int dspgvx_(int *itype, char *jobz, char *range, char *
uplo, int *n, double *ap, double *bp, double *vl,
double *vu, int *il, int *iu, double *abstol, int
*m, double *w, double *z__, int *ldz, double *work,
int *iwork, int *ifail, int *info)
{
/* System generated locals */
int z_dim1, z_offset, i__1;
/* Local variables */
int j;
extern int lsame_(char *, char *);
char trans[1];
int upper;
extern int dtpmv_(char *, char *, char *, int *,
double *, double *, int *),
dtpsv_(char *, char *, char *, int *, double *,
double *, int *);
int wantz, alleig, indeig, valeig;
extern int xerbla_(char *, int *), dpptrf_(
char *, int *, double *, int *), dspgst_(
int *, char *, int *, double *, double *, int
*), dspevx_(char *, char *, char *, int *, double
*, double *, double *, int *, int *, double *,
int *, double *, double *, int *, double *,
int *, int *, int *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DSPGVX computes selected eigenvalues, and optionally, eigenvectors */
/* of a float 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 storage, and B */
/* is also positive definite. Eigenvalues and eigenvectors can be */
/* selected by specifying either a range of values or a range of indices */
/* for the desired eigenvalues. */
/* 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. */
/* RANGE (input) CHARACTER*1 */
/* = 'A': all eigenvalues will be found. */
/* = 'V': all eigenvalues in the half-open interval (VL,VU] */
/* will be found. */
/* = 'I': the IL-th through IU-th eigenvalues will be found. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A and B are stored; */
/* = 'L': Lower triangle of A and B are stored. */
/* N (input) INTEGER */
/* The order of the matrix pencil (A,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. */
/* VL (input) DOUBLE PRECISION */
/* VU (input) DOUBLE PRECISION */
/* If RANGE='V', the lower and upper bounds of the interval to */
/* be searched for eigenvalues. VL < VU. */
/* Not referenced if RANGE = 'A' or 'I'. */
/* IL (input) INTEGER */
/* IU (input) INTEGER */
/* If RANGE='I', the indices (in ascending order) of the */
/* smallest and largest eigenvalues to be returned. */
/* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
/* Not referenced if RANGE = 'A' or 'V'. */
/* ABSTOL (input) DOUBLE PRECISION */
/* The absolute error tolerance for the eigenvalues. */
/* An approximate eigenvalue is accepted as converged */
/* when it is determined to lie in an interval [a,b] */
/* of width less than or equal to */
/* ABSTOL + EPS * MAX( |a|,|b| ) , */
/* where EPS is the machine precision. If ABSTOL is less than */
/* or equal to zero, then EPS*|T| will be used in its place, */
/* where |T| is the 1-norm of the tridiagonal matrix obtained */
/* by reducing A to tridiagonal form. */
/* Eigenvalues will be computed most accurately when ABSTOL is */
/* set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
/* If this routine returns with INFO>0, indicating that some */
/* eigenvectors did not converge, try setting ABSTOL to */
/* 2*DLAMCH('S'). */
/* M (output) INTEGER */
/* The total number of eigenvalues found. 0 <= M <= N. */
/* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
/* W (output) DOUBLE PRECISION array, dimension (N) */
/* On normal exit, the first M elements contain the selected */
/* eigenvalues in ascending order. */
/* Z (output) DOUBLE PRECISION array, dimension (LDZ, MAX(1,M)) */
/* If JOBZ = 'N', then Z is not referenced. */
/* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */
/* contain the orthonormal eigenvectors of the matrix A */
/* corresponding to the selected eigenvalues, with the i-th */
/* column of Z holding the eigenvector associated with W(i). */
/* 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 an eigenvector fails to converge, then that column of Z */
/* contains the latest approximation to the eigenvector, and the */
/* index of the eigenvector is returned in IFAIL. */
/* Note: the user must ensure that at least MAX(1,M) columns are */
/* supplied in the array Z; if RANGE = 'V', the exact value of M */
/* is not known in advance and an upper bound must be used. */
/* 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 (8*N) */
/* IWORK (workspace) INTEGER array, dimension (5*N) */
/* IFAIL (output) INTEGER array, dimension (N) */
/* If JOBZ = 'V', then if INFO = 0, the first M elements of */
/* IFAIL are zero. If INFO > 0, then IFAIL contains the */
/* indices of the eigenvectors that failed to converge. */
/* If JOBZ = 'N', then IFAIL is not referenced. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: DPPTRF or DSPEVX returned an error code: */
/* <= N: if INFO = i, DSPEVX failed to converge; */
/* i eigenvectors failed to converge. Their indices */
/* are stored in array IFAIL. */
/* > 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. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--bp;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--iwork;
--ifail;
/* Function Body */
upper = lsame_(uplo, "U");
wantz = lsame_(jobz, "V");
alleig = lsame_(range, "A");
valeig = lsame_(range, "V");
indeig = lsame_(range, "I");
*info = 0;
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! (wantz || lsame_(jobz, "N"))) {
*info = -2;
} else if (! (alleig || valeig || indeig)) {
*info = -3;
} else if (! (upper || lsame_(uplo, "L"))) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else {
if (valeig) {
if (*n > 0 && *vu <= *vl) {
*info = -9;
}
} else if (indeig) {
if (*il < 1) {
*info = -10;
} else if (*iu < MIN(*n,*il) || *iu > *n) {
*info = -11;
}
}
}
if (*info == 0) {
if (*ldz < 1 || wantz && *ldz < *n) {
*info = -16;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSPGVX", &i__1);
return 0;
}
/* Quick return if possible */
*m = 0;
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);
dspevx_(jobz, range, uplo, n, &ap[1], vl, vu, il, iu, abstol, m, &w[1], &
z__[z_offset], ldz, &work[1], &iwork[1], &ifail[1], info);
if (wantz) {
/* Backtransform eigenvectors to the original problem. */
if (*info > 0) {
*m = *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 = *m;
for (j = 1; j <= i__1; ++j) {
dtpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
1], &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 = *m;
for (j = 1; j <= i__1; ++j) {
dtpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
1], &c__1);
/* L20: */
}
}
}
return 0;
/* End of DSPGVX */
} /* dspgvx_ */
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
/* Declare Variables */
char *ch1 = "V", *ch2 = "I", *ch3 = "L";
void *A, *W, *Z, *work;
double ABSTOLD = 0.0, VLD = 0.0, VUD = 0.0;
float ABSTOLF = 0.0, VLF = 0.0, VUF = 0.0;
#ifdef MWSIZE
mwSize N, *iwork, *ifail, info = 0, numElem, optional, IL, IU, M, num_eigs, isDouble = 1;
#else
int N, *iwork, *ifail, info = 0, numElem, optional, IL, IU, M, num_eigs, isDouble = 1;
#endif
/****** Do Error check *************/
if (nrhs != 4)
{
mexErrMsgTxt("icatb_eig_symm_sel function accepts four input arguments.\nThe usage of the function is [eigen_vectors, eigen_values] = icatb_eig_symm_sel(A, N, num_eigs, opt);\nwhere A is the lower triangular matrix without zeros entered as a vector, N is the original dimension, num_eigs is the number of eigen values and opt is parameter to operate on copy of the matrix or the original array.");
}
#ifdef MWSIZE
/* Inputs Matrix (A), order (N), number of eigen values (num_eigs), parameter (opt) to operate on copy or original matrix*/
numElem = (mwSize) mxGetNumberOfElements(prhs[0]);
N = (mwSize) mxGetScalar(prhs[1]);
num_eigs = (mwSize) mxGetScalar(prhs[2]);
/* Parameter for using the copy or original array to do operations*/
optional = (mwSize) mxGetScalar(prhs[3]);
#else
numElem = (int) mxGetNumberOfElements(prhs[0]);
N = (int) mxGetScalar(prhs[1]);
num_eigs = (int) mxGetScalar(prhs[2]);
optional = (int) mxGetScalar(prhs[3]);
#endif
if (numElem != (N*(N + 1)/2))
{
mexErrMsgTxt("Number of elements of input matrix (A) must be equal to N*(N+1)/2");
}
if (num_eigs > N)
{
mexErrMsgTxt("Number of eigen values desired is greater than the number of rows of matrix");
}
if (nlhs > 2)
{
mexErrMsgTxt("Maximum allowed output arguments is 2.");
}
/********* End for doing error check *********/
/* Eigen values desired */
IL = N - num_eigs + 1;
IU = N;
/* Check isdouble */
if (mxIsDouble(prhs[0]))
{
isDouble = 1;
if (optional == 1)
{
A = (void *) mxCalloc(numElem, sizeof(double));
memcpy(A, mxGetData(prhs[0]), numElem*sizeof(double));
}
else
{
A = mxGetData(prhs[0]);
}
A = (double *) A;
/* Pointer to work */
work = (double *) mxCalloc(8*N, sizeof(double));
/* Pointer to eigen vectors */
plhs[0] = mxCreateDoubleMatrix(N, num_eigs, mxREAL);
Z = mxGetPr(plhs[0]);
/* Pointer to eigen values */
plhs[1] = mxCreateDoubleMatrix(1, num_eigs, mxREAL);
W = mxGetPr(plhs[1]);
/* Tolerance */
ABSTOLD = mxGetEps();
}
else
{
isDouble = 0;
if (optional == 1)
{
A = (void *) mxCalloc(numElem, sizeof(float));
memcpy(A, mxGetData(prhs[0]), numElem*sizeof(float));
}
else
{
A = mxGetData(prhs[0]);
}
A = (float *) A;
/* Pointer to work */
work = (float *) mxCalloc(8*N, sizeof(float));
/* Pointer to eigen vectors */
plhs[0] = mxCreateNumericMatrix(N, num_eigs, mxSINGLE_CLASS, mxREAL);
Z = (float *) mxGetData(plhs[0]);
/* Pointer to eigen values */
plhs[1] = mxCreateNumericMatrix(1, num_eigs, mxSINGLE_CLASS, mxREAL);
W = (float *) mxGetData(plhs[1]);
ABSTOLF = (float) mxGetEps();
}
#ifdef MWSIZE
/* Pointer to iwork */
iwork = (mwSize *) mxCalloc(5*N, sizeof(mwSize));
/* Pointer to ifail */
ifail = (mwSize *) mxCalloc(N, sizeof(mwSize));
#else
/* Pointer to iwork */
iwork = (int *) mxCalloc(5*N, sizeof(int));
/* Pointer to ifail */
ifail = (int *) mxCalloc(N, sizeof(int));
#endif
/* Call subroutine to find eigen values and vectors */
#ifdef PC
/* Handle Windows */
if (isDouble == 1)
{
/* Double precision */
dspevx(ch1, ch2, ch3, &N, A, &VLD, &VUD, &IL, &IU, &ABSTOLD, &M, W, Z, &N, work, iwork, ifail, &info);
}
else
{
/* Use single precision routine */
#ifdef SINGLE_SUPPORT
sspevx(ch1, ch2, ch3, &N, A, &VLF, &VUF, &IL, &IU, &ABSTOLF, &M, W, Z, &N, work, iwork, ifail, &info);
#else
mexErrMsgTxt("Error executing sspevx function on this MATLAB version.\nUse double precision to solve eigen value problem");
#endif
}
/* End for handling Windows */
#else
/* Handle other OS */
if (isDouble == 1)
{
dspevx_(ch1, ch2, ch3, &N, A, &VLD, &VUD, &IL, &IU, &ABSTOLD, &M, W, Z, &N, work, iwork, ifail, &info);
}
else
{
/* Use single precision routine */
#ifdef SINGLE_SUPPORT
sspevx_(ch1, ch2, ch3, &N, A, &VLF, &VUF, &IL, &IU, &ABSTOLF, &M, W, Z, &N, work, iwork, ifail, &info);
#else
mexErrMsgTxt("Error executing sspevx_ function on this MATLAB version.\nUse double precision to solve eigen value problem");
#endif
}
/* End for handling other OS */
#endif
/* End for calling subroutine to find eigen values and vectors */
if (M != num_eigs)
{
mexPrintf("%s%d\t%s%d\n", "No. of eigen values estimated: ", M, "No. of eigen values desired: ", num_eigs);
mexErrMsgTxt("Error executing dspevx function\n");
}
if (info == 1)
{
mexErrMsgTxt("Error executing dspevx/sspevx function.");
}
/* Free memory */
if (optional == 1)
{
mxFree(A);
}
mxFree(work);
mxFree(iwork);
mxFree(ifail);
}