00001 /* zhpgvd.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 zhpgvd_(integer *itype, char *jobz, char *uplo, integer * 00021 n, doublecomplex *ap, doublecomplex *bp, doublereal *w, doublecomplex 00022 *z__, integer *ldz, doublecomplex *work, integer *lwork, doublereal * 00023 rwork, integer *lrwork, integer *iwork, integer *liwork, integer * 00024 info) 00025 { 00026 /* System generated locals */ 00027 integer z_dim1, z_offset, i__1; 00028 doublereal d__1, d__2; 00029 00030 /* Local variables */ 00031 integer j, neig; 00032 extern logical lsame_(char *, char *); 00033 integer lwmin; 00034 char trans[1]; 00035 logical upper, wantz; 00036 extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, 00037 doublecomplex *, doublecomplex *, integer *), ztpsv_(char *, char *, char *, integer *, doublecomplex * 00038 , doublecomplex *, integer *), xerbla_( 00039 char *, integer *); 00040 integer liwmin; 00041 extern /* Subroutine */ int zhpevd_(char *, char *, integer *, 00042 doublecomplex *, doublereal *, doublecomplex *, integer *, 00043 doublecomplex *, integer *, doublereal *, integer *, integer *, 00044 integer *, integer *); 00045 integer lrwmin; 00046 extern /* Subroutine */ int zhpgst_(integer *, char *, integer *, 00047 doublecomplex *, doublecomplex *, integer *); 00048 logical lquery; 00049 extern /* Subroutine */ int zpptrf_(char *, integer *, doublecomplex *, 00050 integer *); 00051 00052 00053 /* -- LAPACK driver routine (version 3.2) -- */ 00054 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00055 /* November 2006 */ 00056 00057 /* .. Scalar Arguments .. */ 00058 /* .. */ 00059 /* .. Array Arguments .. */ 00060 /* .. */ 00061 00062 /* Purpose */ 00063 /* ======= */ 00064 00065 /* ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors */ 00066 /* of a complex generalized Hermitian-definite eigenproblem, of the form */ 00067 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */ 00068 /* B are assumed to be Hermitian, stored in packed format, and B is also */ 00069 /* 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 /* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) */ 00100 /* On entry, the upper or lower triangle of the Hermitian matrix */ 00101 /* A, packed columnwise in a linear array. The j-th column of A */ 00102 /* is stored in the array AP as follows: */ 00103 /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ 00104 /* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */ 00105 00106 /* On exit, the contents of AP are destroyed. */ 00107 00108 /* BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) */ 00109 /* On entry, the upper or lower triangle of the Hermitian matrix */ 00110 /* B, packed columnwise in a linear array. The j-th column of B */ 00111 /* is stored in the array BP as follows: */ 00112 /* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; */ 00113 /* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. */ 00114 00115 /* On exit, the triangular factor U or L from the Cholesky */ 00116 /* factorization B = U**H*U or B = L*L**H, in the same storage */ 00117 /* format as B. */ 00118 00119 /* W (output) DOUBLE PRECISION array, dimension (N) */ 00120 /* If INFO = 0, the eigenvalues in ascending order. */ 00121 00122 /* Z (output) COMPLEX*16 array, dimension (LDZ, N) */ 00123 /* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */ 00124 /* eigenvectors. The eigenvectors are normalized as follows: */ 00125 /* if ITYPE = 1 or 2, Z**H*B*Z = I; */ 00126 /* if ITYPE = 3, Z**H*inv(B)*Z = I. */ 00127 /* If JOBZ = 'N', then Z is not referenced. */ 00128 00129 /* LDZ (input) INTEGER */ 00130 /* The leading dimension of the array Z. LDZ >= 1, and if */ 00131 /* JOBZ = 'V', LDZ >= max(1,N). */ 00132 00133 /* WORK (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) */ 00134 /* On exit, if INFO = 0, WORK(1) returns the required LWORK. */ 00135 00136 /* LWORK (input) INTEGER */ 00137 /* The dimension of array WORK. */ 00138 /* If N <= 1, LWORK >= 1. */ 00139 /* If JOBZ = 'N' and N > 1, LWORK >= N. */ 00140 /* If JOBZ = 'V' and N > 1, LWORK >= 2*N. */ 00141 00142 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00143 /* only calculates the required sizes of the WORK, RWORK and */ 00144 /* IWORK arrays, returns these values as the first entries of */ 00145 /* the WORK, RWORK and IWORK arrays, and no error message */ 00146 /* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ 00147 00148 /* RWORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */ 00149 /* On exit, if INFO = 0, RWORK(1) returns the required LRWORK. */ 00150 00151 /* LRWORK (input) INTEGER */ 00152 /* The dimension of array RWORK. */ 00153 /* If N <= 1, LRWORK >= 1. */ 00154 /* If JOBZ = 'N' and N > 1, LRWORK >= N. */ 00155 /* If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. */ 00156 00157 /* If LRWORK = -1, then a workspace query is assumed; the */ 00158 /* routine only calculates the required sizes of the WORK, RWORK */ 00159 /* and IWORK arrays, returns these values as the first entries */ 00160 /* of the WORK, RWORK and IWORK arrays, and no error message */ 00161 /* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ 00162 00163 /* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */ 00164 /* On exit, if INFO = 0, IWORK(1) returns the required LIWORK. */ 00165 00166 /* LIWORK (input) INTEGER */ 00167 /* The dimension of array IWORK. */ 00168 /* If JOBZ = 'N' or N <= 1, LIWORK >= 1. */ 00169 /* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */ 00170 00171 /* If LIWORK = -1, then a workspace query is assumed; the */ 00172 /* routine only calculates the required sizes of the WORK, RWORK */ 00173 /* and IWORK arrays, returns these values as the first entries */ 00174 /* of the WORK, RWORK and IWORK arrays, and no error message */ 00175 /* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ 00176 00177 /* INFO (output) INTEGER */ 00178 /* = 0: successful exit */ 00179 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00180 /* > 0: ZPPTRF or ZHPEVD returned an error code: */ 00181 /* <= N: if INFO = i, ZHPEVD failed to converge; */ 00182 /* i off-diagonal elements of an intermediate */ 00183 /* tridiagonal form did not convergeto zero; */ 00184 /* > N: if INFO = N + i, for 1 <= i <= n, then the leading */ 00185 /* minor of order i of B is not positive definite. */ 00186 /* The factorization of B could not be completed and */ 00187 /* no eigenvalues or eigenvectors were computed. */ 00188 00189 /* Further Details */ 00190 /* =============== */ 00191 00192 /* Based on contributions by */ 00193 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ 00194 00195 /* ===================================================================== */ 00196 00197 /* .. Local Scalars .. */ 00198 /* .. */ 00199 /* .. External Functions .. */ 00200 /* .. */ 00201 /* .. External Subroutines .. */ 00202 /* .. */ 00203 /* .. Intrinsic Functions .. */ 00204 /* .. */ 00205 /* .. Executable Statements .. */ 00206 00207 /* Test the input parameters. */ 00208 00209 /* Parameter adjustments */ 00210 --ap; 00211 --bp; 00212 --w; 00213 z_dim1 = *ldz; 00214 z_offset = 1 + z_dim1; 00215 z__ -= z_offset; 00216 --work; 00217 --rwork; 00218 --iwork; 00219 00220 /* Function Body */ 00221 wantz = lsame_(jobz, "V"); 00222 upper = lsame_(uplo, "U"); 00223 lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; 00224 00225 *info = 0; 00226 if (*itype < 1 || *itype > 3) { 00227 *info = -1; 00228 } else if (! (wantz || lsame_(jobz, "N"))) { 00229 *info = -2; 00230 } else if (! (upper || lsame_(uplo, "L"))) { 00231 *info = -3; 00232 } else if (*n < 0) { 00233 *info = -4; 00234 } else if (*ldz < 1 || wantz && *ldz < *n) { 00235 *info = -9; 00236 } 00237 00238 if (*info == 0) { 00239 if (*n <= 1) { 00240 lwmin = 1; 00241 liwmin = 1; 00242 lrwmin = 1; 00243 } else { 00244 if (wantz) { 00245 lwmin = *n << 1; 00246 /* Computing 2nd power */ 00247 i__1 = *n; 00248 lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1); 00249 liwmin = *n * 5 + 3; 00250 } else { 00251 lwmin = *n; 00252 lrwmin = *n; 00253 liwmin = 1; 00254 } 00255 } 00256 00257 work[1].r = (doublereal) lwmin, work[1].i = 0.; 00258 rwork[1] = (doublereal) lrwmin; 00259 iwork[1] = liwmin; 00260 if (*lwork < lwmin && ! lquery) { 00261 *info = -11; 00262 } else if (*lrwork < lrwmin && ! lquery) { 00263 *info = -13; 00264 } else if (*liwork < liwmin && ! lquery) { 00265 *info = -15; 00266 } 00267 } 00268 00269 if (*info != 0) { 00270 i__1 = -(*info); 00271 xerbla_("ZHPGVD", &i__1); 00272 return 0; 00273 } else if (lquery) { 00274 return 0; 00275 } 00276 00277 /* Quick return if possible */ 00278 00279 if (*n == 0) { 00280 return 0; 00281 } 00282 00283 /* Form a Cholesky factorization of B. */ 00284 00285 zpptrf_(uplo, n, &bp[1], info); 00286 if (*info != 0) { 00287 *info = *n + *info; 00288 return 0; 00289 } 00290 00291 /* Transform problem to standard eigenvalue problem and solve. */ 00292 00293 zhpgst_(itype, uplo, n, &ap[1], &bp[1], info); 00294 zhpevd_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], 00295 lwork, &rwork[1], lrwork, &iwork[1], liwork, info); 00296 /* Computing MAX */ 00297 d__1 = (doublereal) lwmin, d__2 = work[1].r; 00298 lwmin = (integer) max(d__1,d__2); 00299 /* Computing MAX */ 00300 d__1 = (doublereal) lrwmin; 00301 lrwmin = (integer) max(d__1,rwork[1]); 00302 /* Computing MAX */ 00303 d__1 = (doublereal) liwmin, d__2 = (doublereal) iwork[1]; 00304 liwmin = (integer) max(d__1,d__2); 00305 00306 if (wantz) { 00307 00308 /* Backtransform eigenvectors to the original problem. */ 00309 00310 neig = *n; 00311 if (*info > 0) { 00312 neig = *info - 1; 00313 } 00314 if (*itype == 1 || *itype == 2) { 00315 00316 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00317 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00318 00319 if (upper) { 00320 *(unsigned char *)trans = 'N'; 00321 } else { 00322 *(unsigned char *)trans = 'C'; 00323 } 00324 00325 i__1 = neig; 00326 for (j = 1; j <= i__1; ++j) { 00327 ztpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 00328 1], &c__1); 00329 /* L10: */ 00330 } 00331 00332 } else if (*itype == 3) { 00333 00334 /* For B*A*x=(lambda)*x; */ 00335 /* backtransform eigenvectors: x = L*y or U'*y */ 00336 00337 if (upper) { 00338 *(unsigned char *)trans = 'C'; 00339 } else { 00340 *(unsigned char *)trans = 'N'; 00341 } 00342 00343 i__1 = neig; 00344 for (j = 1; j <= i__1; ++j) { 00345 ztpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 00346 1], &c__1); 00347 /* L20: */ 00348 } 00349 } 00350 } 00351 00352 work[1].r = (doublereal) lwmin, work[1].i = 0.; 00353 rwork[1] = (doublereal) lrwmin; 00354 iwork[1] = liwmin; 00355 return 0; 00356 00357 /* End of ZHPGVD */ 00358 00359 } /* zhpgvd_ */