00001 /* sspgvx.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 00020 /* Subroutine */ int sspgvx_(integer *itype, char *jobz, char *range, char * 00021 uplo, integer *n, real *ap, real *bp, real *vl, real *vu, integer *il, 00022 integer *iu, real *abstol, integer *m, real *w, real *z__, integer * 00023 ldz, real *work, integer *iwork, integer *ifail, integer *info) 00024 { 00025 /* System generated locals */ 00026 integer z_dim1, z_offset, i__1; 00027 00028 /* Local variables */ 00029 integer j; 00030 extern logical lsame_(char *, char *); 00031 char trans[1]; 00032 logical upper, wantz; 00033 extern /* Subroutine */ int stpmv_(char *, char *, char *, integer *, 00034 real *, real *, integer *), stpsv_(char *, 00035 char *, char *, integer *, real *, real *, integer *); 00036 logical alleig, indeig, valeig; 00037 extern /* Subroutine */ int xerbla_(char *, integer *), spptrf_( 00038 char *, integer *, real *, integer *), sspgst_(integer *, 00039 char *, integer *, real *, real *, integer *), sspevx_( 00040 char *, char *, char *, integer *, real *, real *, real *, 00041 integer *, integer *, real *, integer *, real *, real *, integer * 00042 , real *, integer *, integer *, integer *) 00043 ; 00044 00045 00046 /* -- LAPACK driver routine (version 3.2) -- */ 00047 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00048 /* November 2006 */ 00049 00050 /* .. Scalar Arguments .. */ 00051 /* .. */ 00052 /* .. Array Arguments .. */ 00053 /* .. */ 00054 00055 /* Purpose */ 00056 /* ======= */ 00057 00058 /* SSPGVX computes selected eigenvalues, and optionally, eigenvectors */ 00059 /* of a real generalized symmetric-definite eigenproblem, of the form */ 00060 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A */ 00061 /* and B are assumed to be symmetric, stored in packed storage, and B */ 00062 /* is also positive definite. Eigenvalues and eigenvectors can be */ 00063 /* selected by specifying either a range of values or a range of indices */ 00064 /* for the desired eigenvalues. */ 00065 00066 /* Arguments */ 00067 /* ========= */ 00068 00069 /* ITYPE (input) INTEGER */ 00070 /* Specifies the problem type to be solved: */ 00071 /* = 1: A*x = (lambda)*B*x */ 00072 /* = 2: A*B*x = (lambda)*x */ 00073 /* = 3: B*A*x = (lambda)*x */ 00074 00075 /* JOBZ (input) CHARACTER*1 */ 00076 /* = 'N': Compute eigenvalues only; */ 00077 /* = 'V': Compute eigenvalues and eigenvectors. */ 00078 00079 /* RANGE (input) CHARACTER*1 */ 00080 /* = 'A': all eigenvalues will be found. */ 00081 /* = 'V': all eigenvalues in the half-open interval (VL,VU] */ 00082 /* will be found. */ 00083 /* = 'I': the IL-th through IU-th eigenvalues will be found. */ 00084 00085 /* UPLO (input) CHARACTER*1 */ 00086 /* = 'U': Upper triangle of A and B are stored; */ 00087 /* = 'L': Lower triangle of A and B are stored. */ 00088 00089 /* N (input) INTEGER */ 00090 /* The order of the matrix pencil (A,B). N >= 0. */ 00091 00092 /* AP (input/output) REAL array, dimension (N*(N+1)/2) */ 00093 /* On entry, the upper or lower triangle of the symmetric matrix */ 00094 /* A, packed columnwise in a linear array. The j-th column of A */ 00095 /* is stored in the array AP as follows: */ 00096 /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ 00097 /* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */ 00098 00099 /* On exit, the contents of AP are destroyed. */ 00100 00101 /* BP (input/output) REAL array, dimension (N*(N+1)/2) */ 00102 /* On entry, the upper or lower triangle of the symmetric matrix */ 00103 /* B, packed columnwise in a linear array. The j-th column of B */ 00104 /* is stored in the array BP as follows: */ 00105 /* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; */ 00106 /* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. */ 00107 00108 /* On exit, the triangular factor U or L from the Cholesky */ 00109 /* factorization B = U**T*U or B = L*L**T, in the same storage */ 00110 /* format as B. */ 00111 00112 /* VL (input) REAL */ 00113 /* VU (input) REAL */ 00114 /* If RANGE='V', the lower and upper bounds of the interval to */ 00115 /* be searched for eigenvalues. VL < VU. */ 00116 /* Not referenced if RANGE = 'A' or 'I'. */ 00117 00118 /* IL (input) INTEGER */ 00119 /* IU (input) INTEGER */ 00120 /* If RANGE='I', the indices (in ascending order) of the */ 00121 /* smallest and largest eigenvalues to be returned. */ 00122 /* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */ 00123 /* Not referenced if RANGE = 'A' or 'V'. */ 00124 00125 /* ABSTOL (input) REAL */ 00126 /* The absolute error tolerance for the eigenvalues. */ 00127 /* An approximate eigenvalue is accepted as converged */ 00128 /* when it is determined to lie in an interval [a,b] */ 00129 /* of width less than or equal to */ 00130 00131 /* ABSTOL + EPS * max( |a|,|b| ) , */ 00132 00133 /* where EPS is the machine precision. If ABSTOL is less than */ 00134 /* or equal to zero, then EPS*|T| will be used in its place, */ 00135 /* where |T| is the 1-norm of the tridiagonal matrix obtained */ 00136 /* by reducing A to tridiagonal form. */ 00137 00138 /* Eigenvalues will be computed most accurately when ABSTOL is */ 00139 /* set to twice the underflow threshold 2*SLAMCH('S'), not zero. */ 00140 /* If this routine returns with INFO>0, indicating that some */ 00141 /* eigenvectors did not converge, try setting ABSTOL to */ 00142 /* 2*SLAMCH('S'). */ 00143 00144 /* M (output) INTEGER */ 00145 /* The total number of eigenvalues found. 0 <= M <= N. */ 00146 /* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */ 00147 00148 /* W (output) REAL array, dimension (N) */ 00149 /* On normal exit, the first M elements contain the selected */ 00150 /* eigenvalues in ascending order. */ 00151 00152 /* Z (output) REAL array, dimension (LDZ, max(1,M)) */ 00153 /* If JOBZ = 'N', then Z is not referenced. */ 00154 /* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */ 00155 /* contain the orthonormal eigenvectors of the matrix A */ 00156 /* corresponding to the selected eigenvalues, with the i-th */ 00157 /* column of Z holding the eigenvector associated with W(i). */ 00158 /* The eigenvectors are normalized as follows: */ 00159 /* if ITYPE = 1 or 2, Z**T*B*Z = I; */ 00160 /* if ITYPE = 3, Z**T*inv(B)*Z = I. */ 00161 00162 /* If an eigenvector fails to converge, then that column of Z */ 00163 /* contains the latest approximation to the eigenvector, and the */ 00164 /* index of the eigenvector is returned in IFAIL. */ 00165 /* Note: the user must ensure that at least max(1,M) columns are */ 00166 /* supplied in the array Z; if RANGE = 'V', the exact value of M */ 00167 /* is not known in advance and an upper bound must be used. */ 00168 00169 /* LDZ (input) INTEGER */ 00170 /* The leading dimension of the array Z. LDZ >= 1, and if */ 00171 /* JOBZ = 'V', LDZ >= max(1,N). */ 00172 00173 /* WORK (workspace) REAL array, dimension (8*N) */ 00174 00175 /* IWORK (workspace) INTEGER array, dimension (5*N) */ 00176 00177 /* IFAIL (output) INTEGER array, dimension (N) */ 00178 /* If JOBZ = 'V', then if INFO = 0, the first M elements of */ 00179 /* IFAIL are zero. If INFO > 0, then IFAIL contains the */ 00180 /* indices of the eigenvectors that failed to converge. */ 00181 /* If JOBZ = 'N', then IFAIL is not referenced. */ 00182 00183 /* INFO (output) INTEGER */ 00184 /* = 0: successful exit */ 00185 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00186 /* > 0: SPPTRF or SSPEVX returned an error code: */ 00187 /* <= N: if INFO = i, SSPEVX failed to converge; */ 00188 /* i eigenvectors failed to converge. Their indices */ 00189 /* are stored in array IFAIL. */ 00190 /* > N: if INFO = N + i, for 1 <= i <= N, then the leading */ 00191 /* minor of order i of B is not positive definite. */ 00192 /* The factorization of B could not be completed and */ 00193 /* no eigenvalues or eigenvectors were computed. */ 00194 00195 /* Further Details */ 00196 /* =============== */ 00197 00198 /* Based on contributions by */ 00199 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ 00200 00201 /* ===================================================================== */ 00202 00203 /* .. Local Scalars .. */ 00204 /* .. */ 00205 /* .. External Functions .. */ 00206 /* .. */ 00207 /* .. External Subroutines .. */ 00208 /* .. */ 00209 /* .. Intrinsic Functions .. */ 00210 /* .. */ 00211 /* .. Executable Statements .. */ 00212 00213 /* Test the input parameters. */ 00214 00215 /* Parameter adjustments */ 00216 --ap; 00217 --bp; 00218 --w; 00219 z_dim1 = *ldz; 00220 z_offset = 1 + z_dim1; 00221 z__ -= z_offset; 00222 --work; 00223 --iwork; 00224 --ifail; 00225 00226 /* Function Body */ 00227 upper = lsame_(uplo, "U"); 00228 wantz = lsame_(jobz, "V"); 00229 alleig = lsame_(range, "A"); 00230 valeig = lsame_(range, "V"); 00231 indeig = lsame_(range, "I"); 00232 00233 *info = 0; 00234 if (*itype < 1 || *itype > 3) { 00235 *info = -1; 00236 } else if (! (wantz || lsame_(jobz, "N"))) { 00237 *info = -2; 00238 } else if (! (alleig || valeig || indeig)) { 00239 *info = -3; 00240 } else if (! (upper || lsame_(uplo, "L"))) { 00241 *info = -4; 00242 } else if (*n < 0) { 00243 *info = -5; 00244 } else { 00245 if (valeig) { 00246 if (*n > 0 && *vu <= *vl) { 00247 *info = -9; 00248 } 00249 } else if (indeig) { 00250 if (*il < 1) { 00251 *info = -10; 00252 } else if (*iu < min(*n,*il) || *iu > *n) { 00253 *info = -11; 00254 } 00255 } 00256 } 00257 if (*info == 0) { 00258 if (*ldz < 1 || wantz && *ldz < *n) { 00259 *info = -16; 00260 } 00261 } 00262 00263 if (*info != 0) { 00264 i__1 = -(*info); 00265 xerbla_("SSPGVX", &i__1); 00266 return 0; 00267 } 00268 00269 /* Quick return if possible */ 00270 00271 *m = 0; 00272 if (*n == 0) { 00273 return 0; 00274 } 00275 00276 /* Form a Cholesky factorization of B. */ 00277 00278 spptrf_(uplo, n, &bp[1], info); 00279 if (*info != 0) { 00280 *info = *n + *info; 00281 return 0; 00282 } 00283 00284 /* Transform problem to standard eigenvalue problem and solve. */ 00285 00286 sspgst_(itype, uplo, n, &ap[1], &bp[1], info); 00287 sspevx_(jobz, range, uplo, n, &ap[1], vl, vu, il, iu, abstol, m, &w[1], & 00288 z__[z_offset], ldz, &work[1], &iwork[1], &ifail[1], info); 00289 00290 if (wantz) { 00291 00292 /* Backtransform eigenvectors to the original problem. */ 00293 00294 if (*info > 0) { 00295 *m = *info - 1; 00296 } 00297 if (*itype == 1 || *itype == 2) { 00298 00299 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00300 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00301 00302 if (upper) { 00303 *(unsigned char *)trans = 'N'; 00304 } else { 00305 *(unsigned char *)trans = 'T'; 00306 } 00307 00308 i__1 = *m; 00309 for (j = 1; j <= i__1; ++j) { 00310 stpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 00311 1], &c__1); 00312 /* L10: */ 00313 } 00314 00315 } else if (*itype == 3) { 00316 00317 /* For B*A*x=(lambda)*x; */ 00318 /* backtransform eigenvectors: x = L*y or U'*y */ 00319 00320 if (upper) { 00321 *(unsigned char *)trans = 'T'; 00322 } else { 00323 *(unsigned char *)trans = 'N'; 00324 } 00325 00326 i__1 = *m; 00327 for (j = 1; j <= i__1; ++j) { 00328 stpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 00329 1], &c__1); 00330 /* L20: */ 00331 } 00332 } 00333 } 00334 00335 return 0; 00336 00337 /* End of SSPGVX */ 00338 00339 } /* sspgvx_ */