LAPACK 3.3.1
Linear Algebra PACKage

ssygvd.f

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00001       SUBROUTINE SSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
00002      $                   LWORK, IWORK, LIWORK, INFO )
00003 *
00004 *  -- LAPACK driver routine (version 3.3.1) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *  -- April 2011                                                      --
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          JOBZ, UPLO
00011       INTEGER            INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N
00012 *     ..
00013 *     .. Array Arguments ..
00014       INTEGER            IWORK( * )
00015       REAL               A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
00022 *  of a real generalized symmetric-definite eigenproblem, of the form
00023 *  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
00024 *  B are assumed to be symmetric and B is also positive definite.
00025 *  If eigenvectors are desired, it uses a divide and conquer algorithm.
00026 *
00027 *  The divide and conquer algorithm makes very mild assumptions about
00028 *  floating point arithmetic. It will work on machines with a guard
00029 *  digit in add/subtract, or on those binary machines without guard
00030 *  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
00031 *  Cray-2. It could conceivably fail on hexadecimal or decimal machines
00032 *  without guard digits, but we know of none.
00033 *
00034 *  Arguments
00035 *  =========
00036 *
00037 *  ITYPE   (input) INTEGER
00038 *          Specifies the problem type to be solved:
00039 *          = 1:  A*x = (lambda)*B*x
00040 *          = 2:  A*B*x = (lambda)*x
00041 *          = 3:  B*A*x = (lambda)*x
00042 *
00043 *  JOBZ    (input) CHARACTER*1
00044 *          = 'N':  Compute eigenvalues only;
00045 *          = 'V':  Compute eigenvalues and eigenvectors.
00046 *
00047 *  UPLO    (input) CHARACTER*1
00048 *          = 'U':  Upper triangles of A and B are stored;
00049 *          = 'L':  Lower triangles of A and B are stored.
00050 *
00051 *  N       (input) INTEGER
00052 *          The order of the matrices A and B.  N >= 0.
00053 *
00054 *  A       (input/output) REAL array, dimension (LDA, N)
00055 *          On entry, the symmetric matrix A.  If UPLO = 'U', the
00056 *          leading N-by-N upper triangular part of A contains the
00057 *          upper triangular part of the matrix A.  If UPLO = 'L',
00058 *          the leading N-by-N lower triangular part of A contains
00059 *          the lower triangular part of the matrix A.
00060 *
00061 *          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
00062 *          matrix Z of eigenvectors.  The eigenvectors are normalized
00063 *          as follows:
00064 *          if ITYPE = 1 or 2, Z**T*B*Z = I;
00065 *          if ITYPE = 3, Z**T*inv(B)*Z = I.
00066 *          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
00067 *          or the lower triangle (if UPLO='L') of A, including the
00068 *          diagonal, is destroyed.
00069 *
00070 *  LDA     (input) INTEGER
00071 *          The leading dimension of the array A.  LDA >= max(1,N).
00072 *
00073 *  B       (input/output) REAL array, dimension (LDB, N)
00074 *          On entry, the symmetric matrix B.  If UPLO = 'U', the
00075 *          leading N-by-N upper triangular part of B contains the
00076 *          upper triangular part of the matrix B.  If UPLO = 'L',
00077 *          the leading N-by-N lower triangular part of B contains
00078 *          the lower triangular part of the matrix B.
00079 *
00080 *          On exit, if INFO <= N, the part of B containing the matrix is
00081 *          overwritten by the triangular factor U or L from the Cholesky
00082 *          factorization B = U**T*U or B = L*L**T.
00083 *
00084 *  LDB     (input) INTEGER
00085 *          The leading dimension of the array B.  LDB >= max(1,N).
00086 *
00087 *  W       (output) REAL array, dimension (N)
00088 *          If INFO = 0, the eigenvalues in ascending order.
00089 *
00090 *  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
00091 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00092 *
00093 *  LWORK   (input) INTEGER
00094 *          The dimension of the array WORK.
00095 *          If N <= 1,               LWORK >= 1.
00096 *          If JOBZ = 'N' and N > 1, LWORK >= 2*N+1.
00097 *          If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
00098 *
00099 *          If LWORK = -1, then a workspace query is assumed; the routine
00100 *          only calculates the optimal sizes of the WORK and IWORK
00101 *          arrays, returns these values as the first entries of the WORK
00102 *          and IWORK arrays, and no error message related to LWORK or
00103 *          LIWORK is issued by XERBLA.
00104 *
00105 *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
00106 *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
00107 *
00108 *  LIWORK  (input) INTEGER
00109 *          The dimension of the array IWORK.
00110 *          If N <= 1,                LIWORK >= 1.
00111 *          If JOBZ  = 'N' and N > 1, LIWORK >= 1.
00112 *          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
00113 *
00114 *          If LIWORK = -1, then a workspace query is assumed; the
00115 *          routine only calculates the optimal sizes of the WORK and
00116 *          IWORK arrays, returns these values as the first entries of
00117 *          the WORK and IWORK arrays, and no error message related to
00118 *          LWORK or LIWORK is issued by XERBLA.
00119 *
00120 *  INFO    (output) INTEGER
00121 *          = 0:  successful exit
00122 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00123 *          > 0:  SPOTRF or SSYEVD returned an error code:
00124 *             <= N:  if INFO = i and JOBZ = 'N', then the algorithm
00125 *                    failed to converge; i off-diagonal elements of an
00126 *                    intermediate tridiagonal form did not converge to
00127 *                    zero;
00128 *                    if INFO = i and JOBZ = 'V', then the algorithm
00129 *                    failed to compute an eigenvalue while working on
00130 *                    the submatrix lying in rows and columns INFO/(N+1)
00131 *                    through mod(INFO,N+1);
00132 *             > N:   if INFO = N + i, for 1 <= i <= N, then the leading
00133 *                    minor of order i of B is not positive definite.
00134 *                    The factorization of B could not be completed and
00135 *                    no eigenvalues or eigenvectors were computed.
00136 *
00137 *  Further Details
00138 *  ===============
00139 *
00140 *  Based on contributions by
00141 *     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
00142 *
00143 *  Modified so that no backsubstitution is performed if SSYEVD fails to
00144 *  converge (NEIG in old code could be greater than N causing out of
00145 *  bounds reference to A - reported by Ralf Meyer).  Also corrected the
00146 *  description of INFO and the test on ITYPE. Sven, 16 Feb 05.
00147 *  =====================================================================
00148 *
00149 *     .. Parameters ..
00150       REAL               ONE
00151       PARAMETER          ( ONE = 1.0E+0 )
00152 *     ..
00153 *     .. Local Scalars ..
00154       LOGICAL            LQUERY, UPPER, WANTZ
00155       CHARACTER          TRANS
00156       INTEGER            LIOPT, LIWMIN, LOPT, LWMIN
00157 *     ..
00158 *     .. External Functions ..
00159       LOGICAL            LSAME
00160       EXTERNAL           LSAME
00161 *     ..
00162 *     .. External Subroutines ..
00163       EXTERNAL           SPOTRF, SSYEVD, SSYGST, STRMM, STRSM, XERBLA
00164 *     ..
00165 *     .. Intrinsic Functions ..
00166       INTRINSIC          MAX, REAL
00167 *     ..
00168 *     .. Executable Statements ..
00169 *
00170 *     Test the input parameters.
00171 *
00172       WANTZ = LSAME( JOBZ, 'V' )
00173       UPPER = LSAME( UPLO, 'U' )
00174       LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
00175 *
00176       INFO = 0
00177       IF( N.LE.1 ) THEN
00178          LIWMIN = 1
00179          LWMIN = 1
00180       ELSE IF( WANTZ ) THEN
00181          LIWMIN = 3 + 5*N
00182          LWMIN = 1 + 6*N + 2*N**2
00183       ELSE
00184          LIWMIN = 1
00185          LWMIN = 2*N + 1
00186       END IF
00187       LOPT = LWMIN
00188       LIOPT = LIWMIN
00189       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
00190          INFO = -1
00191       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00192          INFO = -2
00193       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
00194          INFO = -3
00195       ELSE IF( N.LT.0 ) THEN
00196          INFO = -4
00197       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00198          INFO = -6
00199       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00200          INFO = -8
00201       END IF
00202 *
00203       IF( INFO.EQ.0 ) THEN
00204          WORK( 1 ) = LOPT
00205          IWORK( 1 ) = LIOPT
00206 *
00207          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
00208             INFO = -11
00209          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
00210             INFO = -13
00211          END IF
00212       END IF
00213 *
00214       IF( INFO.NE.0 ) THEN
00215          CALL XERBLA( 'SSYGVD', -INFO )
00216          RETURN
00217       ELSE IF( LQUERY ) THEN
00218          RETURN
00219       END IF
00220 *
00221 *     Quick return if possible
00222 *
00223       IF( N.EQ.0 )
00224      $   RETURN
00225 *
00226 *     Form a Cholesky factorization of B.
00227 *
00228       CALL SPOTRF( UPLO, N, B, LDB, INFO )
00229       IF( INFO.NE.0 ) THEN
00230          INFO = N + INFO
00231          RETURN
00232       END IF
00233 *
00234 *     Transform problem to standard eigenvalue problem and solve.
00235 *
00236       CALL SSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
00237       CALL SSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK,
00238      $             INFO )
00239       LOPT = MAX( REAL( LOPT ), REAL( WORK( 1 ) ) )
00240       LIOPT = MAX( REAL( LIOPT ), REAL( IWORK( 1 ) ) )
00241 *
00242       IF( WANTZ .AND. INFO.EQ.0 ) THEN
00243 *
00244 *        Backtransform eigenvectors to the original problem.
00245 *
00246          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
00247 *
00248 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
00249 *           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
00250 *
00251             IF( UPPER ) THEN
00252                TRANS = 'N'
00253             ELSE
00254                TRANS = 'T'
00255             END IF
00256 *
00257             CALL STRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE,
00258      $                  B, LDB, A, LDA )
00259 *
00260          ELSE IF( ITYPE.EQ.3 ) THEN
00261 *
00262 *           For B*A*x=(lambda)*x;
00263 *           backtransform eigenvectors: x = L*y or U**T*y
00264 *
00265             IF( UPPER ) THEN
00266                TRANS = 'T'
00267             ELSE
00268                TRANS = 'N'
00269             END IF
00270 *
00271             CALL STRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE,
00272      $                  B, LDB, A, LDA )
00273          END IF
00274       END IF
00275 *
00276       WORK( 1 ) = LOPT
00277       IWORK( 1 ) = LIOPT
00278 *
00279       RETURN
00280 *
00281 *     End of SSYGVD
00282 *
00283       END
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