)) / 2;
target[i] += mat[ind] * vec[j];
if(i != j)
target[j] += mat[ind] * vec[i];
}
}
}
dsaupd_(ido, bmat, nelem, which, nmodes_, tol, resid,
ncv, eigenvectors, nelem, iparam, ipntr, workd, workl,
lworkl, info);
loop = (ido == -1 || ido == 1);
} while ( loop ); // END LOOP
if (info != 0) {
mprinterr("Error: DataSet_Modes: dsaupd returned %i\n",info);
} else {
int rvec = 1;
char howmny = 'A';
double sigma = 0.0;
int* select = new int[ ncv ];
dseupd_(rvec, howmny, select, evalues_, evectors_, nelem, sigma,
bmat, nelem, which, nmodes_, tol, resid,
ncv, eigenvectors, nelem, iparam, ipntr, workd, workl,
lworkl, info);
delete[] select;
}
delete[] mat;
delete[] workl;
delete[] workd;
delete[] resid;
delete[] eigenvectors;
if (info != 0) {
mprinterr("Error: DataSet_Modes: dseupd returned %i\n",info);
return 1;
}
}
// Eigenvalues and eigenvectors are in ascending order. Resort so that
// they are in descending order (i.e. largest eigenvalue first).
int pivot = nmodes_ / 2;
int nmode = nmodes_ - 1;
double* vtmp = 0;
if (evectors_ != 0)
vtmp = new double[ vecsize_ ];
for (int mode = 0; mode < pivot; ++mode) {
// Swap eigenvalue
double eval = evalues_[mode];
evalues_[mode] = evalues_[nmode];
evalues_[nmode] = eval;
// Swap eigenvector
if (vtmp != 0) {
double* Vec0 = evectors_ + (mode * vecsize_);
double* Vec1 = evectors_ + (nmode * vecsize_);
std::copy( Vec0, Vec0 + vecsize_, vtmp );
std::copy( Vec1, Vec1 + vecsize_, Vec0 );
std::copy( vtmp, vtmp + vecsize_, Vec1 );
}
--nmode;
}
if (vtmp != 0) delete[] vtmp;
return 0;
#endif
}
