00001 /* ssygv.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 static integer c_n1 = -1; 00020 static real c_b16 = 1.f; 00021 00022 /* Subroutine */ int ssygv_(integer *itype, char *jobz, char *uplo, integer * 00023 n, real *a, integer *lda, real *b, integer *ldb, real *w, real *work, 00024 integer *lwork, integer *info) 00025 { 00026 /* System generated locals */ 00027 integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; 00028 00029 /* Local variables */ 00030 integer nb, neig; 00031 extern logical lsame_(char *, char *); 00032 char trans[1]; 00033 logical upper; 00034 extern /* Subroutine */ int strmm_(char *, char *, char *, char *, 00035 integer *, integer *, real *, real *, integer *, real *, integer * 00036 ); 00037 logical wantz; 00038 extern /* Subroutine */ int strsm_(char *, char *, char *, char *, 00039 integer *, integer *, real *, real *, integer *, real *, integer * 00040 ), ssyev_(char *, char *, integer 00041 *, real *, integer *, real *, real *, integer *, integer *), xerbla_(char *, integer *); 00042 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00043 integer *, integer *); 00044 integer lwkmin; 00045 extern /* Subroutine */ int spotrf_(char *, integer *, real *, integer *, 00046 integer *); 00047 integer lwkopt; 00048 logical lquery; 00049 extern /* Subroutine */ int ssygst_(integer *, char *, integer *, real *, 00050 integer *, real *, integer *, 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 /* SSYGV computes all the eigenvalues, and optionally, the eigenvectors */ 00066 /* of a real generalized symmetric-definite eigenproblem, of the form */ 00067 /* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. */ 00068 /* Here A and B are assumed to be symmetric and B is also */ 00069 /* positive definite. */ 00070 00071 /* Arguments */ 00072 /* ========= */ 00073 00074 /* ITYPE (input) INTEGER */ 00075 /* Specifies the problem type to be solved: */ 00076 /* = 1: A*x = (lambda)*B*x */ 00077 /* = 2: A*B*x = (lambda)*x */ 00078 /* = 3: B*A*x = (lambda)*x */ 00079 00080 /* JOBZ (input) CHARACTER*1 */ 00081 /* = 'N': Compute eigenvalues only; */ 00082 /* = 'V': Compute eigenvalues and eigenvectors. */ 00083 00084 /* UPLO (input) CHARACTER*1 */ 00085 /* = 'U': Upper triangles of A and B are stored; */ 00086 /* = 'L': Lower triangles of A and B are stored. */ 00087 00088 /* N (input) INTEGER */ 00089 /* The order of the matrices A and B. N >= 0. */ 00090 00091 /* A (input/output) REAL array, dimension (LDA, N) */ 00092 /* On entry, the symmetric matrix A. If UPLO = 'U', the */ 00093 /* leading N-by-N upper triangular part of A contains the */ 00094 /* upper triangular part of the matrix A. If UPLO = 'L', */ 00095 /* the leading N-by-N lower triangular part of A contains */ 00096 /* the lower triangular part of the matrix A. */ 00097 00098 /* On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ 00099 /* matrix Z of eigenvectors. The eigenvectors are normalized */ 00100 /* as follows: */ 00101 /* if ITYPE = 1 or 2, Z**T*B*Z = I; */ 00102 /* if ITYPE = 3, Z**T*inv(B)*Z = I. */ 00103 /* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */ 00104 /* or the lower triangle (if UPLO='L') of A, including the */ 00105 /* diagonal, is destroyed. */ 00106 00107 /* LDA (input) INTEGER */ 00108 /* The leading dimension of the array A. LDA >= max(1,N). */ 00109 00110 /* B (input/output) REAL array, dimension (LDB, N) */ 00111 /* On entry, the symmetric positive definite matrix B. */ 00112 /* If UPLO = 'U', the leading N-by-N upper triangular part of B */ 00113 /* contains the upper triangular part of the matrix B. */ 00114 /* If UPLO = 'L', the leading N-by-N lower triangular part of B */ 00115 /* contains the lower triangular part of the matrix B. */ 00116 00117 /* On exit, if INFO <= N, the part of B containing the matrix is */ 00118 /* overwritten by the triangular factor U or L from the Cholesky */ 00119 /* factorization B = U**T*U or B = L*L**T. */ 00120 00121 /* LDB (input) INTEGER */ 00122 /* The leading dimension of the array B. LDB >= max(1,N). */ 00123 00124 /* W (output) REAL array, dimension (N) */ 00125 /* If INFO = 0, the eigenvalues in ascending order. */ 00126 00127 /* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */ 00128 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00129 00130 /* LWORK (input) INTEGER */ 00131 /* The length of the array WORK. LWORK >= max(1,3*N-1). */ 00132 /* For optimal efficiency, LWORK >= (NB+2)*N, */ 00133 /* where NB is the blocksize for SSYTRD returned by ILAENV. */ 00134 00135 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00136 /* only calculates the optimal size of the WORK array, returns */ 00137 /* this value as the first entry of the WORK array, and no error */ 00138 /* message related to LWORK is issued by XERBLA. */ 00139 00140 /* INFO (output) INTEGER */ 00141 /* = 0: successful exit */ 00142 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00143 /* > 0: SPOTRF or SSYEV returned an error code: */ 00144 /* <= N: if INFO = i, SSYEV failed to converge; */ 00145 /* i off-diagonal elements of an intermediate */ 00146 /* tridiagonal form did not converge to zero; */ 00147 /* > N: if INFO = N + i, for 1 <= i <= N, then the leading */ 00148 /* minor of order i of B is not positive definite. */ 00149 /* The factorization of B could not be completed and */ 00150 /* no eigenvalues or eigenvectors were computed. */ 00151 00152 /* ===================================================================== */ 00153 00154 /* .. Parameters .. */ 00155 /* .. */ 00156 /* .. Local Scalars .. */ 00157 /* .. */ 00158 /* .. External Functions .. */ 00159 /* .. */ 00160 /* .. External Subroutines .. */ 00161 /* .. */ 00162 /* .. Intrinsic Functions .. */ 00163 /* .. */ 00164 /* .. Executable Statements .. */ 00165 00166 /* Test the input parameters. */ 00167 00168 /* Parameter adjustments */ 00169 a_dim1 = *lda; 00170 a_offset = 1 + a_dim1; 00171 a -= a_offset; 00172 b_dim1 = *ldb; 00173 b_offset = 1 + b_dim1; 00174 b -= b_offset; 00175 --w; 00176 --work; 00177 00178 /* Function Body */ 00179 wantz = lsame_(jobz, "V"); 00180 upper = lsame_(uplo, "U"); 00181 lquery = *lwork == -1; 00182 00183 *info = 0; 00184 if (*itype < 1 || *itype > 3) { 00185 *info = -1; 00186 } else if (! (wantz || lsame_(jobz, "N"))) { 00187 *info = -2; 00188 } else if (! (upper || lsame_(uplo, "L"))) { 00189 *info = -3; 00190 } else if (*n < 0) { 00191 *info = -4; 00192 } else if (*lda < max(1,*n)) { 00193 *info = -6; 00194 } else if (*ldb < max(1,*n)) { 00195 *info = -8; 00196 } 00197 00198 if (*info == 0) { 00199 /* Computing MAX */ 00200 i__1 = 1, i__2 = *n * 3 - 1; 00201 lwkmin = max(i__1,i__2); 00202 nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1); 00203 /* Computing MAX */ 00204 i__1 = lwkmin, i__2 = (nb + 2) * *n; 00205 lwkopt = max(i__1,i__2); 00206 work[1] = (real) lwkopt; 00207 00208 if (*lwork < lwkmin && ! lquery) { 00209 *info = -11; 00210 } 00211 } 00212 00213 if (*info != 0) { 00214 i__1 = -(*info); 00215 xerbla_("SSYGV ", &i__1); 00216 return 0; 00217 } else if (lquery) { 00218 return 0; 00219 } 00220 00221 /* Quick return if possible */ 00222 00223 if (*n == 0) { 00224 return 0; 00225 } 00226 00227 /* Form a Cholesky factorization of B. */ 00228 00229 spotrf_(uplo, n, &b[b_offset], ldb, info); 00230 if (*info != 0) { 00231 *info = *n + *info; 00232 return 0; 00233 } 00234 00235 /* Transform problem to standard eigenvalue problem and solve. */ 00236 00237 ssygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info); 00238 ssyev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, info); 00239 00240 if (wantz) { 00241 00242 /* Backtransform eigenvectors to the original problem. */ 00243 00244 neig = *n; 00245 if (*info > 0) { 00246 neig = *info - 1; 00247 } 00248 if (*itype == 1 || *itype == 2) { 00249 00250 /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ 00251 /* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ 00252 00253 if (upper) { 00254 *(unsigned char *)trans = 'N'; 00255 } else { 00256 *(unsigned char *)trans = 'T'; 00257 } 00258 00259 strsm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b16, &b[ 00260 b_offset], ldb, &a[a_offset], lda); 00261 00262 } else if (*itype == 3) { 00263 00264 /* For B*A*x=(lambda)*x; */ 00265 /* backtransform eigenvectors: x = L*y or U'*y */ 00266 00267 if (upper) { 00268 *(unsigned char *)trans = 'T'; 00269 } else { 00270 *(unsigned char *)trans = 'N'; 00271 } 00272 00273 strmm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b16, &b[ 00274 b_offset], ldb, &a[a_offset], lda); 00275 } 00276 } 00277 00278 work[1] = (real) lwkopt; 00279 return 0; 00280 00281 /* End of SSYGV */ 00282 00283 } /* ssygv_ */