00001 /* chegvd.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 00020 /* Subroutine */ int chegvd_(integer *itype, char *jobz, char *uplo, integer * 00021 n, complex *a, integer *lda, complex *b, integer *ldb, real *w, 00022 complex *work, integer *lwork, real *rwork, integer *lrwork, integer * 00023 iwork, integer *liwork, integer *info) 00024 { 00025 /* System generated locals */ 00026 integer a_dim1, a_offset, b_dim1, b_offset, i__1; 00027 real r__1, r__2; 00028 00029 /* Local variables */ 00030 integer lopt; 00031 extern logical lsame_(char *, char *); 00032 extern /* Subroutine */ int ctrmm_(char *, char *, char *, char *, 00033 integer *, integer *, complex *, complex *, integer *, complex *, 00034 integer *); 00035 integer lwmin; 00036 char trans[1]; 00037 integer liopt; 00038 extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 00039 integer *, integer *, complex *, complex *, integer *, complex *, 00040 integer *); 00041 logical upper; 00042 integer lropt; 00043 logical wantz; 00044 extern /* Subroutine */ int cheevd_(char *, char *, integer *, complex *, 00045 integer *, real *, complex *, integer *, real *, integer *, 00046 integer *, integer *, integer *), chegst_(integer 00047 *, char *, integer *, complex *, integer *, complex *, integer *, 00048 integer *), xerbla_(char *, integer *), cpotrf_( 00049 char *, integer *, complex *, integer *, integer *); 00050 integer liwmin, lrwmin; 00051 logical lquery; 00052 00053 00054 /* -- LAPACK driver routine (version 3.2) -- */ 00055 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00056 /* November 2006 */ 00057 00058 /* .. Scalar Arguments .. */ 00059 /* .. */ 00060 /* .. Array Arguments .. */ 00061 /* .. */ 00062 00063 /* Purpose */ 00064 /* ======= */ 00065 00066 /* CHEGVD computes all the eigenvalues, and optionally, the eigenvectors */ 00067 /* of a complex generalized Hermitian-definite eigenproblem, of the form */ 00068 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */ 00069 /* B are assumed to be Hermitian and B is also positive definite. */ 00070 /* If eigenvectors are desired, it uses a divide and conquer algorithm. */ 00071 00072 /* The divide and conquer algorithm makes very mild assumptions about */ 00073 /* floating point arithmetic. It will work on machines with a guard */ 00074 /* digit in add/subtract, or on those binary machines without guard */ 00075 /* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ 00076 /* Cray-2. It could conceivably fail on hexadecimal or decimal machines */ 00077 /* without guard digits, but we know of none. */ 00078 00079 /* Arguments */ 00080 /* ========= */ 00081 00082 /* ITYPE (input) INTEGER */ 00083 /* Specifies the problem type to be solved: */ 00084 /* = 1: A*x = (lambda)*B*x */ 00085 /* = 2: A*B*x = (lambda)*x */ 00086 /* = 3: B*A*x = (lambda)*x */ 00087 00088 /* JOBZ (input) CHARACTER*1 */ 00089 /* = 'N': Compute eigenvalues only; */ 00090 /* = 'V': Compute eigenvalues and eigenvectors. */ 00091 00092 /* UPLO (input) CHARACTER*1 */ 00093 /* = 'U': Upper triangles of A and B are stored; */ 00094 /* = 'L': Lower triangles of A and B are stored. */ 00095 00096 /* N (input) INTEGER */ 00097 /* The order of the matrices A and B. N >= 0. */ 00098 00099 /* A (input/output) COMPLEX array, dimension (LDA, N) */ 00100 /* On entry, the Hermitian matrix A. If UPLO = 'U', the */ 00101 /* leading N-by-N upper triangular part of A contains the */ 00102 /* upper triangular part of the matrix A. If UPLO = 'L', */ 00103 /* the leading N-by-N lower triangular part of A contains */ 00104 /* the lower triangular part of the matrix A. */ 00105 00106 /* On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ 00107 /* matrix Z of eigenvectors. The eigenvectors are normalized */ 00108 /* as follows: */ 00109 /* if ITYPE = 1 or 2, Z**H*B*Z = I; */ 00110 /* if ITYPE = 3, Z**H*inv(B)*Z = I. */ 00111 /* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */ 00112 /* or the lower triangle (if UPLO='L') of A, including the */ 00113 /* diagonal, is destroyed. */ 00114 00115 /* LDA (input) INTEGER */ 00116 /* The leading dimension of the array A. LDA >= max(1,N). */ 00117 00118 /* B (input/output) COMPLEX 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 /* W (output) REAL array, dimension (N) */ 00133 /* If INFO = 0, the eigenvalues in ascending order. */ 00134 00135 /* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */ 00136 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00137 00138 /* LWORK (input) INTEGER */ 00139 /* The length of the array WORK. */ 00140 /* If N <= 1, LWORK >= 1. */ 00141 /* If JOBZ = 'N' and N > 1, LWORK >= N + 1. */ 00142 /* If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2. */ 00143 00144 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00145 /* only calculates the optimal sizes of the WORK, RWORK and */ 00146 /* IWORK arrays, returns these values as the first entries of */ 00147 /* the WORK, RWORK and IWORK arrays, and no error message */ 00148 /* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ 00149 00150 /* RWORK (workspace/output) REAL array, dimension (MAX(1,LRWORK)) */ 00151 /* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */ 00152 00153 /* LRWORK (input) INTEGER */ 00154 /* The dimension of the array RWORK. */ 00155 /* If N <= 1, LRWORK >= 1. */ 00156 /* If JOBZ = 'N' and N > 1, LRWORK >= N. */ 00157 /* If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. */ 00158 00159 /* If LRWORK = -1, then a workspace query is assumed; the */ 00160 /* routine only calculates the optimal sizes of the WORK, RWORK */ 00161 /* and IWORK arrays, returns these values as the first entries */ 00162 /* of the WORK, RWORK and IWORK arrays, and no error message */ 00163 /* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ 00164 00165 /* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */ 00166 /* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ 00167 00168 /* LIWORK (input) INTEGER */ 00169 /* The dimension of the array IWORK. */ 00170 /* If N <= 1, LIWORK >= 1. */ 00171 /* If JOBZ = 'N' and N > 1, LIWORK >= 1. */ 00172 /* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */ 00173 00174 /* If LIWORK = -1, then a workspace query is assumed; the */ 00175 /* routine only calculates the optimal sizes of the WORK, RWORK */ 00176 /* and IWORK arrays, returns these values as the first entries */ 00177 /* of the WORK, RWORK and IWORK arrays, and no error message */ 00178 /* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ 00179 00180 /* INFO (output) INTEGER */ 00181 /* = 0: successful exit */ 00182 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00183 /* > 0: CPOTRF or CHEEVD returned an error code: */ 00184 /* <= N: if INFO = i and JOBZ = 'N', then the algorithm */ 00185 /* failed to converge; i off-diagonal elements of an */ 00186 /* intermediate tridiagonal form did not converge to */ 00187 /* zero; */ 00188 /* if INFO = i and JOBZ = 'V', then the algorithm */ 00189 /* failed to compute an eigenvalue while working on */ 00190 /* the submatrix lying in rows and columns INFO/(N+1) */ 00191 /* through mod(INFO,N+1); */ 00192 /* > N: if INFO = N + i, for 1 <= i <= N, then the leading */ 00193 /* minor of order i of B is not positive definite. */ 00194 /* The factorization of B could not be completed and */ 00195 /* no eigenvalues or eigenvectors were computed. */ 00196 00197 /* Further Details */ 00198 /* =============== */ 00199 00200 /* Based on contributions by */ 00201 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ 00202 00203 /* Modified so that no backsubstitution is performed if CHEEVD fails to */ 00204 /* converge (NEIG in old code could be greater than N causing out of */ 00205 /* bounds reference to A - reported by Ralf Meyer). Also corrected the */ 00206 /* description of INFO and the test on ITYPE. Sven, 16 Feb 05. */ 00207 /* ===================================================================== */ 00208 00209 /* .. Parameters .. */ 00210 /* .. */ 00211 /* .. Local Scalars .. */ 00212 /* .. */ 00213 /* .. External Functions .. */ 00214 /* .. */ 00215 /* .. External Subroutines .. */ 00216 /* .. */ 00217 /* .. Intrinsic Functions .. */ 00218 /* .. */ 00219 /* .. Executable Statements .. */ 00220 00221 /* Test the input parameters. */ 00222 00223 /* Parameter adjustments */ 00224 a_dim1 = *lda; 00225 a_offset = 1 + a_dim1; 00226 a -= a_offset; 00227 b_dim1 = *ldb; 00228 b_offset = 1 + b_dim1; 00229 b -= b_offset; 00230 --w; 00231 --work; 00232 --rwork; 00233 --iwork; 00234 00235 /* Function Body */ 00236 wantz = lsame_(jobz, "V"); 00237 upper = lsame_(uplo, "U"); 00238 lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; 00239 00240 *info = 0; 00241 if (*n <= 1) { 00242 lwmin = 1; 00243 lrwmin = 1; 00244 liwmin = 1; 00245 } else if (wantz) { 00246 lwmin = (*n << 1) + *n * *n; 00247 lrwmin = *n * 5 + 1 + (*n << 1) * *n; 00248 liwmin = *n * 5 + 3; 00249 } else { 00250 lwmin = *n + 1; 00251 lrwmin = *n; 00252 liwmin = 1; 00253 } 00254 lopt = lwmin; 00255 lropt = lrwmin; 00256 liopt = liwmin; 00257 if (*itype < 1 || *itype > 3) { 00258 *info = -1; 00259 } else if (! (wantz || lsame_(jobz, "N"))) { 00260 *info = -2; 00261 } else if (! (upper || lsame_(uplo, "L"))) { 00262 *info = -3; 00263 } else if (*n < 0) { 00264 *info = -4; 00265 } else if (*lda < max(1,*n)) { 00266 *info = -6; 00267 } else if (*ldb < max(1,*n)) { 00268 *info = -8; 00269 } 00270 00271 if (*info == 0) { 00272 work[1].r = (real) lopt, work[1].i = 0.f; 00273 rwork[1] = (real) lropt; 00274 iwork[1] = liopt; 00275 00276 if (*lwork < lwmin && ! lquery) { 00277 *info = -11; 00278 } else if (*lrwork < lrwmin && ! lquery) { 00279 *info = -13; 00280 } else if (*liwork < liwmin && ! lquery) { 00281 *info = -15; 00282 } 00283 } 00284 00285 if (*info != 0) { 00286 i__1 = -(*info); 00287 xerbla_("CHEGVD", &i__1); 00288 return 0; 00289 } else if (lquery) { 00290 return 0; 00291 } 00292 00293 /* Quick return if possible */ 00294 00295 if (*n == 0) { 00296 return 0; 00297 } 00298 00299 /* Form a Cholesky factorization of B. */ 00300 00301 cpotrf_(uplo, n, &b[b_offset], ldb, info); 00302 if (*info != 0) { 00303 *info = *n + *info; 00304 return 0; 00305 } 00306 00307 /* Transform problem to standard eigenvalue problem and solve. */ 00308 00309 chegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info); 00310 cheevd_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &rwork[ 00311 1], lrwork, &iwork[1], liwork, info); 00312 /* Computing MAX */ 00313 r__1 = (real) lopt, r__2 = work[1].r; 00314 lopt = dmax(r__1,r__2); 00315 /* Computing MAX */ 00316 r__1 = (real) lropt; 00317 lropt = dmax(r__1,rwork[1]); 00318 /* Computing MAX */ 00319 r__1 = (real) liopt, r__2 = (real) iwork[1]; 00320 liopt = dmax(r__1,r__2); 00321 00322 if (wantz && *info == 0) { 00323 00324 /* Backtransform eigenvectors to the original problem. */ 00325 00326 if (*itype == 1 || *itype == 2) { 00327 00328 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00329 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00330 00331 if (upper) { 00332 *(unsigned char *)trans = 'N'; 00333 } else { 00334 *(unsigned char *)trans = 'C'; 00335 } 00336 00337 ctrsm_("Left", uplo, trans, "Non-unit", n, n, &c_b1, &b[b_offset], 00338 ldb, &a[a_offset], lda); 00339 00340 } else if (*itype == 3) { 00341 00342 /* For B*A*x=(lambda)*x; */ 00343 /* backtransform eigenvectors: x = L*y or U'*y */ 00344 00345 if (upper) { 00346 *(unsigned char *)trans = 'C'; 00347 } else { 00348 *(unsigned char *)trans = 'N'; 00349 } 00350 00351 ctrmm_("Left", uplo, trans, "Non-unit", n, n, &c_b1, &b[b_offset], 00352 ldb, &a[a_offset], lda); 00353 } 00354 } 00355 00356 work[1].r = (real) lopt, work[1].i = 0.f; 00357 rwork[1] = (real) lropt; 00358 iwork[1] = liopt; 00359 00360 return 0; 00361 00362 /* End of CHEGVD */ 00363 00364 } /* chegvd_ */