```001:       SUBROUTINE SSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
002:      \$                  LWORK, INFO )
003: *
004: *  -- LAPACK driver routine (version 3.2) --
005: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
006: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
007: *     November 2006
008: *
009: *     .. Scalar Arguments ..
010:       CHARACTER          JOBZ, UPLO
011:       INTEGER            INFO, ITYPE, LDA, LDB, LWORK, N
012: *     ..
013: *     .. Array Arguments ..
014:       REAL               A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
015: *     ..
016: *
017: *  Purpose
018: *  =======
019: *
020: *  SSYGV computes all the eigenvalues, and optionally, the eigenvectors
021: *  of a real generalized symmetric-definite eigenproblem, of the form
022: *  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
023: *  Here A and B are assumed to be symmetric and B is also
024: *  positive definite.
025: *
026: *  Arguments
027: *  =========
028: *
029: *  ITYPE   (input) INTEGER
030: *          Specifies the problem type to be solved:
031: *          = 1:  A*x = (lambda)*B*x
032: *          = 2:  A*B*x = (lambda)*x
033: *          = 3:  B*A*x = (lambda)*x
034: *
035: *  JOBZ    (input) CHARACTER*1
036: *          = 'N':  Compute eigenvalues only;
037: *          = 'V':  Compute eigenvalues and eigenvectors.
038: *
039: *  UPLO    (input) CHARACTER*1
040: *          = 'U':  Upper triangles of A and B are stored;
041: *          = 'L':  Lower triangles of A and B are stored.
042: *
043: *  N       (input) INTEGER
044: *          The order of the matrices A and B.  N >= 0.
045: *
046: *  A       (input/output) REAL array, dimension (LDA, N)
047: *          On entry, the symmetric matrix A.  If UPLO = 'U', the
048: *          leading N-by-N upper triangular part of A contains the
049: *          upper triangular part of the matrix A.  If UPLO = 'L',
050: *          the leading N-by-N lower triangular part of A contains
051: *          the lower triangular part of the matrix A.
052: *
053: *          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
054: *          matrix Z of eigenvectors.  The eigenvectors are normalized
055: *          as follows:
056: *          if ITYPE = 1 or 2, Z**T*B*Z = I;
057: *          if ITYPE = 3, Z**T*inv(B)*Z = I.
058: *          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
059: *          or the lower triangle (if UPLO='L') of A, including the
060: *          diagonal, is destroyed.
061: *
062: *  LDA     (input) INTEGER
063: *          The leading dimension of the array A.  LDA >= max(1,N).
064: *
065: *  B       (input/output) REAL array, dimension (LDB, N)
066: *          On entry, the symmetric positive definite matrix B.
067: *          If UPLO = 'U', the leading N-by-N upper triangular part of B
068: *          contains the upper triangular part of the matrix B.
069: *          If UPLO = 'L', the leading N-by-N lower triangular part of B
070: *          contains the lower triangular part of the matrix B.
071: *
072: *          On exit, if INFO <= N, the part of B containing the matrix is
073: *          overwritten by the triangular factor U or L from the Cholesky
074: *          factorization B = U**T*U or B = L*L**T.
075: *
076: *  LDB     (input) INTEGER
077: *          The leading dimension of the array B.  LDB >= max(1,N).
078: *
079: *  W       (output) REAL array, dimension (N)
080: *          If INFO = 0, the eigenvalues in ascending order.
081: *
082: *  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
083: *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
084: *
085: *  LWORK   (input) INTEGER
086: *          The length of the array WORK.  LWORK >= max(1,3*N-1).
087: *          For optimal efficiency, LWORK >= (NB+2)*N,
088: *          where NB is the blocksize for SSYTRD returned by ILAENV.
089: *
090: *          If LWORK = -1, then a workspace query is assumed; the routine
091: *          only calculates the optimal size of the WORK array, returns
092: *          this value as the first entry of the WORK array, and no error
093: *          message related to LWORK is issued by XERBLA.
094: *
095: *  INFO    (output) INTEGER
096: *          = 0:  successful exit
097: *          < 0:  if INFO = -i, the i-th argument had an illegal value
098: *          > 0:  SPOTRF or SSYEV returned an error code:
099: *             <= N:  if INFO = i, SSYEV failed to converge;
100: *                    i off-diagonal elements of an intermediate
101: *                    tridiagonal form did not converge to zero;
102: *             > N:   if INFO = N + i, for 1 <= i <= N, then the leading
103: *                    minor of order i of B is not positive definite.
104: *                    The factorization of B could not be completed and
105: *                    no eigenvalues or eigenvectors were computed.
106: *
107: *  =====================================================================
108: *
109: *     .. Parameters ..
110:       REAL               ONE
111:       PARAMETER          ( ONE = 1.0E+0 )
112: *     ..
113: *     .. Local Scalars ..
114:       LOGICAL            LQUERY, UPPER, WANTZ
115:       CHARACTER          TRANS
116:       INTEGER            LWKMIN, LWKOPT, NB, NEIG
117: *     ..
118: *     .. External Functions ..
119:       LOGICAL            LSAME
120:       INTEGER            ILAENV
121:       EXTERNAL           ILAENV, LSAME
122: *     ..
123: *     .. External Subroutines ..
124:       EXTERNAL           SPOTRF, SSYEV, SSYGST, STRMM, STRSM, XERBLA
125: *     ..
126: *     .. Intrinsic Functions ..
127:       INTRINSIC          MAX
128: *     ..
129: *     .. Executable Statements ..
130: *
131: *     Test the input parameters.
132: *
133:       WANTZ = LSAME( JOBZ, 'V' )
134:       UPPER = LSAME( UPLO, 'U' )
135:       LQUERY = ( LWORK.EQ.-1 )
136: *
137:       INFO = 0
138:       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
139:          INFO = -1
140:       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
141:          INFO = -2
142:       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
143:          INFO = -3
144:       ELSE IF( N.LT.0 ) THEN
145:          INFO = -4
146:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
147:          INFO = -6
148:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
149:          INFO = -8
150:       END IF
151: *
152:       IF( INFO.EQ.0 ) THEN
153:          LWKMIN = MAX( 1, 3*N - 1 )
154:          NB = ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 )
155:          LWKOPT = MAX( LWKMIN, ( NB + 2 )*N )
156:          WORK( 1 ) = LWKOPT
157: *
158:          IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
159:             INFO = -11
160:          END IF
161:       END IF
162: *
163:       IF( INFO.NE.0 ) THEN
164:          CALL XERBLA( 'SSYGV ', -INFO )
165:          RETURN
166:       ELSE IF( LQUERY ) THEN
167:          RETURN
168:       END IF
169: *
170: *     Quick return if possible
171: *
172:       IF( N.EQ.0 )
173:      \$   RETURN
174: *
175: *     Form a Cholesky factorization of B.
176: *
177:       CALL SPOTRF( UPLO, N, B, LDB, INFO )
178:       IF( INFO.NE.0 ) THEN
179:          INFO = N + INFO
180:          RETURN
181:       END IF
182: *
183: *     Transform problem to standard eigenvalue problem and solve.
184: *
185:       CALL SSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
186:       CALL SSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
187: *
188:       IF( WANTZ ) THEN
189: *
190: *        Backtransform eigenvectors to the original problem.
191: *
192:          NEIG = N
193:          IF( INFO.GT.0 )
194:      \$      NEIG = INFO - 1
195:          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
196: *
197: *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
198: *           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
199: *
200:             IF( UPPER ) THEN
201:                TRANS = 'N'
202:             ELSE
203:                TRANS = 'T'
204:             END IF
205: *
206:             CALL STRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
207:      \$                  B, LDB, A, LDA )
208: *
209:          ELSE IF( ITYPE.EQ.3 ) THEN
210: *
211: *           For B*A*x=(lambda)*x;
212: *           backtransform eigenvectors: x = L*y or U'*y
213: *
214:             IF( UPPER ) THEN
215:                TRANS = 'T'
216:             ELSE
217:                TRANS = 'N'
218:             END IF
219: *
220:             CALL STRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
221:      \$                  B, LDB, A, LDA )
222:          END IF
223:       END IF
224: *
225:       WORK( 1 ) = LWKOPT
226:       RETURN
227: *
228: *     End of SSYGV
229: *
230:       END
231: ```