LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sspgvd.f
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00001 *> \brief \b SSPGST
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SSPGVD + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sspgvd.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sspgvd.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
00022 *                          LWORK, IWORK, LIWORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          JOBZ, UPLO
00026 *       INTEGER            INFO, ITYPE, LDZ, LIWORK, LWORK, N
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       INTEGER            IWORK( * )
00030 *       REAL               AP( * ), BP( * ), W( * ), WORK( * ),
00031 *      $                   Z( LDZ, * )
00032 *       ..
00033 *  
00034 *
00035 *> \par Purpose:
00036 *  =============
00037 *>
00038 *> \verbatim
00039 *>
00040 *> SSPGVD computes all the eigenvalues, and optionally, the eigenvectors
00041 *> of a real generalized symmetric-definite eigenproblem, of the form
00042 *> A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
00043 *> B are assumed to be symmetric, stored in packed format, and B is also
00044 *> positive definite.
00045 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
00046 *>
00047 *> The divide and conquer algorithm makes very mild assumptions about
00048 *> floating point arithmetic. It will work on machines with a guard
00049 *> digit in add/subtract, or on those binary machines without guard
00050 *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
00051 *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
00052 *> without guard digits, but we know of none.
00053 *> \endverbatim
00054 *
00055 *  Arguments:
00056 *  ==========
00057 *
00058 *> \param[in] ITYPE
00059 *> \verbatim
00060 *>          ITYPE is INTEGER
00061 *>          Specifies the problem type to be solved:
00062 *>          = 1:  A*x = (lambda)*B*x
00063 *>          = 2:  A*B*x = (lambda)*x
00064 *>          = 3:  B*A*x = (lambda)*x
00065 *> \endverbatim
00066 *>
00067 *> \param[in] JOBZ
00068 *> \verbatim
00069 *>          JOBZ is CHARACTER*1
00070 *>          = 'N':  Compute eigenvalues only;
00071 *>          = 'V':  Compute eigenvalues and eigenvectors.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] UPLO
00075 *> \verbatim
00076 *>          UPLO is CHARACTER*1
00077 *>          = 'U':  Upper triangles of A and B are stored;
00078 *>          = 'L':  Lower triangles of A and B are stored.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] N
00082 *> \verbatim
00083 *>          N is INTEGER
00084 *>          The order of the matrices A and B.  N >= 0.
00085 *> \endverbatim
00086 *>
00087 *> \param[in,out] AP
00088 *> \verbatim
00089 *>          AP is REAL array, dimension (N*(N+1)/2)
00090 *>          On entry, the upper or lower triangle of the symmetric matrix
00091 *>          A, packed columnwise in a linear array.  The j-th column of A
00092 *>          is stored in the array AP as follows:
00093 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00094 *>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
00095 *>
00096 *>          On exit, the contents of AP are destroyed.
00097 *> \endverbatim
00098 *>
00099 *> \param[in,out] BP
00100 *> \verbatim
00101 *>          BP is REAL array, dimension (N*(N+1)/2)
00102 *>          On entry, the upper or lower triangle of the symmetric matrix
00103 *>          B, packed columnwise in a linear array.  The j-th column of B
00104 *>          is stored in the array BP as follows:
00105 *>          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
00106 *>          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
00107 *>
00108 *>          On exit, the triangular factor U or L from the Cholesky
00109 *>          factorization B = U**T*U or B = L*L**T, in the same storage
00110 *>          format as B.
00111 *> \endverbatim
00112 *>
00113 *> \param[out] W
00114 *> \verbatim
00115 *>          W is REAL array, dimension (N)
00116 *>          If INFO = 0, the eigenvalues in ascending order.
00117 *> \endverbatim
00118 *>
00119 *> \param[out] Z
00120 *> \verbatim
00121 *>          Z is REAL array, dimension (LDZ, N)
00122 *>          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
00123 *>          eigenvectors.  The eigenvectors are normalized as follows:
00124 *>          if ITYPE = 1 or 2, Z**T*B*Z = I;
00125 *>          if ITYPE = 3, Z**T*inv(B)*Z = I.
00126 *>          If JOBZ = 'N', then Z is not referenced.
00127 *> \endverbatim
00128 *>
00129 *> \param[in] LDZ
00130 *> \verbatim
00131 *>          LDZ is INTEGER
00132 *>          The leading dimension of the array Z.  LDZ >= 1, and if
00133 *>          JOBZ = 'V', LDZ >= max(1,N).
00134 *> \endverbatim
00135 *>
00136 *> \param[out] WORK
00137 *> \verbatim
00138 *>          WORK is REAL array, dimension (MAX(1,LWORK))
00139 *>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
00140 *> \endverbatim
00141 *>
00142 *> \param[in] LWORK
00143 *> \verbatim
00144 *>          LWORK is INTEGER
00145 *>          The dimension of the array WORK.
00146 *>          If N <= 1,               LWORK >= 1.
00147 *>          If JOBZ = 'N' and N > 1, LWORK >= 2*N.
00148 *>          If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
00149 *>
00150 *>          If LWORK = -1, then a workspace query is assumed; the routine
00151 *>          only calculates the required sizes of the WORK and IWORK
00152 *>          arrays, returns these values as the first entries of the WORK
00153 *>          and IWORK arrays, and no error message related to LWORK or
00154 *>          LIWORK is issued by XERBLA.
00155 *> \endverbatim
00156 *>
00157 *> \param[out] IWORK
00158 *> \verbatim
00159 *>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
00160 *>          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
00161 *> \endverbatim
00162 *>
00163 *> \param[in] LIWORK
00164 *> \verbatim
00165 *>          LIWORK is INTEGER
00166 *>          The dimension of the array IWORK.
00167 *>          If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
00168 *>          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
00169 *>
00170 *>          If LIWORK = -1, then a workspace query is assumed; the
00171 *>          routine only calculates the required sizes of the WORK and
00172 *>          IWORK arrays, returns these values as the first entries of
00173 *>          the WORK and IWORK arrays, and no error message related to
00174 *>          LWORK or LIWORK is issued by XERBLA.
00175 *> \endverbatim
00176 *>
00177 *> \param[out] INFO
00178 *> \verbatim
00179 *>          INFO is INTEGER
00180 *>          = 0:  successful exit
00181 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00182 *>          > 0:  SPPTRF or SSPEVD returned an error code:
00183 *>             <= N:  if INFO = i, SSPEVD failed to converge;
00184 *>                    i off-diagonal elements of an intermediate
00185 *>                    tridiagonal form did not converge to zero;
00186 *>             > N:   if INFO = N + i, for 1 <= i <= N, then the leading
00187 *>                    minor of order i of B is not positive definite.
00188 *>                    The factorization of B could not be completed and
00189 *>                    no eigenvalues or eigenvectors were computed.
00190 *> \endverbatim
00191 *
00192 *  Authors:
00193 *  ========
00194 *
00195 *> \author Univ. of Tennessee 
00196 *> \author Univ. of California Berkeley 
00197 *> \author Univ. of Colorado Denver 
00198 *> \author NAG Ltd. 
00199 *
00200 *> \date November 2011
00201 *
00202 *> \ingroup realOTHEReigen
00203 *
00204 *> \par Contributors:
00205 *  ==================
00206 *>
00207 *>     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
00208 *
00209 *  =====================================================================
00210       SUBROUTINE SSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
00211      $                   LWORK, IWORK, LIWORK, INFO )
00212 *
00213 *  -- LAPACK driver routine (version 3.4.0) --
00214 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00215 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00216 *     November 2011
00217 *
00218 *     .. Scalar Arguments ..
00219       CHARACTER          JOBZ, UPLO
00220       INTEGER            INFO, ITYPE, LDZ, LIWORK, LWORK, N
00221 *     ..
00222 *     .. Array Arguments ..
00223       INTEGER            IWORK( * )
00224       REAL               AP( * ), BP( * ), W( * ), WORK( * ),
00225      $                   Z( LDZ, * )
00226 *     ..
00227 *
00228 *  =====================================================================
00229 *
00230 *     .. Local Scalars ..
00231       LOGICAL            LQUERY, UPPER, WANTZ
00232       CHARACTER          TRANS
00233       INTEGER            J, LIWMIN, LWMIN, NEIG
00234 *     ..
00235 *     .. External Functions ..
00236       LOGICAL            LSAME
00237       EXTERNAL           LSAME
00238 *     ..
00239 *     .. External Subroutines ..
00240       EXTERNAL           SPPTRF, SSPEVD, SSPGST, STPMV, STPSV, XERBLA
00241 *     ..
00242 *     .. Intrinsic Functions ..
00243       INTRINSIC          MAX, REAL
00244 *     ..
00245 *     .. Executable Statements ..
00246 *
00247 *     Test the input parameters.
00248 *
00249       WANTZ = LSAME( JOBZ, 'V' )
00250       UPPER = LSAME( UPLO, 'U' )
00251       LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
00252 *
00253       INFO = 0
00254       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
00255          INFO = -1
00256       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00257          INFO = -2
00258       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
00259          INFO = -3
00260       ELSE IF( N.LT.0 ) THEN
00261          INFO = -4
00262       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
00263          INFO = -9
00264       END IF
00265 *
00266       IF( INFO.EQ.0 ) THEN
00267          IF( N.LE.1 ) THEN
00268             LIWMIN = 1
00269             LWMIN = 1
00270          ELSE
00271             IF( WANTZ ) THEN
00272                LIWMIN = 3 + 5*N
00273                LWMIN = 1 + 6*N + 2*N**2
00274             ELSE
00275                LIWMIN = 1
00276                LWMIN = 2*N
00277             END IF
00278          END IF
00279          WORK( 1 ) = LWMIN
00280          IWORK( 1 ) = LIWMIN
00281          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
00282             INFO = -11
00283          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
00284             INFO = -13
00285          END IF
00286       END IF
00287 *
00288       IF( INFO.NE.0 ) THEN
00289          CALL XERBLA( 'SSPGVD', -INFO )
00290          RETURN
00291       ELSE IF( LQUERY ) THEN
00292          RETURN
00293       END IF
00294 *
00295 *     Quick return if possible
00296 *
00297       IF( N.EQ.0 )
00298      $   RETURN
00299 *
00300 *     Form a Cholesky factorization of BP.
00301 *
00302       CALL SPPTRF( UPLO, N, BP, INFO )
00303       IF( INFO.NE.0 ) THEN
00304          INFO = N + INFO
00305          RETURN
00306       END IF
00307 *
00308 *     Transform problem to standard eigenvalue problem and solve.
00309 *
00310       CALL SSPGST( ITYPE, UPLO, N, AP, BP, INFO )
00311       CALL SSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
00312      $             LIWORK, INFO )
00313       LWMIN = MAX( REAL( LWMIN ), REAL( WORK( 1 ) ) )
00314       LIWMIN = MAX( REAL( LIWMIN ), REAL( IWORK( 1 ) ) )
00315 *
00316       IF( WANTZ ) THEN
00317 *
00318 *        Backtransform eigenvectors to the original problem.
00319 *
00320          NEIG = N
00321          IF( INFO.GT.0 )
00322      $      NEIG = INFO - 1
00323          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
00324 *
00325 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
00326 *           backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y
00327 *
00328             IF( UPPER ) THEN
00329                TRANS = 'N'
00330             ELSE
00331                TRANS = 'T'
00332             END IF
00333 *
00334             DO 10 J = 1, NEIG
00335                CALL STPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
00336      $                     1 )
00337    10       CONTINUE
00338 *
00339          ELSE IF( ITYPE.EQ.3 ) THEN
00340 *
00341 *           For B*A*x=(lambda)*x;
00342 *           backtransform eigenvectors: x = L*y or U**T *y
00343 *
00344             IF( UPPER ) THEN
00345                TRANS = 'T'
00346             ELSE
00347                TRANS = 'N'
00348             END IF
00349 *
00350             DO 20 J = 1, NEIG
00351                CALL STPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
00352      $                     1 )
00353    20       CONTINUE
00354          END IF
00355       END IF
00356 *
00357       WORK( 1 ) = LWMIN
00358       IWORK( 1 ) = LIWMIN
00359 *
00360       RETURN
00361 *
00362 *     End of SSPGVD
00363 *
00364       END
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