00001 /* dsygvx.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 static integer c_n1 = -1; 00020 static doublereal c_b19 = 1.; 00021 00022 /* Subroutine */ int dsygvx_(integer *itype, char *jobz, char *range, char * 00023 uplo, integer *n, doublereal *a, integer *lda, doublereal *b, integer 00024 *ldb, doublereal *vl, doublereal *vu, integer *il, integer *iu, 00025 doublereal *abstol, integer *m, doublereal *w, doublereal *z__, 00026 integer *ldz, doublereal *work, integer *lwork, integer *iwork, 00027 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 extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, 00036 integer *, integer *, doublereal *, doublereal *, integer *, 00037 doublereal *, integer *); 00038 char trans[1]; 00039 extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, 00040 integer *, integer *, doublereal *, doublereal *, integer *, 00041 doublereal *, integer *); 00042 logical upper, wantz, alleig, indeig, valeig; 00043 extern /* Subroutine */ int xerbla_(char *, integer *); 00044 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00045 integer *, integer *); 00046 extern /* Subroutine */ int dpotrf_(char *, integer *, doublereal *, 00047 integer *, integer *); 00048 integer lwkmin; 00049 extern /* Subroutine */ int dsygst_(integer *, char *, integer *, 00050 doublereal *, integer *, doublereal *, integer *, integer *); 00051 integer lwkopt; 00052 logical lquery; 00053 extern /* Subroutine */ int dsyevx_(char *, char *, char *, integer *, 00054 doublereal *, integer *, doublereal *, doublereal *, integer *, 00055 integer *, doublereal *, integer *, doublereal *, doublereal *, 00056 integer *, doublereal *, integer *, integer *, integer *, integer 00057 *); 00058 00059 00060 /* -- LAPACK driver routine (version 3.2) -- */ 00061 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00062 /* November 2006 */ 00063 00064 /* .. Scalar Arguments .. */ 00065 /* .. */ 00066 /* .. Array Arguments .. */ 00067 /* .. */ 00068 00069 /* Purpose */ 00070 /* ======= */ 00071 00072 /* DSYGVX computes selected eigenvalues, and optionally, eigenvectors */ 00073 /* of a real generalized symmetric-definite eigenproblem, of the form */ 00074 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A */ 00075 /* and B are assumed to be symmetric and B is also positive definite. */ 00076 /* Eigenvalues and eigenvectors can be selected by specifying either a */ 00077 /* range of values or a range of indices for the desired eigenvalues. */ 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 /* RANGE (input) CHARACTER*1 */ 00093 /* = 'A': all eigenvalues will be found. */ 00094 /* = 'V': all eigenvalues in the half-open interval (VL,VU] */ 00095 /* will be found. */ 00096 /* = 'I': the IL-th through IU-th eigenvalues will be found. */ 00097 00098 /* UPLO (input) CHARACTER*1 */ 00099 /* = 'U': Upper triangle of A and B are stored; */ 00100 /* = 'L': Lower triangle of A and B are stored. */ 00101 00102 /* N (input) INTEGER */ 00103 /* The order of the matrix pencil (A,B). N >= 0. */ 00104 00105 /* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) */ 00106 /* On entry, the symmetric matrix A. If UPLO = 'U', the */ 00107 /* leading N-by-N upper triangular part of A contains the */ 00108 /* upper triangular part of the matrix A. If UPLO = 'L', */ 00109 /* the leading N-by-N lower triangular part of A contains */ 00110 /* the lower triangular part of the matrix A. */ 00111 00112 /* On exit, the lower triangle (if UPLO='L') or the upper */ 00113 /* triangle (if UPLO='U') of A, including the diagonal, is */ 00114 /* destroyed. */ 00115 00116 /* LDA (input) INTEGER */ 00117 /* The leading dimension of the array A. LDA >= max(1,N). */ 00118 00119 /* B (input/output) DOUBLE PRECISION array, dimension (LDA, N) */ 00120 /* On entry, the symmetric matrix B. If UPLO = 'U', the */ 00121 /* leading N-by-N upper triangular part of B contains the */ 00122 /* upper triangular part of the matrix B. If UPLO = 'L', */ 00123 /* the leading N-by-N lower triangular part of B contains */ 00124 /* the lower triangular part of the matrix B. */ 00125 00126 /* On exit, if INFO <= N, the part of B containing the matrix is */ 00127 /* overwritten by the triangular factor U or L from the Cholesky */ 00128 /* factorization B = U**T*U or B = L*L**T. */ 00129 00130 /* LDB (input) INTEGER */ 00131 /* The leading dimension of the array B. LDB >= max(1,N). */ 00132 00133 /* VL (input) DOUBLE PRECISION */ 00134 /* VU (input) DOUBLE PRECISION */ 00135 /* If RANGE='V', the lower and upper bounds of the interval to */ 00136 /* be searched for eigenvalues. VL < VU. */ 00137 /* Not referenced if RANGE = 'A' or 'I'. */ 00138 00139 /* IL (input) INTEGER */ 00140 /* IU (input) INTEGER */ 00141 /* If RANGE='I', the indices (in ascending order) of the */ 00142 /* smallest and largest eigenvalues to be returned. */ 00143 /* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */ 00144 /* Not referenced if RANGE = 'A' or 'V'. */ 00145 00146 /* ABSTOL (input) DOUBLE PRECISION */ 00147 /* The absolute error tolerance for the eigenvalues. */ 00148 /* An approximate eigenvalue is accepted as converged */ 00149 /* when it is determined to lie in an interval [a,b] */ 00150 /* of width less than or equal to */ 00151 00152 /* ABSTOL + EPS * max( |a|,|b| ) , */ 00153 00154 /* where EPS is the machine precision. If ABSTOL is less than */ 00155 /* or equal to zero, then EPS*|T| will be used in its place, */ 00156 /* where |T| is the 1-norm of the tridiagonal matrix obtained */ 00157 /* by reducing A to tridiagonal form. */ 00158 00159 /* Eigenvalues will be computed most accurately when ABSTOL is */ 00160 /* set to twice the underflow threshold 2*DLAMCH('S'), not zero. */ 00161 /* If this routine returns with INFO>0, indicating that some */ 00162 /* eigenvectors did not converge, try setting ABSTOL to */ 00163 /* 2*DLAMCH('S'). */ 00164 00165 /* M (output) INTEGER */ 00166 /* The total number of eigenvalues found. 0 <= M <= N. */ 00167 /* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */ 00168 00169 /* W (output) DOUBLE PRECISION array, dimension (N) */ 00170 /* On normal exit, the first M elements contain the selected */ 00171 /* eigenvalues in ascending order. */ 00172 00173 /* Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M)) */ 00174 /* If JOBZ = 'N', then Z is not referenced. */ 00175 /* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */ 00176 /* contain the orthonormal eigenvectors of the matrix A */ 00177 /* corresponding to the selected eigenvalues, with the i-th */ 00178 /* column of Z holding the eigenvector associated with W(i). */ 00179 /* The eigenvectors are normalized as follows: */ 00180 /* if ITYPE = 1 or 2, Z**T*B*Z = I; */ 00181 /* if ITYPE = 3, Z**T*inv(B)*Z = I. */ 00182 00183 /* If an eigenvector fails to converge, then that column of Z */ 00184 /* contains the latest approximation to the eigenvector, and the */ 00185 /* index of the eigenvector is returned in IFAIL. */ 00186 /* Note: the user must ensure that at least max(1,M) columns are */ 00187 /* supplied in the array Z; if RANGE = 'V', the exact value of M */ 00188 /* is not known in advance and an upper bound must be used. */ 00189 00190 /* LDZ (input) INTEGER */ 00191 /* The leading dimension of the array Z. LDZ >= 1, and if */ 00192 /* JOBZ = 'V', LDZ >= max(1,N). */ 00193 00194 /* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ 00195 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00196 00197 /* LWORK (input) INTEGER */ 00198 /* The length of the array WORK. LWORK >= max(1,8*N). */ 00199 /* For optimal efficiency, LWORK >= (NB+3)*N, */ 00200 /* where NB is the blocksize for DSYTRD returned by ILAENV. */ 00201 00202 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00203 /* only calculates the optimal size of the WORK array, returns */ 00204 /* this value as the first entry of the WORK array, and no error */ 00205 /* message related to LWORK is issued by XERBLA. */ 00206 00207 /* IWORK (workspace) INTEGER array, dimension (5*N) */ 00208 00209 /* IFAIL (output) INTEGER array, dimension (N) */ 00210 /* If JOBZ = 'V', then if INFO = 0, the first M elements of */ 00211 /* IFAIL are zero. If INFO > 0, then IFAIL contains the */ 00212 /* indices of the eigenvectors that failed to converge. */ 00213 /* If JOBZ = 'N', then IFAIL is not referenced. */ 00214 00215 /* INFO (output) INTEGER */ 00216 /* = 0: successful exit */ 00217 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00218 /* > 0: DPOTRF or DSYEVX returned an error code: */ 00219 /* <= N: if INFO = i, DSYEVX failed to converge; */ 00220 /* i eigenvectors failed to converge. Their indices */ 00221 /* are stored in array IFAIL. */ 00222 /* > N: if INFO = N + i, for 1 <= i <= N, then the leading */ 00223 /* minor of order i of B is not positive definite. */ 00224 /* The factorization of B could not be completed and */ 00225 /* no eigenvalues or eigenvectors were computed. */ 00226 00227 /* Further Details */ 00228 /* =============== */ 00229 00230 /* Based on contributions by */ 00231 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ 00232 00233 /* ===================================================================== */ 00234 00235 /* .. Parameters .. */ 00236 /* .. */ 00237 /* .. Local Scalars .. */ 00238 /* .. */ 00239 /* .. External Functions .. */ 00240 /* .. */ 00241 /* .. External Subroutines .. */ 00242 /* .. */ 00243 /* .. Intrinsic Functions .. */ 00244 /* .. */ 00245 /* .. Executable Statements .. */ 00246 00247 /* Test the input parameters. */ 00248 00249 /* Parameter adjustments */ 00250 a_dim1 = *lda; 00251 a_offset = 1 + a_dim1; 00252 a -= a_offset; 00253 b_dim1 = *ldb; 00254 b_offset = 1 + b_dim1; 00255 b -= b_offset; 00256 --w; 00257 z_dim1 = *ldz; 00258 z_offset = 1 + z_dim1; 00259 z__ -= z_offset; 00260 --work; 00261 --iwork; 00262 --ifail; 00263 00264 /* Function Body */ 00265 upper = lsame_(uplo, "U"); 00266 wantz = lsame_(jobz, "V"); 00267 alleig = lsame_(range, "A"); 00268 valeig = lsame_(range, "V"); 00269 indeig = lsame_(range, "I"); 00270 lquery = *lwork == -1; 00271 00272 *info = 0; 00273 if (*itype < 1 || *itype > 3) { 00274 *info = -1; 00275 } else if (! (wantz || lsame_(jobz, "N"))) { 00276 *info = -2; 00277 } else if (! (alleig || valeig || indeig)) { 00278 *info = -3; 00279 } else if (! (upper || lsame_(uplo, "L"))) { 00280 *info = -4; 00281 } else if (*n < 0) { 00282 *info = -5; 00283 } else if (*lda < max(1,*n)) { 00284 *info = -7; 00285 } else if (*ldb < max(1,*n)) { 00286 *info = -9; 00287 } else { 00288 if (valeig) { 00289 if (*n > 0 && *vu <= *vl) { 00290 *info = -11; 00291 } 00292 } else if (indeig) { 00293 if (*il < 1 || *il > max(1,*n)) { 00294 *info = -12; 00295 } else if (*iu < min(*n,*il) || *iu > *n) { 00296 *info = -13; 00297 } 00298 } 00299 } 00300 if (*info == 0) { 00301 if (*ldz < 1 || wantz && *ldz < *n) { 00302 *info = -18; 00303 } 00304 } 00305 00306 if (*info == 0) { 00307 /* Computing MAX */ 00308 i__1 = 1, i__2 = *n << 3; 00309 lwkmin = max(i__1,i__2); 00310 nb = ilaenv_(&c__1, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1); 00311 /* Computing MAX */ 00312 i__1 = lwkmin, i__2 = (nb + 3) * *n; 00313 lwkopt = max(i__1,i__2); 00314 work[1] = (doublereal) lwkopt; 00315 00316 if (*lwork < lwkmin && ! lquery) { 00317 *info = -20; 00318 } 00319 } 00320 00321 if (*info != 0) { 00322 i__1 = -(*info); 00323 xerbla_("DSYGVX", &i__1); 00324 return 0; 00325 } else if (lquery) { 00326 return 0; 00327 } 00328 00329 /* Quick return if possible */ 00330 00331 *m = 0; 00332 if (*n == 0) { 00333 return 0; 00334 } 00335 00336 /* Form a Cholesky factorization of B. */ 00337 00338 dpotrf_(uplo, n, &b[b_offset], ldb, info); 00339 if (*info != 0) { 00340 *info = *n + *info; 00341 return 0; 00342 } 00343 00344 /* Transform problem to standard eigenvalue problem and solve. */ 00345 00346 dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info); 00347 dsyevx_(jobz, range, uplo, n, &a[a_offset], lda, vl, vu, il, iu, abstol, 00348 m, &w[1], &z__[z_offset], ldz, &work[1], lwork, &iwork[1], &ifail[ 00349 1], info); 00350 00351 if (wantz) { 00352 00353 /* Backtransform eigenvectors to the original problem. */ 00354 00355 if (*info > 0) { 00356 *m = *info - 1; 00357 } 00358 if (*itype == 1 || *itype == 2) { 00359 00360 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00361 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00362 00363 if (upper) { 00364 *(unsigned char *)trans = 'N'; 00365 } else { 00366 *(unsigned char *)trans = 'T'; 00367 } 00368 00369 dtrsm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset] 00370 , ldb, &z__[z_offset], ldz); 00371 00372 } else if (*itype == 3) { 00373 00374 /* For B*A*x=(lambda)*x; */ 00375 /* backtransform eigenvectors: x = L*y or U'*y */ 00376 00377 if (upper) { 00378 *(unsigned char *)trans = 'T'; 00379 } else { 00380 *(unsigned char *)trans = 'N'; 00381 } 00382 00383 dtrmm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset] 00384 , ldb, &z__[z_offset], ldz); 00385 } 00386 } 00387 00388 /* Set WORK(1) to optimal workspace size. */ 00389 00390 work[1] = (doublereal) lwkopt; 00391 00392 return 0; 00393 00394 /* End of DSYGVX */ 00395 00396 } /* dsygvx_ */