00001 /* dspgvd.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 dspgvd_(integer *itype, char *jobz, char *uplo, integer * 00021 n, doublereal *ap, doublereal *bp, doublereal *w, doublereal *z__, 00022 integer *ldz, doublereal *work, integer *lwork, integer *iwork, 00023 integer *liwork, integer *info) 00024 { 00025 /* System generated locals */ 00026 integer z_dim1, z_offset, i__1; 00027 doublereal d__1, d__2; 00028 00029 /* Local variables */ 00030 integer j, neig; 00031 extern logical lsame_(char *, char *); 00032 integer lwmin; 00033 char trans[1]; 00034 logical upper; 00035 extern /* Subroutine */ int dtpmv_(char *, char *, char *, integer *, 00036 doublereal *, doublereal *, integer *), 00037 dtpsv_(char *, char *, char *, integer *, doublereal *, 00038 doublereal *, integer *); 00039 logical wantz; 00040 extern /* Subroutine */ int xerbla_(char *, integer *), dspevd_( 00041 char *, char *, integer *, doublereal *, doublereal *, doublereal 00042 *, integer *, doublereal *, integer *, integer *, integer *, 00043 integer *); 00044 integer liwmin; 00045 extern /* Subroutine */ int dpptrf_(char *, integer *, doublereal *, 00046 integer *), dspgst_(integer *, char *, integer *, 00047 doublereal *, doublereal *, integer *); 00048 logical lquery; 00049 00050 00051 /* -- LAPACK driver routine (version 3.2) -- */ 00052 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00053 /* November 2006 */ 00054 00055 /* .. Scalar Arguments .. */ 00056 /* .. */ 00057 /* .. Array Arguments .. */ 00058 /* .. */ 00059 00060 /* Purpose */ 00061 /* ======= */ 00062 00063 /* DSPGVD computes all the eigenvalues, and optionally, the eigenvectors */ 00064 /* of a real generalized symmetric-definite eigenproblem, of the form */ 00065 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */ 00066 /* B are assumed to be symmetric, stored in packed format, and B is also */ 00067 /* positive definite. */ 00068 /* If eigenvectors are desired, it uses a divide and conquer algorithm. */ 00069 00070 /* The divide and conquer algorithm makes very mild assumptions about */ 00071 /* floating point arithmetic. It will work on machines with a guard */ 00072 /* digit in add/subtract, or on those binary machines without guard */ 00073 /* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ 00074 /* Cray-2. It could conceivably fail on hexadecimal or decimal machines */ 00075 /* without guard digits, but we know of none. */ 00076 00077 /* Arguments */ 00078 /* ========= */ 00079 00080 /* ITYPE (input) INTEGER */ 00081 /* Specifies the problem type to be solved: */ 00082 /* = 1: A*x = (lambda)*B*x */ 00083 /* = 2: A*B*x = (lambda)*x */ 00084 /* = 3: B*A*x = (lambda)*x */ 00085 00086 /* JOBZ (input) CHARACTER*1 */ 00087 /* = 'N': Compute eigenvalues only; */ 00088 /* = 'V': Compute eigenvalues and eigenvectors. */ 00089 00090 /* UPLO (input) CHARACTER*1 */ 00091 /* = 'U': Upper triangles of A and B are stored; */ 00092 /* = 'L': Lower triangles of A and B are stored. */ 00093 00094 /* N (input) INTEGER */ 00095 /* The order of the matrices A and B. N >= 0. */ 00096 00097 /* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */ 00098 /* On entry, the upper or lower triangle of the symmetric matrix */ 00099 /* A, packed columnwise in a linear array. The j-th column of A */ 00100 /* is stored in the array AP as follows: */ 00101 /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ 00102 /* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */ 00103 00104 /* On exit, the contents of AP are destroyed. */ 00105 00106 /* BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */ 00107 /* On entry, the upper or lower triangle of the symmetric matrix */ 00108 /* B, packed columnwise in a linear array. The j-th column of B */ 00109 /* is stored in the array BP as follows: */ 00110 /* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; */ 00111 /* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. */ 00112 00113 /* On exit, the triangular factor U or L from the Cholesky */ 00114 /* factorization B = U**T*U or B = L*L**T, in the same storage */ 00115 /* format as B. */ 00116 00117 /* W (output) DOUBLE PRECISION array, dimension (N) */ 00118 /* If INFO = 0, the eigenvalues in ascending order. */ 00119 00120 /* Z (output) DOUBLE PRECISION array, dimension (LDZ, N) */ 00121 /* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */ 00122 /* eigenvectors. The eigenvectors are normalized as follows: */ 00123 /* if ITYPE = 1 or 2, Z**T*B*Z = I; */ 00124 /* if ITYPE = 3, Z**T*inv(B)*Z = I. */ 00125 /* If JOBZ = 'N', then Z is not referenced. */ 00126 00127 /* LDZ (input) INTEGER */ 00128 /* The leading dimension of the array Z. LDZ >= 1, and if */ 00129 /* JOBZ = 'V', LDZ >= max(1,N). */ 00130 00131 /* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ 00132 /* On exit, if INFO = 0, WORK(1) returns the required LWORK. */ 00133 00134 /* LWORK (input) INTEGER */ 00135 /* The dimension of the array WORK. */ 00136 /* If N <= 1, LWORK >= 1. */ 00137 /* If JOBZ = 'N' and N > 1, LWORK >= 2*N. */ 00138 /* If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. */ 00139 00140 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00141 /* only calculates the required sizes of the WORK and IWORK */ 00142 /* arrays, returns these values as the first entries of the WORK */ 00143 /* and IWORK arrays, and no error message related to LWORK or */ 00144 /* LIWORK is issued by XERBLA. */ 00145 00146 /* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */ 00147 /* On exit, if INFO = 0, IWORK(1) returns the required LIWORK. */ 00148 00149 /* LIWORK (input) INTEGER */ 00150 /* The dimension of the array IWORK. */ 00151 /* If JOBZ = 'N' or N <= 1, LIWORK >= 1. */ 00152 /* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */ 00153 00154 /* If LIWORK = -1, then a workspace query is assumed; the */ 00155 /* routine only calculates the required sizes of the WORK and */ 00156 /* IWORK arrays, returns these values as the first entries of */ 00157 /* the WORK and IWORK arrays, and no error message related to */ 00158 /* LWORK or LIWORK is issued by XERBLA. */ 00159 00160 /* INFO (output) INTEGER */ 00161 /* = 0: successful exit */ 00162 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00163 /* > 0: DPPTRF or DSPEVD returned an error code: */ 00164 /* <= N: if INFO = i, DSPEVD failed to converge; */ 00165 /* i off-diagonal elements of an intermediate */ 00166 /* tridiagonal form did not converge to zero; */ 00167 /* > N: if INFO = N + i, for 1 <= i <= N, then the leading */ 00168 /* minor of order i of B is not positive definite. */ 00169 /* The factorization of B could not be completed and */ 00170 /* no eigenvalues or eigenvectors were computed. */ 00171 00172 /* Further Details */ 00173 /* =============== */ 00174 00175 /* Based on contributions by */ 00176 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ 00177 00178 /* ===================================================================== */ 00179 00180 /* .. Parameters .. */ 00181 /* .. */ 00182 /* .. Local Scalars .. */ 00183 /* .. */ 00184 /* .. External Functions .. */ 00185 /* .. */ 00186 /* .. External Subroutines .. */ 00187 /* .. */ 00188 /* .. Intrinsic Functions .. */ 00189 /* .. */ 00190 /* .. Executable Statements .. */ 00191 00192 /* Test the input parameters. */ 00193 00194 /* Parameter adjustments */ 00195 --ap; 00196 --bp; 00197 --w; 00198 z_dim1 = *ldz; 00199 z_offset = 1 + z_dim1; 00200 z__ -= z_offset; 00201 --work; 00202 --iwork; 00203 00204 /* Function Body */ 00205 wantz = lsame_(jobz, "V"); 00206 upper = lsame_(uplo, "U"); 00207 lquery = *lwork == -1 || *liwork == -1; 00208 00209 *info = 0; 00210 if (*itype < 1 || *itype > 3) { 00211 *info = -1; 00212 } else if (! (wantz || lsame_(jobz, "N"))) { 00213 *info = -2; 00214 } else if (! (upper || lsame_(uplo, "L"))) { 00215 *info = -3; 00216 } else if (*n < 0) { 00217 *info = -4; 00218 } else if (*ldz < 1 || wantz && *ldz < *n) { 00219 *info = -9; 00220 } 00221 00222 if (*info == 0) { 00223 if (*n <= 1) { 00224 liwmin = 1; 00225 lwmin = 1; 00226 } else { 00227 if (wantz) { 00228 liwmin = *n * 5 + 3; 00229 /* Computing 2nd power */ 00230 i__1 = *n; 00231 lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); 00232 } else { 00233 liwmin = 1; 00234 lwmin = *n << 1; 00235 } 00236 } 00237 work[1] = (doublereal) lwmin; 00238 iwork[1] = liwmin; 00239 00240 if (*lwork < lwmin && ! lquery) { 00241 *info = -11; 00242 } else if (*liwork < liwmin && ! lquery) { 00243 *info = -13; 00244 } 00245 } 00246 00247 if (*info != 0) { 00248 i__1 = -(*info); 00249 xerbla_("DSPGVD", &i__1); 00250 return 0; 00251 } else if (lquery) { 00252 return 0; 00253 } 00254 00255 /* Quick return if possible */ 00256 00257 if (*n == 0) { 00258 return 0; 00259 } 00260 00261 /* Form a Cholesky factorization of BP. */ 00262 00263 dpptrf_(uplo, n, &bp[1], info); 00264 if (*info != 0) { 00265 *info = *n + *info; 00266 return 0; 00267 } 00268 00269 /* Transform problem to standard eigenvalue problem and solve. */ 00270 00271 dspgst_(itype, uplo, n, &ap[1], &bp[1], info); 00272 dspevd_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], 00273 lwork, &iwork[1], liwork, info); 00274 /* Computing MAX */ 00275 d__1 = (doublereal) lwmin; 00276 lwmin = (integer) max(d__1,work[1]); 00277 /* Computing MAX */ 00278 d__1 = (doublereal) liwmin, d__2 = (doublereal) iwork[1]; 00279 liwmin = (integer) max(d__1,d__2); 00280 00281 if (wantz) { 00282 00283 /* Backtransform eigenvectors to the original problem. */ 00284 00285 neig = *n; 00286 if (*info > 0) { 00287 neig = *info - 1; 00288 } 00289 if (*itype == 1 || *itype == 2) { 00290 00291 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00292 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00293 00294 if (upper) { 00295 *(unsigned char *)trans = 'N'; 00296 } else { 00297 *(unsigned char *)trans = 'T'; 00298 } 00299 00300 i__1 = neig; 00301 for (j = 1; j <= i__1; ++j) { 00302 dtpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 00303 1], &c__1); 00304 /* L10: */ 00305 } 00306 00307 } else if (*itype == 3) { 00308 00309 /* For B*A*x=(lambda)*x; */ 00310 /* backtransform eigenvectors: x = L*y or U'*y */ 00311 00312 if (upper) { 00313 *(unsigned char *)trans = 'T'; 00314 } else { 00315 *(unsigned char *)trans = 'N'; 00316 } 00317 00318 i__1 = neig; 00319 for (j = 1; j <= i__1; ++j) { 00320 dtpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 00321 1], &c__1); 00322 /* L20: */ 00323 } 00324 } 00325 } 00326 00327 work[1] = (doublereal) lwmin; 00328 iwork[1] = liwmin; 00329 00330 return 0; 00331 00332 /* End of DSPGVD */ 00333 00334 } /* dspgvd_ */