LAPACK: SRC/dsygst.f Source File

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00001       SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            INFO, ITYPE, LDA, LDB, N
00011 *     ..
00012 *     .. Array Arguments ..
00013       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  DSYGST reduces a real symmetric-definite generalized eigenproblem
00020 *  to standard form.
00021 *
00022 *  If ITYPE = 1, the problem is A*x = lambda*B*x,
00023 *  and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
00024 *
00025 *  If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
00026 *  B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
00027 *
00028 *  B must have been previously factorized as U**T*U or L*L**T by DPOTRF.
00029 *
00030 *  Arguments
00031 *  =========
00032 *
00033 *  ITYPE   (input) INTEGER
00034 *          = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
00035 *          = 2 or 3: compute U*A*U**T or L**T*A*L.
00036 *
00037 *  UPLO    (input) CHARACTER*1
00038 *          = 'U':  Upper triangle of A is stored and B is factored as
00039 *                  U**T*U;
00040 *          = 'L':  Lower triangle of A is stored and B is factored as
00041 *                  L*L**T.
00042 *
00043 *  N       (input) INTEGER
00044 *          The order of the matrices A and B.  N >= 0.
00045 *
00046 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
00047 *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
00048 *          N-by-N upper triangular part of A contains the upper
00049 *          triangular part of the matrix A, and the strictly lower
00050 *          triangular part of A is not referenced.  If UPLO = 'L', the
00051 *          leading N-by-N lower triangular part of A contains the lower
00052 *          triangular part of the matrix A, and the strictly upper
00053 *          triangular part of A is not referenced.
00054 *
00055 *          On exit, if INFO = 0, the transformed matrix, stored in the
00056 *          same format as A.
00057 *
00058 *  LDA     (input) INTEGER
00059 *          The leading dimension of the array A.  LDA >= max(1,N).
00060 *
00061 *  B       (input) DOUBLE PRECISION array, dimension (LDB,N)
00062 *          The triangular factor from the Cholesky factorization of B,
00063 *          as returned by DPOTRF.
00064 *
00065 *  LDB     (input) INTEGER
00066 *          The leading dimension of the array B.  LDB >= max(1,N).
00067 *
00068 *  INFO    (output) INTEGER
00069 *          = 0:  successful exit
00070 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00071 *
00072 *  =====================================================================
00073 *
00074 *     .. Parameters ..
00075       DOUBLE PRECISION   ONE, HALF
00076       PARAMETER          ( ONE = 1.0D0, HALF = 0.5D0 )
00077 *     ..
00078 *     .. Local Scalars ..
00079       LOGICAL            UPPER
00080       INTEGER            K, KB, NB
00081 *     ..
00082 *     .. External Subroutines ..
00083       EXTERNAL           DSYGS2, DSYMM, DSYR2K, DTRMM, DTRSM, XERBLA
00084 *     ..
00085 *     .. Intrinsic Functions ..
00086       INTRINSIC          MAX, MIN
00087 *     ..
00088 *     .. External Functions ..
00089       LOGICAL            LSAME
00090       INTEGER            ILAENV
00091       EXTERNAL           LSAME, ILAENV
00092 *     ..
00093 *     .. Executable Statements ..
00094 *
00095 *     Test the input parameters.
00096 *
00097       INFO = 0
00098       UPPER = LSAME( UPLO, 'U' )
00099       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
00100          INFO = -1
00101       ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00102          INFO = -2
00103       ELSE IF( N.LT.0 ) THEN
00104          INFO = -3
00105       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00106          INFO = -5
00107       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00108          INFO = -7
00109       END IF
00110       IF( INFO.NE.0 ) THEN
00111          CALL XERBLA( 'DSYGST', -INFO )
00112          RETURN
00113       END IF
00114 *
00115 *     Quick return if possible
00116 *
00117       IF( N.EQ.0 )
00118      $   RETURN
00119 *
00120 *     Determine the block size for this environment.
00121 *
00122       NB = ILAENV( 1, 'DSYGST', UPLO, N, -1, -1, -1 )
00123 *
00124       IF( NB.LE.1 .OR. NB.GE.N ) THEN
00125 *
00126 *        Use unblocked code
00127 *
00128          CALL DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
00129       ELSE
00130 *
00131 *        Use blocked code
00132 *
00133          IF( ITYPE.EQ.1 ) THEN
00134             IF( UPPER ) THEN
00135 *
00136 *              Compute inv(U')*A*inv(U)
00137 *
00138                DO 10 K = 1, N, NB
00139                   KB = MIN( N-K+1, NB )
00140 *
00141 *                 Update the upper triangle of A(k:n,k:n)
00142 *
00143                   CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
00144      $                         B( K, K ), LDB, INFO )
00145                   IF( K+KB.LE.N ) THEN
00146                      CALL DTRSM( 'Left', UPLO, 'Transpose', 'Non-unit',
00147      $                           KB, N-K-KB+1, ONE, B( K, K ), LDB,
00148      $                           A( K, K+KB ), LDA )
00149                      CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
00150      $                           A( K, K ), LDA, B( K, K+KB ), LDB, ONE,
00151      $                           A( K, K+KB ), LDA )
00152                      CALL DSYR2K( UPLO, 'Transpose', N-K-KB+1, KB, -ONE,
00153      $                            A( K, K+KB ), LDA, B( K, K+KB ), LDB,
00154      $                            ONE, A( K+KB, K+KB ), LDA )
00155                      CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
00156      $                           A( K, K ), LDA, B( K, K+KB ), LDB, ONE,
00157      $                           A( K, K+KB ), LDA )
00158                      CALL DTRSM( 'Right', UPLO, 'No transpose',
00159      $                           'Non-unit', KB, N-K-KB+1, ONE,
00160      $                           B( K+KB, K+KB ), LDB, A( K, K+KB ),
00161      $                           LDA )
00162                   END IF
00163    10          CONTINUE
00164             ELSE
00165 *
00166 *              Compute inv(L)*A*inv(L')
00167 *
00168                DO 20 K = 1, N, NB
00169                   KB = MIN( N-K+1, NB )
00170 *
00171 *                 Update the lower triangle of A(k:n,k:n)
00172 *
00173                   CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
00174      $                         B( K, K ), LDB, INFO )
00175                   IF( K+KB.LE.N ) THEN
00176                      CALL DTRSM( 'Right', UPLO, 'Transpose', 'Non-unit',
00177      $                           N-K-KB+1, KB, ONE, B( K, K ), LDB,
00178      $                           A( K+KB, K ), LDA )
00179                      CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
00180      $                           A( K, K ), LDA, B( K+KB, K ), LDB, ONE,
00181      $                           A( K+KB, K ), LDA )
00182                      CALL DSYR2K( UPLO, 'No transpose', N-K-KB+1, KB,
00183      $                            -ONE, A( K+KB, K ), LDA, B( K+KB, K ),
00184      $                            LDB, ONE, A( K+KB, K+KB ), LDA )
00185                      CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
00186      $                           A( K, K ), LDA, B( K+KB, K ), LDB, ONE,
00187      $                           A( K+KB, K ), LDA )
00188                      CALL DTRSM( 'Left', UPLO, 'No transpose',
00189      $                           'Non-unit', N-K-KB+1, KB, ONE,
00190      $                           B( K+KB, K+KB ), LDB, A( K+KB, K ),
00191      $                           LDA )
00192                   END IF
00193    20          CONTINUE
00194             END IF
00195          ELSE
00196             IF( UPPER ) THEN
00197 *
00198 *              Compute U*A*U'
00199 *
00200                DO 30 K = 1, N, NB
00201                   KB = MIN( N-K+1, NB )
00202 *
00203 *                 Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
00204 *
00205                   CALL DTRMM( 'Left', UPLO, 'No transpose', 'Non-unit',
00206      $                        K-1, KB, ONE, B, LDB, A( 1, K ), LDA )
00207                   CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
00208      $                        LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA )
00209                   CALL DSYR2K( UPLO, 'No transpose', K-1, KB, ONE,
00210      $                         A( 1, K ), LDA, B( 1, K ), LDB, ONE, A,
00211      $                         LDA )
00212                   CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
00213      $                        LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA )
00214                   CALL DTRMM( 'Right', UPLO, 'Transpose', 'Non-unit',
00215      $                        K-1, KB, ONE, B( K, K ), LDB, A( 1, K ),
00216      $                        LDA )
00217                   CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
00218      $                         B( K, K ), LDB, INFO )
00219    30          CONTINUE
00220             ELSE
00221 *
00222 *              Compute L'*A*L
00223 *
00224                DO 40 K = 1, N, NB
00225                   KB = MIN( N-K+1, NB )
00226 *
00227 *                 Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
00228 *
00229                   CALL DTRMM( 'Right', UPLO, 'No transpose', 'Non-unit',
00230      $                        KB, K-1, ONE, B, LDB, A( K, 1 ), LDA )
00231                   CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
00232      $                        LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA )
00233                   CALL DSYR2K( UPLO, 'Transpose', K-1, KB, ONE,
00234      $                         A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A,
00235      $                         LDA )
00236                   CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
00237      $                        LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA )
00238                   CALL DTRMM( 'Left', UPLO, 'Transpose', 'Non-unit', KB,
00239      $                        K-1, ONE, B( K, K ), LDB, A( K, 1 ), LDA )
00240                   CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
00241      $                         B( K, K ), LDB, INFO )
00242    40          CONTINUE
00243             END IF
00244          END IF
00245       END IF
00246       RETURN
00247 *
00248 *     End of DSYGST
00249 *
00250       END