00001 /* chpgvx.f -- translated by f2c (version 20061008). 00002 You must link the resulting object file with libf2c: 00003 on Microsoft Windows system, link with libf2c.lib; 00004 on Linux or Unix systems, link with .../path/to/libf2c.a -lm 00005 or, if you install libf2c.a in a standard place, with -lf2c -lm 00006 -- in that order, at the end of the command line, as in 00007 cc *.o -lf2c -lm 00008 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., 00009 00010 http://www.netlib.org/f2c/libf2c.zip 00011 */ 00012 00013 #include "f2c.h" 00014 #include "blaswrap.h" 00015 00016 /* Table of constant values */ 00017 00018 static integer c__1 = 1; 00019 00020 /* Subroutine */ int chpgvx_(integer *itype, char *jobz, char *range, char * 00021 uplo, integer *n, complex *ap, complex *bp, real *vl, real *vu, 00022 integer *il, integer *iu, real *abstol, integer *m, real *w, complex * 00023 z__, integer *ldz, complex *work, real *rwork, integer *iwork, 00024 integer *ifail, integer *info) 00025 { 00026 /* System generated locals */ 00027 integer z_dim1, z_offset, i__1; 00028 00029 /* Local variables */ 00030 integer j; 00031 extern logical lsame_(char *, char *); 00032 char trans[1]; 00033 extern /* Subroutine */ int ctpmv_(char *, char *, char *, integer *, 00034 complex *, complex *, integer *); 00035 logical upper; 00036 extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *, 00037 complex *, complex *, integer *); 00038 logical wantz, alleig, indeig, valeig; 00039 extern /* Subroutine */ int xerbla_(char *, integer *), chpgst_( 00040 integer *, char *, integer *, complex *, complex *, integer *), chpevx_(char *, char *, char *, integer *, complex *, 00041 real *, real *, integer *, integer *, real *, integer *, real *, 00042 complex *, integer *, complex *, real *, integer *, integer *, 00043 integer *), cpptrf_(char *, integer *, 00044 complex *, integer *); 00045 00046 00047 /* -- LAPACK driver routine (version 3.2) -- */ 00048 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00049 /* November 2006 */ 00050 00051 /* .. Scalar Arguments .. */ 00052 /* .. */ 00053 /* .. Array Arguments .. */ 00054 /* .. */ 00055 00056 /* Purpose */ 00057 /* ======= */ 00058 00059 /* CHPGVX computes selected eigenvalues and, optionally, eigenvectors */ 00060 /* of a complex generalized Hermitian-definite eigenproblem, of the form */ 00061 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */ 00062 /* B are assumed to be Hermitian, stored in packed format, and B is also */ 00063 /* positive definite. Eigenvalues and eigenvectors can be selected by */ 00064 /* specifying either a range of values or a range of indices for the */ 00065 /* desired eigenvalues. */ 00066 00067 /* Arguments */ 00068 /* ========= */ 00069 00070 /* ITYPE (input) INTEGER */ 00071 /* Specifies the problem type to be solved: */ 00072 /* = 1: A*x = (lambda)*B*x */ 00073 /* = 2: A*B*x = (lambda)*x */ 00074 /* = 3: B*A*x = (lambda)*x */ 00075 00076 /* JOBZ (input) CHARACTER*1 */ 00077 /* = 'N': Compute eigenvalues only; */ 00078 /* = 'V': Compute eigenvalues and eigenvectors. */ 00079 00080 /* RANGE (input) CHARACTER*1 */ 00081 /* = 'A': all eigenvalues will be found; */ 00082 /* = 'V': all eigenvalues in the half-open interval (VL,VU] */ 00083 /* will be found; */ 00084 /* = 'I': the IL-th through IU-th eigenvalues will be found. */ 00085 00086 /* UPLO (input) CHARACTER*1 */ 00087 /* = 'U': Upper triangles of A and B are stored; */ 00088 /* = 'L': Lower triangles of A and B are stored. */ 00089 00090 /* N (input) INTEGER */ 00091 /* The order of the matrices A and B. N >= 0. */ 00092 00093 /* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) */ 00094 /* On entry, the upper or lower triangle of the Hermitian matrix */ 00095 /* A, packed columnwise in a linear array. The j-th column of A */ 00096 /* is stored in the array AP as follows: */ 00097 /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ 00098 /* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */ 00099 00100 /* On exit, the contents of AP are destroyed. */ 00101 00102 /* BP (input/output) COMPLEX array, dimension (N*(N+1)/2) */ 00103 /* On entry, the upper or lower triangle of the Hermitian matrix */ 00104 /* B, packed columnwise in a linear array. The j-th column of B */ 00105 /* is stored in the array BP as follows: */ 00106 /* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; */ 00107 /* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. */ 00108 00109 /* On exit, the triangular factor U or L from the Cholesky */ 00110 /* factorization B = U**H*U or B = L*L**H, in the same storage */ 00111 /* format as B. */ 00112 00113 /* VL (input) REAL */ 00114 /* VU (input) REAL */ 00115 /* If RANGE='V', the lower and upper bounds of the interval to */ 00116 /* be searched for eigenvalues. VL < VU. */ 00117 /* Not referenced if RANGE = 'A' or 'I'. */ 00118 00119 /* IL (input) INTEGER */ 00120 /* IU (input) INTEGER */ 00121 /* If RANGE='I', the indices (in ascending order) of the */ 00122 /* smallest and largest eigenvalues to be returned. */ 00123 /* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */ 00124 /* Not referenced if RANGE = 'A' or 'V'. */ 00125 00126 /* ABSTOL (input) REAL */ 00127 /* The absolute error tolerance for the eigenvalues. */ 00128 /* An approximate eigenvalue is accepted as converged */ 00129 /* when it is determined to lie in an interval [a,b] */ 00130 /* of width less than or equal to */ 00131 00132 /* ABSTOL + EPS * max( |a|,|b| ) , */ 00133 00134 /* where EPS is the machine precision. If ABSTOL is less than */ 00135 /* or equal to zero, then EPS*|T| will be used in its place, */ 00136 /* where |T| is the 1-norm of the tridiagonal matrix obtained */ 00137 /* by reducing AP to tridiagonal form. */ 00138 00139 /* Eigenvalues will be computed most accurately when ABSTOL is */ 00140 /* set to twice the underflow threshold 2*SLAMCH('S'), not zero. */ 00141 /* If this routine returns with INFO>0, indicating that some */ 00142 /* eigenvectors did not converge, try setting ABSTOL to */ 00143 /* 2*SLAMCH('S'). */ 00144 00145 /* M (output) INTEGER */ 00146 /* The total number of eigenvalues found. 0 <= M <= N. */ 00147 /* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */ 00148 00149 /* W (output) REAL array, dimension (N) */ 00150 /* On normal exit, the first M elements contain the selected */ 00151 /* eigenvalues in ascending order. */ 00152 00153 /* Z (output) COMPLEX array, dimension (LDZ, N) */ 00154 /* If JOBZ = 'N', then Z is not referenced. */ 00155 /* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */ 00156 /* contain the orthonormal eigenvectors of the matrix A */ 00157 /* corresponding to the selected eigenvalues, with the i-th */ 00158 /* column of Z holding the eigenvector associated with W(i). */ 00159 /* The eigenvectors are normalized as follows: */ 00160 /* if ITYPE = 1 or 2, Z**H*B*Z = I; */ 00161 /* if ITYPE = 3, Z**H*inv(B)*Z = I. */ 00162 00163 /* If an eigenvector fails to converge, then that column of Z */ 00164 /* contains the latest approximation to the eigenvector, and the */ 00165 /* index of the eigenvector is returned in IFAIL. */ 00166 /* Note: the user must ensure that at least max(1,M) columns are */ 00167 /* supplied in the array Z; if RANGE = 'V', the exact value of M */ 00168 /* is not known in advance and an upper bound must be used. */ 00169 00170 /* LDZ (input) INTEGER */ 00171 /* The leading dimension of the array Z. LDZ >= 1, and if */ 00172 /* JOBZ = 'V', LDZ >= max(1,N). */ 00173 00174 /* WORK (workspace) COMPLEX array, dimension (2*N) */ 00175 00176 /* RWORK (workspace) REAL array, dimension (7*N) */ 00177 00178 /* IWORK (workspace) INTEGER array, dimension (5*N) */ 00179 00180 /* IFAIL (output) INTEGER array, dimension (N) */ 00181 /* If JOBZ = 'V', then if INFO = 0, the first M elements of */ 00182 /* IFAIL are zero. If INFO > 0, then IFAIL contains the */ 00183 /* indices of the eigenvectors that failed to converge. */ 00184 /* If JOBZ = 'N', then IFAIL is not referenced. */ 00185 00186 /* INFO (output) INTEGER */ 00187 /* = 0: successful exit */ 00188 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00189 /* > 0: CPPTRF or CHPEVX returned an error code: */ 00190 /* <= N: if INFO = i, CHPEVX failed to converge; */ 00191 /* i eigenvectors failed to converge. Their indices */ 00192 /* are stored in array IFAIL. */ 00193 /* > N: if INFO = N + i, for 1 <= i <= n, then the leading */ 00194 /* minor of order i of B is not positive definite. */ 00195 /* The factorization of B could not be completed and */ 00196 /* no eigenvalues or eigenvectors were computed. */ 00197 00198 /* Further Details */ 00199 /* =============== */ 00200 00201 /* Based on contributions by */ 00202 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ 00203 00204 /* ===================================================================== */ 00205 00206 /* .. Local Scalars .. */ 00207 /* .. */ 00208 /* .. External Functions .. */ 00209 /* .. */ 00210 /* .. External Subroutines .. */ 00211 /* .. */ 00212 /* .. Intrinsic Functions .. */ 00213 /* .. */ 00214 /* .. Executable Statements .. */ 00215 00216 /* Test the input parameters. */ 00217 00218 /* Parameter adjustments */ 00219 --ap; 00220 --bp; 00221 --w; 00222 z_dim1 = *ldz; 00223 z_offset = 1 + z_dim1; 00224 z__ -= z_offset; 00225 --work; 00226 --rwork; 00227 --iwork; 00228 --ifail; 00229 00230 /* Function Body */ 00231 wantz = lsame_(jobz, "V"); 00232 upper = lsame_(uplo, "U"); 00233 alleig = lsame_(range, "A"); 00234 valeig = lsame_(range, "V"); 00235 indeig = lsame_(range, "I"); 00236 00237 *info = 0; 00238 if (*itype < 1 || *itype > 3) { 00239 *info = -1; 00240 } else if (! (wantz || lsame_(jobz, "N"))) { 00241 *info = -2; 00242 } else if (! (alleig || valeig || indeig)) { 00243 *info = -3; 00244 } else if (! (upper || lsame_(uplo, "L"))) { 00245 *info = -4; 00246 } else if (*n < 0) { 00247 *info = -5; 00248 } else { 00249 if (valeig) { 00250 if (*n > 0 && *vu <= *vl) { 00251 *info = -9; 00252 } 00253 } else if (indeig) { 00254 if (*il < 1) { 00255 *info = -10; 00256 } else if (*iu < min(*n,*il) || *iu > *n) { 00257 *info = -11; 00258 } 00259 } 00260 } 00261 if (*info == 0) { 00262 if (*ldz < 1 || wantz && *ldz < *n) { 00263 *info = -16; 00264 } 00265 } 00266 00267 if (*info != 0) { 00268 i__1 = -(*info); 00269 xerbla_("CHPGVX", &i__1); 00270 return 0; 00271 } 00272 00273 /* Quick return if possible */ 00274 00275 if (*n == 0) { 00276 return 0; 00277 } 00278 00279 /* Form a Cholesky factorization of B. */ 00280 00281 cpptrf_(uplo, n, &bp[1], info); 00282 if (*info != 0) { 00283 *info = *n + *info; 00284 return 0; 00285 } 00286 00287 /* Transform problem to standard eigenvalue problem and solve. */ 00288 00289 chpgst_(itype, uplo, n, &ap[1], &bp[1], info); 00290 chpevx_(jobz, range, uplo, n, &ap[1], vl, vu, il, iu, abstol, m, &w[1], & 00291 z__[z_offset], ldz, &work[1], &rwork[1], &iwork[1], &ifail[1], 00292 info); 00293 00294 if (wantz) { 00295 00296 /* Backtransform eigenvectors to the original problem. */ 00297 00298 if (*info > 0) { 00299 *m = *info - 1; 00300 } 00301 if (*itype == 1 || *itype == 2) { 00302 00303 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00304 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00305 00306 if (upper) { 00307 *(unsigned char *)trans = 'N'; 00308 } else { 00309 *(unsigned char *)trans = 'C'; 00310 } 00311 00312 i__1 = *m; 00313 for (j = 1; j <= i__1; ++j) { 00314 ctpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 00315 1], &c__1); 00316 /* L10: */ 00317 } 00318 00319 } else if (*itype == 3) { 00320 00321 /* For B*A*x=(lambda)*x; */ 00322 /* backtransform eigenvectors: x = L*y or U'*y */ 00323 00324 if (upper) { 00325 *(unsigned char *)trans = 'C'; 00326 } else { 00327 *(unsigned char *)trans = 'N'; 00328 } 00329 00330 i__1 = *m; 00331 for (j = 1; j <= i__1; ++j) { 00332 ctpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 00333 1], &c__1); 00334 /* L20: */ 00335 } 00336 } 00337 } 00338 00339 return 0; 00340 00341 /* End of CHPGVX */ 00342 00343 } /* chpgvx_ */