00001 /* chegvx.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 complex c_b1 = {1.f,0.f}; 00019 static integer c__1 = 1; 00020 static integer c_n1 = -1; 00021 00022 /* Subroutine */ int chegvx_(integer *itype, char *jobz, char *range, char * 00023 uplo, integer *n, complex *a, integer *lda, complex *b, integer *ldb, 00024 real *vl, real *vu, integer *il, integer *iu, real *abstol, integer * 00025 m, real *w, complex *z__, integer *ldz, complex *work, integer *lwork, 00026 real *rwork, integer *iwork, integer *ifail, integer *info) 00027 { 00028 /* System generated locals */ 00029 integer a_dim1, a_offset, b_dim1, b_offset, z_dim1, z_offset, i__1, i__2; 00030 00031 /* Local variables */ 00032 integer nb; 00033 extern logical lsame_(char *, char *); 00034 extern /* Subroutine */ int ctrmm_(char *, char *, char *, char *, 00035 integer *, integer *, complex *, complex *, integer *, complex *, 00036 integer *); 00037 char trans[1]; 00038 extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 00039 integer *, integer *, complex *, complex *, integer *, complex *, 00040 integer *); 00041 logical upper, wantz, alleig, indeig, valeig; 00042 extern /* Subroutine */ int chegst_(integer *, char *, integer *, complex 00043 *, integer *, complex *, integer *, integer *); 00044 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00045 integer *, integer *); 00046 extern /* Subroutine */ int xerbla_(char *, integer *), cheevx_( 00047 char *, char *, char *, integer *, complex *, integer *, real *, 00048 real *, integer *, integer *, real *, integer *, real *, complex * 00049 , integer *, complex *, integer *, real *, integer *, integer *, 00050 integer *), cpotrf_(char *, integer *, 00051 complex *, integer *, integer *); 00052 integer lwkopt; 00053 logical lquery; 00054 00055 00056 /* -- LAPACK driver routine (version 3.2) -- */ 00057 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00058 /* November 2006 */ 00059 00060 /* .. Scalar Arguments .. */ 00061 /* .. */ 00062 /* .. Array Arguments .. */ 00063 /* .. */ 00064 00065 /* Purpose */ 00066 /* ======= */ 00067 00068 /* CHEGVX computes selected eigenvalues, and optionally, eigenvectors */ 00069 /* of a complex generalized Hermitian-definite eigenproblem, of the form */ 00070 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */ 00071 /* B are assumed to be Hermitian and B is also positive definite. */ 00072 /* Eigenvalues and eigenvectors can be selected by specifying either a */ 00073 /* range of values or a range of indices for the desired eigenvalues. */ 00074 00075 /* Arguments */ 00076 /* ========= */ 00077 00078 /* ITYPE (input) INTEGER */ 00079 /* Specifies the problem type to be solved: */ 00080 /* = 1: A*x = (lambda)*B*x */ 00081 /* = 2: A*B*x = (lambda)*x */ 00082 /* = 3: B*A*x = (lambda)*x */ 00083 00084 /* JOBZ (input) CHARACTER*1 */ 00085 /* = 'N': Compute eigenvalues only; */ 00086 /* = 'V': Compute eigenvalues and eigenvectors. */ 00087 00088 /* RANGE (input) CHARACTER*1 */ 00089 /* = 'A': all eigenvalues will be found. */ 00090 /* = 'V': all eigenvalues in the half-open interval (VL,VU] */ 00091 /* will be found. */ 00092 /* = 'I': the IL-th through IU-th eigenvalues will be found. */ 00093 /* * */ 00094 /* UPLO (input) CHARACTER*1 */ 00095 /* = 'U': Upper triangles of A and B are stored; */ 00096 /* = 'L': Lower triangles of A and B are stored. */ 00097 00098 /* N (input) INTEGER */ 00099 /* The order of the matrices A and B. N >= 0. */ 00100 00101 /* A (input/output) COMPLEX array, dimension (LDA, N) */ 00102 /* On entry, the Hermitian matrix A. If UPLO = 'U', the */ 00103 /* leading N-by-N upper triangular part of A contains the */ 00104 /* upper triangular part of the matrix A. If UPLO = 'L', */ 00105 /* the leading N-by-N lower triangular part of A contains */ 00106 /* the lower triangular part of the matrix A. */ 00107 00108 /* On exit, the lower triangle (if UPLO='L') or the upper */ 00109 /* triangle (if UPLO='U') of A, including the diagonal, is */ 00110 /* destroyed. */ 00111 00112 /* LDA (input) INTEGER */ 00113 /* The leading dimension of the array A. LDA >= max(1,N). */ 00114 00115 /* B (input/output) COMPLEX array, dimension (LDB, N) */ 00116 /* On entry, the Hermitian matrix B. If UPLO = 'U', the */ 00117 /* leading N-by-N upper triangular part of B contains the */ 00118 /* upper triangular part of the matrix B. If UPLO = 'L', */ 00119 /* the leading N-by-N lower triangular part of B contains */ 00120 /* the lower triangular part of the matrix B. */ 00121 00122 /* On exit, if INFO <= N, the part of B containing the matrix is */ 00123 /* overwritten by the triangular factor U or L from the Cholesky */ 00124 /* factorization B = U**H*U or B = L*L**H. */ 00125 00126 /* LDB (input) INTEGER */ 00127 /* The leading dimension of the array B. LDB >= max(1,N). */ 00128 00129 /* VL (input) REAL */ 00130 /* VU (input) REAL */ 00131 /* If RANGE='V', the lower and upper bounds of the interval to */ 00132 /* be searched for eigenvalues. VL < VU. */ 00133 /* Not referenced if RANGE = 'A' or 'I'. */ 00134 00135 /* IL (input) INTEGER */ 00136 /* IU (input) INTEGER */ 00137 /* If RANGE='I', the indices (in ascending order) of the */ 00138 /* smallest and largest eigenvalues to be returned. */ 00139 /* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */ 00140 /* Not referenced if RANGE = 'A' or 'V'. */ 00141 00142 /* ABSTOL (input) REAL */ 00143 /* The absolute error tolerance for the eigenvalues. */ 00144 /* An approximate eigenvalue is accepted as converged */ 00145 /* when it is determined to lie in an interval [a,b] */ 00146 /* of width less than or equal to */ 00147 00148 /* ABSTOL + EPS * max( |a|,|b| ) , */ 00149 00150 /* where EPS is the machine precision. If ABSTOL is less than */ 00151 /* or equal to zero, then EPS*|T| will be used in its place, */ 00152 /* where |T| is the 1-norm of the tridiagonal matrix obtained */ 00153 /* by reducing A to tridiagonal form. */ 00154 00155 /* Eigenvalues will be computed most accurately when ABSTOL is */ 00156 /* set to twice the underflow threshold 2*SLAMCH('S'), not zero. */ 00157 /* If this routine returns with INFO>0, indicating that some */ 00158 /* eigenvectors did not converge, try setting ABSTOL to */ 00159 /* 2*SLAMCH('S'). */ 00160 00161 /* M (output) INTEGER */ 00162 /* The total number of eigenvalues found. 0 <= M <= N. */ 00163 /* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */ 00164 00165 /* W (output) REAL array, dimension (N) */ 00166 /* The first M elements contain the selected */ 00167 /* eigenvalues in ascending order. */ 00168 00169 /* Z (output) COMPLEX array, dimension (LDZ, max(1,M)) */ 00170 /* If JOBZ = 'N', then Z is not referenced. */ 00171 /* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */ 00172 /* contain the orthonormal eigenvectors of the matrix A */ 00173 /* corresponding to the selected eigenvalues, with the i-th */ 00174 /* column of Z holding the eigenvector associated with W(i). */ 00175 /* The eigenvectors are normalized as follows: */ 00176 /* if ITYPE = 1 or 2, Z**T*B*Z = I; */ 00177 /* if ITYPE = 3, Z**T*inv(B)*Z = I. */ 00178 00179 /* If an eigenvector fails to converge, then that column of Z */ 00180 /* contains the latest approximation to the eigenvector, and the */ 00181 /* index of the eigenvector is returned in IFAIL. */ 00182 /* Note: the user must ensure that at least max(1,M) columns are */ 00183 /* supplied in the array Z; if RANGE = 'V', the exact value of M */ 00184 /* is not known in advance and an upper bound must be used. */ 00185 00186 /* LDZ (input) INTEGER */ 00187 /* The leading dimension of the array Z. LDZ >= 1, and if */ 00188 /* JOBZ = 'V', LDZ >= max(1,N). */ 00189 00190 /* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */ 00191 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00192 00193 /* LWORK (input) INTEGER */ 00194 /* The length of the array WORK. LWORK >= max(1,2*N). */ 00195 /* For optimal efficiency, LWORK >= (NB+1)*N, */ 00196 /* where NB is the blocksize for CHETRD returned by ILAENV. */ 00197 00198 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00199 /* only calculates the optimal size of the WORK array, returns */ 00200 /* this value as the first entry of the WORK array, and no error */ 00201 /* message related to LWORK is issued by XERBLA. */ 00202 00203 /* RWORK (workspace) REAL array, dimension (7*N) */ 00204 00205 /* IWORK (workspace) INTEGER array, dimension (5*N) */ 00206 00207 /* IFAIL (output) INTEGER array, dimension (N) */ 00208 /* If JOBZ = 'V', then if INFO = 0, the first M elements of */ 00209 /* IFAIL are zero. If INFO > 0, then IFAIL contains the */ 00210 /* indices of the eigenvectors that failed to converge. */ 00211 /* If JOBZ = 'N', then IFAIL is not referenced. */ 00212 00213 /* INFO (output) INTEGER */ 00214 /* = 0: successful exit */ 00215 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00216 /* > 0: CPOTRF or CHEEVX returned an error code: */ 00217 /* <= N: if INFO = i, CHEEVX failed to converge; */ 00218 /* i eigenvectors failed to converge. Their indices */ 00219 /* are stored in array IFAIL. */ 00220 /* > N: if INFO = N + i, for 1 <= i <= N, then the leading */ 00221 /* minor of order i of B is not positive definite. */ 00222 /* The factorization of B could not be completed and */ 00223 /* no eigenvalues or eigenvectors were computed. */ 00224 00225 /* Further Details */ 00226 /* =============== */ 00227 00228 /* Based on contributions by */ 00229 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ 00230 00231 /* ===================================================================== */ 00232 00233 /* .. Parameters .. */ 00234 /* .. */ 00235 /* .. Local Scalars .. */ 00236 /* .. */ 00237 /* .. External Functions .. */ 00238 /* .. */ 00239 /* .. External Subroutines .. */ 00240 /* .. */ 00241 /* .. Intrinsic Functions .. */ 00242 /* .. */ 00243 /* .. Executable Statements .. */ 00244 00245 /* Test the input parameters. */ 00246 00247 /* Parameter adjustments */ 00248 a_dim1 = *lda; 00249 a_offset = 1 + a_dim1; 00250 a -= a_offset; 00251 b_dim1 = *ldb; 00252 b_offset = 1 + b_dim1; 00253 b -= b_offset; 00254 --w; 00255 z_dim1 = *ldz; 00256 z_offset = 1 + z_dim1; 00257 z__ -= z_offset; 00258 --work; 00259 --rwork; 00260 --iwork; 00261 --ifail; 00262 00263 /* Function Body */ 00264 wantz = lsame_(jobz, "V"); 00265 upper = lsame_(uplo, "U"); 00266 alleig = lsame_(range, "A"); 00267 valeig = lsame_(range, "V"); 00268 indeig = lsame_(range, "I"); 00269 lquery = *lwork == -1; 00270 00271 *info = 0; 00272 if (*itype < 1 || *itype > 3) { 00273 *info = -1; 00274 } else if (! (wantz || lsame_(jobz, "N"))) { 00275 *info = -2; 00276 } else if (! (alleig || valeig || indeig)) { 00277 *info = -3; 00278 } else if (! (upper || lsame_(uplo, "L"))) { 00279 *info = -4; 00280 } else if (*n < 0) { 00281 *info = -5; 00282 } else if (*lda < max(1,*n)) { 00283 *info = -7; 00284 } else if (*ldb < max(1,*n)) { 00285 *info = -9; 00286 } else { 00287 if (valeig) { 00288 if (*n > 0 && *vu <= *vl) { 00289 *info = -11; 00290 } 00291 } else if (indeig) { 00292 if (*il < 1 || *il > max(1,*n)) { 00293 *info = -12; 00294 } else if (*iu < min(*n,*il) || *iu > *n) { 00295 *info = -13; 00296 } 00297 } 00298 } 00299 if (*info == 0) { 00300 if (*ldz < 1 || wantz && *ldz < *n) { 00301 *info = -18; 00302 } 00303 } 00304 00305 if (*info == 0) { 00306 nb = ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1); 00307 /* Computing MAX */ 00308 i__1 = 1, i__2 = (nb + 1) * *n; 00309 lwkopt = max(i__1,i__2); 00310 work[1].r = (real) lwkopt, work[1].i = 0.f; 00311 00312 /* Computing MAX */ 00313 i__1 = 1, i__2 = *n << 1; 00314 if (*lwork < max(i__1,i__2) && ! lquery) { 00315 *info = -20; 00316 } 00317 } 00318 00319 if (*info != 0) { 00320 i__1 = -(*info); 00321 xerbla_("CHEGVX", &i__1); 00322 return 0; 00323 } else if (lquery) { 00324 return 0; 00325 } 00326 00327 /* Quick return if possible */ 00328 00329 *m = 0; 00330 if (*n == 0) { 00331 return 0; 00332 } 00333 00334 /* Form a Cholesky factorization of B. */ 00335 00336 cpotrf_(uplo, n, &b[b_offset], ldb, info); 00337 if (*info != 0) { 00338 *info = *n + *info; 00339 return 0; 00340 } 00341 00342 /* Transform problem to standard eigenvalue problem and solve. */ 00343 00344 chegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info); 00345 cheevx_(jobz, range, uplo, n, &a[a_offset], lda, vl, vu, il, iu, abstol, 00346 m, &w[1], &z__[z_offset], ldz, &work[1], lwork, &rwork[1], &iwork[ 00347 1], &ifail[1], info); 00348 00349 if (wantz) { 00350 00351 /* Backtransform eigenvectors to the original problem. */ 00352 00353 if (*info > 0) { 00354 *m = *info - 1; 00355 } 00356 if (*itype == 1 || *itype == 2) { 00357 00358 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00359 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00360 00361 if (upper) { 00362 *(unsigned char *)trans = 'N'; 00363 } else { 00364 *(unsigned char *)trans = 'C'; 00365 } 00366 00367 ctrsm_("Left", uplo, trans, "Non-unit", n, m, &c_b1, &b[b_offset], 00368 ldb, &z__[z_offset], ldz); 00369 00370 } else if (*itype == 3) { 00371 00372 /* For B*A*x=(lambda)*x; */ 00373 /* backtransform eigenvectors: x = L*y or U'*y */ 00374 00375 if (upper) { 00376 *(unsigned char *)trans = 'C'; 00377 } else { 00378 *(unsigned char *)trans = 'N'; 00379 } 00380 00381 ctrmm_("Left", uplo, trans, "Non-unit", n, m, &c_b1, &b[b_offset], 00382 ldb, &z__[z_offset], ldz); 00383 } 00384 } 00385 00386 /* Set WORK(1) to optimal complex workspace size. */ 00387 00388 work[1].r = (real) lwkopt, work[1].i = 0.f; 00389 00390 return 0; 00391 00392 /* End of CHEGVX */ 00393 00394 } /* chegvx_ */