00001 /* zhegv.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 doublecomplex c_b1 = {1.,0.}; 00019 static integer c__1 = 1; 00020 static integer c_n1 = -1; 00021 00022 /* Subroutine */ int zhegv_(integer *itype, char *jobz, char *uplo, integer * 00023 n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 00024 doublereal *w, doublecomplex *work, integer *lwork, doublereal *rwork, 00025 integer *info) 00026 { 00027 /* System generated locals */ 00028 integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; 00029 00030 /* Local variables */ 00031 integer nb, neig; 00032 extern logical lsame_(char *, char *); 00033 extern /* Subroutine */ int zheev_(char *, char *, integer *, 00034 doublecomplex *, integer *, doublereal *, doublecomplex *, 00035 integer *, doublereal *, integer *); 00036 char trans[1]; 00037 logical upper, wantz; 00038 extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *, 00039 integer *, integer *, doublecomplex *, doublecomplex *, integer *, 00040 doublecomplex *, integer *), 00041 ztrsm_(char *, char *, char *, char *, integer *, integer *, 00042 doublecomplex *, doublecomplex *, integer *, doublecomplex *, 00043 integer *), xerbla_(char *, 00044 integer *); 00045 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00046 integer *, integer *); 00047 extern /* Subroutine */ int zhegst_(integer *, char *, integer *, 00048 doublecomplex *, integer *, doublecomplex *, integer *, integer *); 00049 integer lwkopt; 00050 logical lquery; 00051 extern /* Subroutine */ int zpotrf_(char *, integer *, doublecomplex *, 00052 integer *, integer *); 00053 00054 00055 /* -- LAPACK driver routine (version 3.2) -- */ 00056 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00057 /* November 2006 */ 00058 00059 /* .. Scalar Arguments .. */ 00060 /* .. */ 00061 /* .. Array Arguments .. */ 00062 /* .. */ 00063 00064 /* Purpose */ 00065 /* ======= */ 00066 00067 /* ZHEGV computes all the eigenvalues, and optionally, the eigenvectors */ 00068 /* of a complex generalized Hermitian-definite eigenproblem, of the form */ 00069 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. */ 00070 /* Here A and B are assumed to be Hermitian and B is also */ 00071 /* positive definite. */ 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 /* A (input/output) COMPLEX*16 array, dimension (LDA, N) */ 00094 /* On entry, the Hermitian matrix A. If UPLO = 'U', the */ 00095 /* leading N-by-N upper triangular part of A contains the */ 00096 /* upper triangular part of the matrix A. If UPLO = 'L', */ 00097 /* the leading N-by-N lower triangular part of A contains */ 00098 /* the lower triangular part of the matrix A. */ 00099 00100 /* On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ 00101 /* matrix Z of eigenvectors. The eigenvectors are normalized */ 00102 /* as follows: */ 00103 /* if ITYPE = 1 or 2, Z**H*B*Z = I; */ 00104 /* if ITYPE = 3, Z**H*inv(B)*Z = I. */ 00105 /* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */ 00106 /* or the lower triangle (if UPLO='L') of A, including the */ 00107 /* diagonal, is destroyed. */ 00108 00109 /* LDA (input) INTEGER */ 00110 /* The leading dimension of the array A. LDA >= max(1,N). */ 00111 00112 /* B (input/output) COMPLEX*16 array, dimension (LDB, N) */ 00113 /* On entry, the Hermitian positive definite matrix B. */ 00114 /* If UPLO = 'U', the leading N-by-N upper triangular part of B */ 00115 /* contains the upper triangular part of the matrix B. */ 00116 /* If UPLO = 'L', the leading N-by-N lower triangular part of B */ 00117 /* contains the lower triangular part of the matrix B. */ 00118 00119 /* On exit, if INFO <= N, the part of B containing the matrix is */ 00120 /* overwritten by the triangular factor U or L from the Cholesky */ 00121 /* factorization B = U**H*U or B = L*L**H. */ 00122 00123 /* LDB (input) INTEGER */ 00124 /* The leading dimension of the array B. LDB >= max(1,N). */ 00125 00126 /* W (output) DOUBLE PRECISION array, dimension (N) */ 00127 /* If INFO = 0, the eigenvalues in ascending order. */ 00128 00129 /* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */ 00130 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00131 00132 /* LWORK (input) INTEGER */ 00133 /* The length of the array WORK. LWORK >= max(1,2*N-1). */ 00134 /* For optimal efficiency, LWORK >= (NB+1)*N, */ 00135 /* where NB is the blocksize for ZHETRD returned by ILAENV. */ 00136 00137 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00138 /* only calculates the optimal size of the WORK array, returns */ 00139 /* this value as the first entry of the WORK array, and no error */ 00140 /* message related to LWORK is issued by XERBLA. */ 00141 00142 /* RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2)) */ 00143 00144 /* INFO (output) INTEGER */ 00145 /* = 0: successful exit */ 00146 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00147 /* > 0: ZPOTRF or ZHEEV returned an error code: */ 00148 /* <= N: if INFO = i, ZHEEV failed to converge; */ 00149 /* i off-diagonal elements of an intermediate */ 00150 /* tridiagonal form did not converge to zero; */ 00151 /* > N: if INFO = N + i, for 1 <= i <= N, then the leading */ 00152 /* minor of order i of B is not positive definite. */ 00153 /* The factorization of B could not be completed and */ 00154 /* no eigenvalues or eigenvectors were computed. */ 00155 00156 /* ===================================================================== */ 00157 00158 /* .. Parameters .. */ 00159 /* .. */ 00160 /* .. Local Scalars .. */ 00161 /* .. */ 00162 /* .. External Functions .. */ 00163 /* .. */ 00164 /* .. External Subroutines .. */ 00165 /* .. */ 00166 /* .. Intrinsic Functions .. */ 00167 /* .. */ 00168 /* .. Executable Statements .. */ 00169 00170 /* Test the input parameters. */ 00171 00172 /* Parameter adjustments */ 00173 a_dim1 = *lda; 00174 a_offset = 1 + a_dim1; 00175 a -= a_offset; 00176 b_dim1 = *ldb; 00177 b_offset = 1 + b_dim1; 00178 b -= b_offset; 00179 --w; 00180 --work; 00181 --rwork; 00182 00183 /* Function Body */ 00184 wantz = lsame_(jobz, "V"); 00185 upper = lsame_(uplo, "U"); 00186 lquery = *lwork == -1; 00187 00188 *info = 0; 00189 if (*itype < 1 || *itype > 3) { 00190 *info = -1; 00191 } else if (! (wantz || lsame_(jobz, "N"))) { 00192 *info = -2; 00193 } else if (! (upper || lsame_(uplo, "L"))) { 00194 *info = -3; 00195 } else if (*n < 0) { 00196 *info = -4; 00197 } else if (*lda < max(1,*n)) { 00198 *info = -6; 00199 } else if (*ldb < max(1,*n)) { 00200 *info = -8; 00201 } 00202 00203 if (*info == 0) { 00204 nb = ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1); 00205 /* Computing MAX */ 00206 i__1 = 1, i__2 = (nb + 1) * *n; 00207 lwkopt = max(i__1,i__2); 00208 work[1].r = (doublereal) lwkopt, work[1].i = 0.; 00209 00210 /* Computing MAX */ 00211 i__1 = 1, i__2 = (*n << 1) - 1; 00212 if (*lwork < max(i__1,i__2) && ! lquery) { 00213 *info = -11; 00214 } 00215 } 00216 00217 if (*info != 0) { 00218 i__1 = -(*info); 00219 xerbla_("ZHEGV ", &i__1); 00220 return 0; 00221 } else if (lquery) { 00222 return 0; 00223 } 00224 00225 /* Quick return if possible */ 00226 00227 if (*n == 0) { 00228 return 0; 00229 } 00230 00231 /* Form a Cholesky factorization of B. */ 00232 00233 zpotrf_(uplo, n, &b[b_offset], ldb, info); 00234 if (*info != 0) { 00235 *info = *n + *info; 00236 return 0; 00237 } 00238 00239 /* Transform problem to standard eigenvalue problem and solve. */ 00240 00241 zhegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info); 00242 zheev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &rwork[1] 00243 , info); 00244 00245 if (wantz) { 00246 00247 /* Backtransform eigenvectors to the original problem. */ 00248 00249 neig = *n; 00250 if (*info > 0) { 00251 neig = *info - 1; 00252 } 00253 if (*itype == 1 || *itype == 2) { 00254 00255 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00256 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00257 00258 if (upper) { 00259 *(unsigned char *)trans = 'N'; 00260 } else { 00261 *(unsigned char *)trans = 'C'; 00262 } 00263 00264 ztrsm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[ 00265 b_offset], ldb, &a[a_offset], lda); 00266 00267 } else if (*itype == 3) { 00268 00269 /* For B*A*x=(lambda)*x; */ 00270 /* backtransform eigenvectors: x = L*y or U'*y */ 00271 00272 if (upper) { 00273 *(unsigned char *)trans = 'C'; 00274 } else { 00275 *(unsigned char *)trans = 'N'; 00276 } 00277 00278 ztrmm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[ 00279 b_offset], ldb, &a[a_offset], lda); 00280 } 00281 } 00282 00283 work[1].r = (doublereal) lwkopt, work[1].i = 0.; 00284 00285 return 0; 00286 00287 /* End of ZHEGV */ 00288 00289 } /* zhegv_ */