00001 /* ssygvx.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 real c_b19 = 1.f; 00021 00022 /* Subroutine */ int ssygvx_(integer *itype, char *jobz, char *range, char * 00023 uplo, integer *n, real *a, integer *lda, real *b, integer *ldb, real * 00024 vl, real *vu, integer *il, integer *iu, real *abstol, integer *m, 00025 real *w, real *z__, integer *ldz, real *work, integer *lwork, integer 00026 *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 char trans[1]; 00035 logical upper; 00036 extern /* Subroutine */ int strmm_(char *, char *, char *, char *, 00037 integer *, integer *, real *, real *, integer *, real *, integer * 00038 ); 00039 logical wantz; 00040 extern /* Subroutine */ int strsm_(char *, char *, char *, char *, 00041 integer *, integer *, real *, real *, integer *, real *, integer * 00042 ); 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 integer lwkmin; 00048 extern /* Subroutine */ int spotrf_(char *, integer *, real *, integer *, 00049 integer *); 00050 integer lwkopt; 00051 logical lquery; 00052 extern /* Subroutine */ int ssygst_(integer *, char *, integer *, real *, 00053 integer *, real *, integer *, integer *), ssyevx_(char *, 00054 char *, char *, integer *, real *, integer *, real *, real *, 00055 integer *, integer *, real *, integer *, real *, real *, integer * 00056 , real *, integer *, integer *, 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 /* SSYGVX computes selected eigenvalues, and optionally, eigenvectors */ 00072 /* of a real generalized symmetric-definite eigenproblem, of the form */ 00073 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A */ 00074 /* and B are assumed to be symmetric 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 triangle of A and B are stored; */ 00099 /* = 'L': Lower triangle of A and B are stored. */ 00100 00101 /* N (input) INTEGER */ 00102 /* The order of the matrix pencil (A,B). N >= 0. */ 00103 00104 /* A (input/output) REAL array, dimension (LDA, N) */ 00105 /* On entry, the symmetric 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) REAL array, dimension (LDA, N) */ 00119 /* On entry, the symmetric 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**T*U or B = L*L**T. */ 00128 00129 /* LDB (input) INTEGER */ 00130 /* The leading dimension of the array B. LDB >= max(1,N). */ 00131 00132 /* VL (input) REAL */ 00133 /* VU (input) REAL */ 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) REAL */ 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*SLAMCH('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) REAL array, dimension (N) */ 00169 /* On normal exit, the first M elements contain the selected */ 00170 /* eigenvalues in ascending order. */ 00171 00172 /* Z (output) REAL 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) REAL 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(1,8*N). */ 00198 /* For optimal efficiency, LWORK >= (NB+3)*N, */ 00199 /* where NB is the blocksize for SSYTRD 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 /* IWORK (workspace) INTEGER array, dimension (5*N) */ 00207 00208 /* IFAIL (output) INTEGER array, dimension (N) */ 00209 /* If JOBZ = 'V', then if INFO = 0, the first M elements of */ 00210 /* IFAIL are zero. If INFO > 0, then IFAIL contains the */ 00211 /* indices of the eigenvectors that failed to converge. */ 00212 /* If JOBZ = 'N', then IFAIL is not referenced. */ 00213 00214 /* INFO (output) INTEGER */ 00215 /* = 0: successful exit */ 00216 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00217 /* > 0: SPOTRF or SSYEVX returned an error code: */ 00218 /* <= N: if INFO = i, SSYEVX failed to converge; */ 00219 /* i eigenvectors failed to converge. Their indices */ 00220 /* are stored in array IFAIL. */ 00221 /* > N: if INFO = N + i, for 1 <= i <= N, then the leading */ 00222 /* minor of order i of B is not positive definite. */ 00223 /* The factorization of B could not be completed and */ 00224 /* no eigenvalues or eigenvectors were computed. */ 00225 00226 /* Further Details */ 00227 /* =============== */ 00228 00229 /* Based on contributions by */ 00230 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ 00231 00232 /* ===================================================================== */ 00233 00234 /* .. Parameters .. */ 00235 /* .. */ 00236 /* .. Local Scalars .. */ 00237 /* .. */ 00238 /* .. External Functions .. */ 00239 /* .. */ 00240 /* .. External Subroutines .. */ 00241 /* .. */ 00242 /* .. Intrinsic Functions .. */ 00243 /* .. */ 00244 /* .. Executable Statements .. */ 00245 00246 /* Test the input parameters. */ 00247 00248 /* Parameter adjustments */ 00249 a_dim1 = *lda; 00250 a_offset = 1 + a_dim1; 00251 a -= a_offset; 00252 b_dim1 = *ldb; 00253 b_offset = 1 + b_dim1; 00254 b -= b_offset; 00255 --w; 00256 z_dim1 = *ldz; 00257 z_offset = 1 + z_dim1; 00258 z__ -= z_offset; 00259 --work; 00260 --iwork; 00261 --ifail; 00262 00263 /* Function Body */ 00264 upper = lsame_(uplo, "U"); 00265 wantz = lsame_(jobz, "V"); 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 /* Computing MAX */ 00307 i__1 = 1, i__2 = *n << 3; 00308 lwkmin = max(i__1,i__2); 00309 nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1); 00310 /* Computing MAX */ 00311 i__1 = lwkmin, i__2 = (nb + 3) * *n; 00312 lwkopt = max(i__1,i__2); 00313 work[1] = (real) lwkopt; 00314 00315 if (*lwork < lwkmin && ! lquery) { 00316 *info = -20; 00317 } 00318 } 00319 00320 if (*info != 0) { 00321 i__1 = -(*info); 00322 xerbla_("SSYGVX", &i__1); 00323 return 0; 00324 } else if (lquery) { 00325 return 0; 00326 } 00327 00328 /* Quick return if possible */ 00329 00330 *m = 0; 00331 if (*n == 0) { 00332 return 0; 00333 } 00334 00335 /* Form a Cholesky factorization of B. */ 00336 00337 spotrf_(uplo, n, &b[b_offset], ldb, info); 00338 if (*info != 0) { 00339 *info = *n + *info; 00340 return 0; 00341 } 00342 00343 /* Transform problem to standard eigenvalue problem and solve. */ 00344 00345 ssygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info); 00346 ssyevx_(jobz, range, uplo, n, &a[a_offset], lda, vl, vu, il, iu, abstol, 00347 m, &w[1], &z__[z_offset], ldz, &work[1], lwork, &iwork[1], &ifail[ 00348 1], info); 00349 00350 if (wantz) { 00351 00352 /* Backtransform eigenvectors to the original problem. */ 00353 00354 if (*info > 0) { 00355 *m = *info - 1; 00356 } 00357 if (*itype == 1 || *itype == 2) { 00358 00359 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00360 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00361 00362 if (upper) { 00363 *(unsigned char *)trans = 'N'; 00364 } else { 00365 *(unsigned char *)trans = 'T'; 00366 } 00367 00368 strsm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset] 00369 , ldb, &z__[z_offset], ldz); 00370 00371 } else if (*itype == 3) { 00372 00373 /* For B*A*x=(lambda)*x; */ 00374 /* backtransform eigenvectors: x = L*y or U'*y */ 00375 00376 if (upper) { 00377 *(unsigned char *)trans = 'T'; 00378 } else { 00379 *(unsigned char *)trans = 'N'; 00380 } 00381 00382 strmm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset] 00383 , ldb, &z__[z_offset], ldz); 00384 } 00385 } 00386 00387 /* Set WORK(1) to optimal workspace size. */ 00388 00389 work[1] = (real) lwkopt; 00390 00391 return 0; 00392 00393 /* End of SSYGVX */ 00394 00395 } /* ssygvx_ */