00001 /* sspgvd.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 sspgvd_(integer *itype, char *jobz, char *uplo, integer * 00021 n, real *ap, real *bp, real *w, real *z__, integer *ldz, real *work, 00022 integer *lwork, integer *iwork, integer *liwork, integer *info) 00023 { 00024 /* System generated locals */ 00025 integer z_dim1, z_offset, i__1; 00026 real r__1, r__2; 00027 00028 /* Local variables */ 00029 integer j, neig; 00030 extern logical lsame_(char *, char *); 00031 integer lwmin; 00032 char trans[1]; 00033 logical upper, wantz; 00034 extern /* Subroutine */ int stpmv_(char *, char *, char *, integer *, 00035 real *, real *, integer *), stpsv_(char *, 00036 char *, char *, integer *, real *, real *, integer *), xerbla_(char *, integer *); 00037 integer liwmin; 00038 extern /* Subroutine */ int sspevd_(char *, char *, integer *, real *, 00039 real *, real *, integer *, real *, integer *, integer *, integer * 00040 , integer *), spptrf_(char *, integer *, real *, 00041 integer *); 00042 logical lquery; 00043 extern /* Subroutine */ int sspgst_(integer *, char *, integer *, real *, 00044 real *, integer *); 00045 00046 00047 /* -- LAPACK driver routine (version 3.2) -- */ 00048 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00049 /* November 2006 */ 00050 00051 /* .. Scalar Arguments .. */ 00052 /* .. */ 00053 /* .. Array Arguments .. */ 00054 /* .. */ 00055 00056 /* Purpose */ 00057 /* ======= */ 00058 00059 /* SSPGVD computes all the eigenvalues, and optionally, the eigenvectors */ 00060 /* of a real generalized symmetric-definite eigenproblem, of the form */ 00061 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */ 00062 /* B are assumed to be symmetric, stored in packed format, and B is also */ 00063 /* positive definite. */ 00064 /* If eigenvectors are desired, it uses a divide and conquer algorithm. */ 00065 00066 /* The divide and conquer algorithm makes very mild assumptions about */ 00067 /* floating point arithmetic. It will work on machines with a guard */ 00068 /* digit in add/subtract, or on those binary machines without guard */ 00069 /* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ 00070 /* Cray-2. It could conceivably fail on hexadecimal or decimal machines */ 00071 /* without guard digits, but we know of none. */ 00072 00073 /* Arguments */ 00074 /* ========= */ 00075 00076 /* ITYPE (input) INTEGER */ 00077 /* Specifies the problem type to be solved: */ 00078 /* = 1: A*x = (lambda)*B*x */ 00079 /* = 2: A*B*x = (lambda)*x */ 00080 /* = 3: B*A*x = (lambda)*x */ 00081 00082 /* JOBZ (input) CHARACTER*1 */ 00083 /* = 'N': Compute eigenvalues only; */ 00084 /* = 'V': Compute eigenvalues and eigenvectors. */ 00085 00086 /* UPLO (input) CHARACTER*1 */ 00087 /* = 'U': Upper triangles of A and B are stored; */ 00088 /* = 'L': Lower triangles of A and B are stored. */ 00089 00090 /* N (input) INTEGER */ 00091 /* The order of the matrices A and B. N >= 0. */ 00092 00093 /* AP (input/output) REAL array, dimension (N*(N+1)/2) */ 00094 /* On entry, the upper or lower triangle of the symmetric matrix */ 00095 /* A, packed columnwise in a linear array. The j-th column of A */ 00096 /* is stored in the array AP as follows: */ 00097 /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ 00098 /* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */ 00099 00100 /* On exit, the contents of AP are destroyed. */ 00101 00102 /* BP (input/output) REAL array, dimension (N*(N+1)/2) */ 00103 /* On entry, the upper or lower triangle of the symmetric matrix */ 00104 /* B, packed columnwise in a linear array. The j-th column of B */ 00105 /* is stored in the array BP as follows: */ 00106 /* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; */ 00107 /* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. */ 00108 00109 /* On exit, the triangular factor U or L from the Cholesky */ 00110 /* factorization B = U**T*U or B = L*L**T, in the same storage */ 00111 /* format as B. */ 00112 00113 /* W (output) REAL array, dimension (N) */ 00114 /* If INFO = 0, the eigenvalues in ascending order. */ 00115 00116 /* Z (output) REAL array, dimension (LDZ, N) */ 00117 /* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */ 00118 /* eigenvectors. The eigenvectors are normalized as follows: */ 00119 /* if ITYPE = 1 or 2, Z**T*B*Z = I; */ 00120 /* if ITYPE = 3, Z**T*inv(B)*Z = I. */ 00121 /* If JOBZ = 'N', then Z is not referenced. */ 00122 00123 /* LDZ (input) INTEGER */ 00124 /* The leading dimension of the array Z. LDZ >= 1, and if */ 00125 /* JOBZ = 'V', LDZ >= max(1,N). */ 00126 00127 /* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */ 00128 /* On exit, if INFO = 0, WORK(1) returns the required LWORK. */ 00129 00130 /* LWORK (input) INTEGER */ 00131 /* The dimension of the array WORK. */ 00132 /* If N <= 1, LWORK >= 1. */ 00133 /* If JOBZ = 'N' and N > 1, LWORK >= 2*N. */ 00134 /* If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. */ 00135 00136 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00137 /* only calculates the required sizes of the WORK and IWORK */ 00138 /* arrays, returns these values as the first entries of the WORK */ 00139 /* and IWORK arrays, and no error message related to LWORK or */ 00140 /* LIWORK is issued by XERBLA. */ 00141 00142 /* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */ 00143 /* On exit, if INFO = 0, IWORK(1) returns the required LIWORK. */ 00144 00145 /* LIWORK (input) INTEGER */ 00146 /* The dimension of the array IWORK. */ 00147 /* If JOBZ = 'N' or N <= 1, LIWORK >= 1. */ 00148 /* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */ 00149 00150 /* If LIWORK = -1, then a workspace query is assumed; the */ 00151 /* routine only calculates the required sizes of the WORK and */ 00152 /* IWORK arrays, returns these values as the first entries of */ 00153 /* the WORK and IWORK arrays, and no error message related to */ 00154 /* LWORK or LIWORK is issued by XERBLA. */ 00155 00156 /* INFO (output) INTEGER */ 00157 /* = 0: successful exit */ 00158 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00159 /* > 0: SPPTRF or SSPEVD returned an error code: */ 00160 /* <= N: if INFO = i, SSPEVD failed to converge; */ 00161 /* i off-diagonal elements of an intermediate */ 00162 /* tridiagonal form did not converge to zero; */ 00163 /* > N: if INFO = N + i, for 1 <= i <= N, then the leading */ 00164 /* minor of order i of B is not positive definite. */ 00165 /* The factorization of B could not be completed and */ 00166 /* no eigenvalues or eigenvectors were computed. */ 00167 00168 /* Further Details */ 00169 /* =============== */ 00170 00171 /* Based on contributions by */ 00172 /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ 00173 00174 /* ===================================================================== */ 00175 00176 /* .. Parameters .. */ 00177 /* .. */ 00178 /* .. Local Scalars .. */ 00179 /* .. */ 00180 /* .. External Functions .. */ 00181 /* .. */ 00182 /* .. External Subroutines .. */ 00183 /* .. */ 00184 /* .. Intrinsic Functions .. */ 00185 /* .. */ 00186 /* .. Executable Statements .. */ 00187 00188 /* Test the input parameters. */ 00189 00190 /* Parameter adjustments */ 00191 --ap; 00192 --bp; 00193 --w; 00194 z_dim1 = *ldz; 00195 z_offset = 1 + z_dim1; 00196 z__ -= z_offset; 00197 --work; 00198 --iwork; 00199 00200 /* Function Body */ 00201 wantz = lsame_(jobz, "V"); 00202 upper = lsame_(uplo, "U"); 00203 lquery = *lwork == -1 || *liwork == -1; 00204 00205 *info = 0; 00206 if (*itype < 1 || *itype > 3) { 00207 *info = -1; 00208 } else if (! (wantz || lsame_(jobz, "N"))) { 00209 *info = -2; 00210 } else if (! (upper || lsame_(uplo, "L"))) { 00211 *info = -3; 00212 } else if (*n < 0) { 00213 *info = -4; 00214 } else if (*ldz < 1 || wantz && *ldz < *n) { 00215 *info = -9; 00216 } 00217 00218 if (*info == 0) { 00219 if (*n <= 1) { 00220 liwmin = 1; 00221 lwmin = 1; 00222 } else { 00223 if (wantz) { 00224 liwmin = *n * 5 + 3; 00225 /* Computing 2nd power */ 00226 i__1 = *n; 00227 lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); 00228 } else { 00229 liwmin = 1; 00230 lwmin = *n << 1; 00231 } 00232 } 00233 work[1] = (real) lwmin; 00234 iwork[1] = liwmin; 00235 00236 if (*lwork < lwmin && ! lquery) { 00237 *info = -11; 00238 } else if (*liwork < liwmin && ! lquery) { 00239 *info = -13; 00240 } 00241 } 00242 00243 if (*info != 0) { 00244 i__1 = -(*info); 00245 xerbla_("SSPGVD", &i__1); 00246 return 0; 00247 } else if (lquery) { 00248 return 0; 00249 } 00250 00251 /* Quick return if possible */ 00252 00253 if (*n == 0) { 00254 return 0; 00255 } 00256 00257 /* Form a Cholesky factorization of BP. */ 00258 00259 spptrf_(uplo, n, &bp[1], info); 00260 if (*info != 0) { 00261 *info = *n + *info; 00262 return 0; 00263 } 00264 00265 /* Transform problem to standard eigenvalue problem and solve. */ 00266 00267 sspgst_(itype, uplo, n, &ap[1], &bp[1], info); 00268 sspevd_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], 00269 lwork, &iwork[1], liwork, info); 00270 /* Computing MAX */ 00271 r__1 = (real) lwmin; 00272 lwmin = dmax(r__1,work[1]); 00273 /* Computing MAX */ 00274 r__1 = (real) liwmin, r__2 = (real) iwork[1]; 00275 liwmin = dmax(r__1,r__2); 00276 00277 if (wantz) { 00278 00279 /* Backtransform eigenvectors to the original problem. */ 00280 00281 neig = *n; 00282 if (*info > 0) { 00283 neig = *info - 1; 00284 } 00285 if (*itype == 1 || *itype == 2) { 00286 00287 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00288 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00289 00290 if (upper) { 00291 *(unsigned char *)trans = 'N'; 00292 } else { 00293 *(unsigned char *)trans = 'T'; 00294 } 00295 00296 i__1 = neig; 00297 for (j = 1; j <= i__1; ++j) { 00298 stpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 00299 1], &c__1); 00300 /* L10: */ 00301 } 00302 00303 } else if (*itype == 3) { 00304 00305 /* For B*A*x=(lambda)*x; */ 00306 /* backtransform eigenvectors: x = L*y or U'*y */ 00307 00308 if (upper) { 00309 *(unsigned char *)trans = 'T'; 00310 } else { 00311 *(unsigned char *)trans = 'N'; 00312 } 00313 00314 i__1 = neig; 00315 for (j = 1; j <= i__1; ++j) { 00316 stpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 00317 1], &c__1); 00318 /* L20: */ 00319 } 00320 } 00321 } 00322 00323 work[1] = (real) lwmin; 00324 iwork[1] = liwmin; 00325 00326 return 0; 00327 00328 /* End of SSPGVD */ 00329 00330 } /* sspgvd_ */