00001 /* zhegvx.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 doublecomplex c_b1 = {1.,0.}; 00019 static integer c__1 = 1; 00020 static integer c_n1 = -1; 00021 00022 /* Subroutine */ int zhegvx_(integer *itype, char *jobz, char *range, char * 00023 uplo, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, 00024 integer *ldb, doublereal *vl, doublereal *vu, integer *il, integer * 00025 iu, doublereal *abstol, integer *m, doublereal *w, doublecomplex *z__, 00026 integer *ldz, doublecomplex *work, integer *lwork, doublereal *rwork, 00027 integer *iwork, integer *ifail, integer *info) 00028 { 00029 /* System generated locals */ 00030 integer a_dim1, a_offset, b_dim1, b_offset, z_dim1, z_offset, i__1, i__2; 00031 00032 /* Local variables */ 00033 integer nb; 00034 extern logical lsame_(char *, char *); 00035 char trans[1]; 00036 logical upper, wantz; 00037 extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *, 00038 integer *, integer *, doublecomplex *, doublecomplex *, integer *, 00039 doublecomplex *, integer *), 00040 ztrsm_(char *, char *, char *, char *, integer *, integer *, 00041 doublecomplex *, doublecomplex *, integer *, doublecomplex *, 00042 integer *); 00043 logical alleig, indeig, valeig; 00044 extern /* Subroutine */ int xerbla_(char *, integer *); 00045 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00046 integer *, integer *); 00047 extern /* Subroutine */ int zhegst_(integer *, char *, integer *, 00048 doublecomplex *, integer *, doublecomplex *, integer *, integer *), zheevx_(char *, char *, char *, integer *, 00049 doublecomplex *, integer *, doublereal *, doublereal *, integer *, 00050 integer *, doublereal *, integer *, doublereal *, doublecomplex * 00051 , integer *, doublecomplex *, integer *, doublereal *, integer *, 00052 integer *, integer *); 00053 integer lwkopt; 00054 logical lquery; 00055 extern /* Subroutine */ int zpotrf_(char *, integer *, doublecomplex *, 00056 integer *, integer *); 00057 00058 00059 /* -- LAPACK driver routine (version 3.2) -- */ 00060 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00061 /* November 2006 */ 00062 00063 /* .. Scalar Arguments .. */ 00064 /* .. */ 00065 /* .. Array Arguments .. */ 00066 /* .. */ 00067 00068 /* Purpose */ 00069 /* ======= */ 00070 00071 /* ZHEGVX computes selected eigenvalues, and optionally, eigenvectors */ 00072 /* of a complex generalized Hermitian-definite eigenproblem, of the form */ 00073 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */ 00074 /* B are assumed to be Hermitian and B is also positive definite. */ 00075 /* Eigenvalues and eigenvectors can be selected by specifying either a */ 00076 /* range of values or a range of indices for the desired eigenvalues. */ 00077 00078 /* Arguments */ 00079 /* ========= */ 00080 00081 /* ITYPE (input) INTEGER */ 00082 /* Specifies the problem type to be solved: */ 00083 /* = 1: A*x = (lambda)*B*x */ 00084 /* = 2: A*B*x = (lambda)*x */ 00085 /* = 3: B*A*x = (lambda)*x */ 00086 00087 /* JOBZ (input) CHARACTER*1 */ 00088 /* = 'N': Compute eigenvalues only; */ 00089 /* = 'V': Compute eigenvalues and eigenvectors. */ 00090 00091 /* RANGE (input) CHARACTER*1 */ 00092 /* = 'A': all eigenvalues will be found. */ 00093 /* = 'V': all eigenvalues in the half-open interval (VL,VU] */ 00094 /* will be found. */ 00095 /* = 'I': the IL-th through IU-th eigenvalues will be found. */ 00096 /* * */ 00097 /* UPLO (input) CHARACTER*1 */ 00098 /* = 'U': Upper triangles of A and B are stored; */ 00099 /* = 'L': Lower triangles of A and B are stored. */ 00100 00101 /* N (input) INTEGER */ 00102 /* The order of the matrices A and B. N >= 0. */ 00103 00104 /* A (input/output) COMPLEX*16 array, dimension (LDA, N) */ 00105 /* On entry, the Hermitian matrix A. If UPLO = 'U', the */ 00106 /* leading N-by-N upper triangular part of A contains the */ 00107 /* upper triangular part of the matrix A. If UPLO = 'L', */ 00108 /* the leading N-by-N lower triangular part of A contains */ 00109 /* the lower triangular part of the matrix A. */ 00110 00111 /* On exit, the lower triangle (if UPLO='L') or the upper */ 00112 /* triangle (if UPLO='U') of A, including the diagonal, is */ 00113 /* destroyed. */ 00114 00115 /* LDA (input) INTEGER */ 00116 /* The leading dimension of the array A. LDA >= max(1,N). */ 00117 00118 /* B (input/output) COMPLEX*16 array, dimension (LDB, N) */ 00119 /* On entry, the Hermitian matrix B. If UPLO = 'U', the */ 00120 /* leading N-by-N upper triangular part of B contains the */ 00121 /* upper triangular part of the matrix B. If UPLO = 'L', */ 00122 /* the leading N-by-N lower triangular part of B contains */ 00123 /* the lower triangular part of the matrix B. */ 00124 00125 /* On exit, if INFO <= N, the part of B containing the matrix is */ 00126 /* overwritten by the triangular factor U or L from the Cholesky */ 00127 /* factorization B = U**H*U or B = L*L**H. */ 00128 00129 /* LDB (input) INTEGER */ 00130 /* The leading dimension of the array B. LDB >= max(1,N). */ 00131 00132 /* VL (input) DOUBLE PRECISION */ 00133 /* VU (input) DOUBLE PRECISION */ 00134 /* If RANGE='V', the lower and upper bounds of the interval to */ 00135 /* be searched for eigenvalues. VL < VU. */ 00136 /* Not referenced if RANGE = 'A' or 'I'. */ 00137 00138 /* IL (input) INTEGER */ 00139 /* IU (input) INTEGER */ 00140 /* If RANGE='I', the indices (in ascending order) of the */ 00141 /* smallest and largest eigenvalues to be returned. */ 00142 /* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */ 00143 /* Not referenced if RANGE = 'A' or 'V'. */ 00144 00145 /* ABSTOL (input) DOUBLE PRECISION */ 00146 /* The absolute error tolerance for the eigenvalues. */ 00147 /* An approximate eigenvalue is accepted as converged */ 00148 /* when it is determined to lie in an interval [a,b] */ 00149 /* of width less than or equal to */ 00150 00151 /* ABSTOL + EPS * max( |a|,|b| ) , */ 00152 00153 /* where EPS is the machine precision. If ABSTOL is less than */ 00154 /* or equal to zero, then EPS*|T| will be used in its place, */ 00155 /* where |T| is the 1-norm of the tridiagonal matrix obtained */ 00156 /* by reducing A to tridiagonal form. */ 00157 00158 /* Eigenvalues will be computed most accurately when ABSTOL is */ 00159 /* set to twice the underflow threshold 2*DLAMCH('S'), not zero. */ 00160 /* If this routine returns with INFO>0, indicating that some */ 00161 /* eigenvectors did not converge, try setting ABSTOL to */ 00162 /* 2*DLAMCH('S'). */ 00163 00164 /* M (output) INTEGER */ 00165 /* The total number of eigenvalues found. 0 <= M <= N. */ 00166 /* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */ 00167 00168 /* W (output) DOUBLE PRECISION array, dimension (N) */ 00169 /* The first M elements contain the selected */ 00170 /* eigenvalues in ascending order. */ 00171 00172 /* Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M)) */ 00173 /* If JOBZ = 'N', then Z is not referenced. */ 00174 /* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */ 00175 /* contain the orthonormal eigenvectors of the matrix A */ 00176 /* corresponding to the selected eigenvalues, with the i-th */ 00177 /* column of Z holding the eigenvector associated with W(i). */ 00178 /* The eigenvectors are normalized as follows: */ 00179 /* if ITYPE = 1 or 2, Z**T*B*Z = I; */ 00180 /* if ITYPE = 3, Z**T*inv(B)*Z = I. */ 00181 00182 /* If an eigenvector fails to converge, then that column of Z */ 00183 /* contains the latest approximation to the eigenvector, and the */ 00184 /* index of the eigenvector is returned in IFAIL. */ 00185 /* Note: the user must ensure that at least max(1,M) columns are */ 00186 /* supplied in the array Z; if RANGE = 'V', the exact value of M */ 00187 /* is not known in advance and an upper bound must be used. */ 00188 00189 /* LDZ (input) INTEGER */ 00190 /* The leading dimension of the array Z. LDZ >= 1, and if */ 00191 /* JOBZ = 'V', LDZ >= max(1,N). */ 00192 00193 /* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */ 00194 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00195 00196 /* LWORK (input) INTEGER */ 00197 /* The length of the array WORK. LWORK >= max(1,2*N). */ 00198 /* For optimal efficiency, LWORK >= (NB+1)*N, */ 00199 /* where NB is the blocksize for ZHETRD returned by ILAENV. */ 00200 00201 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00202 /* only calculates the optimal size of the WORK array, returns */ 00203 /* this value as the first entry of the WORK array, and no error */ 00204 /* message related to LWORK is issued by XERBLA. */ 00205 00206 /* RWORK (workspace) DOUBLE PRECISION array, dimension (7*N) */ 00207 00208 /* IWORK (workspace) INTEGER array, dimension (5*N) */ 00209 00210 /* IFAIL (output) INTEGER array, dimension (N) */ 00211 /* If JOBZ = 'V', then if INFO = 0, the first M elements of */ 00212 /* IFAIL are zero. If INFO > 0, then IFAIL contains the */ 00213 /* indices of the eigenvectors that failed to converge. */ 00214 /* If JOBZ = 'N', then IFAIL is not referenced. */ 00215 00216 /* INFO (output) INTEGER */ 00217 /* = 0: successful exit */ 00218 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00219 /* > 0: ZPOTRF or ZHEEVX returned an error code: */ 00220 /* <= N: if INFO = i, ZHEEVX failed to converge; */ 00221 /* i eigenvectors failed to converge. Their indices */ 00222 /* are stored in array IFAIL. */ 00223 /* > N: if INFO = N + i, for 1 <= i <= N, then the leading */ 00224 /* minor of order i of B is not positive definite. */ 00225 /* The factorization of B could not be completed and */ 00226 /* no eigenvalues or eigenvectors were computed. */ 00227 00228 /* Further Details */ 00229 /* =============== */ 00230 00231 /* Based on contributions by */ 00232 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ 00233 00234 /* ===================================================================== */ 00235 00236 /* .. Parameters .. */ 00237 /* .. */ 00238 /* .. Local Scalars .. */ 00239 /* .. */ 00240 /* .. External Functions .. */ 00241 /* .. */ 00242 /* .. External Subroutines .. */ 00243 /* .. */ 00244 /* .. Intrinsic Functions .. */ 00245 /* .. */ 00246 /* .. Executable Statements .. */ 00247 00248 /* Test the input parameters. */ 00249 00250 /* Parameter adjustments */ 00251 a_dim1 = *lda; 00252 a_offset = 1 + a_dim1; 00253 a -= a_offset; 00254 b_dim1 = *ldb; 00255 b_offset = 1 + b_dim1; 00256 b -= b_offset; 00257 --w; 00258 z_dim1 = *ldz; 00259 z_offset = 1 + z_dim1; 00260 z__ -= z_offset; 00261 --work; 00262 --rwork; 00263 --iwork; 00264 --ifail; 00265 00266 /* Function Body */ 00267 wantz = lsame_(jobz, "V"); 00268 upper = lsame_(uplo, "U"); 00269 alleig = lsame_(range, "A"); 00270 valeig = lsame_(range, "V"); 00271 indeig = lsame_(range, "I"); 00272 lquery = *lwork == -1; 00273 00274 *info = 0; 00275 if (*itype < 1 || *itype > 3) { 00276 *info = -1; 00277 } else if (! (wantz || lsame_(jobz, "N"))) { 00278 *info = -2; 00279 } else if (! (alleig || valeig || indeig)) { 00280 *info = -3; 00281 } else if (! (upper || lsame_(uplo, "L"))) { 00282 *info = -4; 00283 } else if (*n < 0) { 00284 *info = -5; 00285 } else if (*lda < max(1,*n)) { 00286 *info = -7; 00287 } else if (*ldb < max(1,*n)) { 00288 *info = -9; 00289 } else { 00290 if (valeig) { 00291 if (*n > 0 && *vu <= *vl) { 00292 *info = -11; 00293 } 00294 } else if (indeig) { 00295 if (*il < 1 || *il > max(1,*n)) { 00296 *info = -12; 00297 } else if (*iu < min(*n,*il) || *iu > *n) { 00298 *info = -13; 00299 } 00300 } 00301 } 00302 if (*info == 0) { 00303 if (*ldz < 1 || wantz && *ldz < *n) { 00304 *info = -18; 00305 } 00306 } 00307 00308 if (*info == 0) { 00309 nb = ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1); 00310 /* Computing MAX */ 00311 i__1 = 1, i__2 = (nb + 1) * *n; 00312 lwkopt = max(i__1,i__2); 00313 work[1].r = (doublereal) lwkopt, work[1].i = 0.; 00314 00315 /* Computing MAX */ 00316 i__1 = 1, i__2 = *n << 1; 00317 if (*lwork < max(i__1,i__2) && ! lquery) { 00318 *info = -20; 00319 } 00320 } 00321 00322 if (*info != 0) { 00323 i__1 = -(*info); 00324 xerbla_("ZHEGVX", &i__1); 00325 return 0; 00326 } else if (lquery) { 00327 return 0; 00328 } 00329 00330 /* Quick return if possible */ 00331 00332 *m = 0; 00333 if (*n == 0) { 00334 return 0; 00335 } 00336 00337 /* Form a Cholesky factorization of B. */ 00338 00339 zpotrf_(uplo, n, &b[b_offset], ldb, info); 00340 if (*info != 0) { 00341 *info = *n + *info; 00342 return 0; 00343 } 00344 00345 /* Transform problem to standard eigenvalue problem and solve. */ 00346 00347 zhegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info); 00348 zheevx_(jobz, range, uplo, n, &a[a_offset], lda, vl, vu, il, iu, abstol, 00349 m, &w[1], &z__[z_offset], ldz, &work[1], lwork, &rwork[1], &iwork[ 00350 1], &ifail[1], info); 00351 00352 if (wantz) { 00353 00354 /* Backtransform eigenvectors to the original problem. */ 00355 00356 if (*info > 0) { 00357 *m = *info - 1; 00358 } 00359 if (*itype == 1 || *itype == 2) { 00360 00361 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00362 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00363 00364 if (upper) { 00365 *(unsigned char *)trans = 'N'; 00366 } else { 00367 *(unsigned char *)trans = 'C'; 00368 } 00369 00370 ztrsm_("Left", uplo, trans, "Non-unit", n, m, &c_b1, &b[b_offset], 00371 ldb, &z__[z_offset], ldz); 00372 00373 } else if (*itype == 3) { 00374 00375 /* For B*A*x=(lambda)*x; */ 00376 /* backtransform eigenvectors: x = L*y or U'*y */ 00377 00378 if (upper) { 00379 *(unsigned char *)trans = 'C'; 00380 } else { 00381 *(unsigned char *)trans = 'N'; 00382 } 00383 00384 ztrmm_("Left", uplo, trans, "Non-unit", n, m, &c_b1, &b[b_offset], 00385 ldb, &z__[z_offset], ldz); 00386 } 00387 } 00388 00389 /* Set WORK(1) to optimal complex workspace size. */ 00390 00391 work[1].r = (doublereal) lwkopt, work[1].i = 0.; 00392 00393 return 0; 00394 00395 /* End of ZHEGVX */ 00396 00397 } /* zhegvx_ */