LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sspgv.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 SSPGV + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
00022 *                         INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          JOBZ, UPLO
00026 *       INTEGER            INFO, ITYPE, LDZ, N
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       REAL               AP( * ), BP( * ), W( * ), WORK( * ),
00030 *      $                   Z( LDZ, * )
00031 *       ..
00032 *  
00033 *
00034 *> \par Purpose:
00035 *  =============
00036 *>
00037 *> \verbatim
00038 *>
00039 *> SSPGV computes all the eigenvalues and, optionally, the eigenvectors
00040 *> of a real generalized symmetric-definite eigenproblem, of the form
00041 *> A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
00042 *> Here A and B are assumed to be symmetric, stored in packed format,
00043 *> and B is also positive definite.
00044 *> \endverbatim
00045 *
00046 *  Arguments:
00047 *  ==========
00048 *
00049 *> \param[in] ITYPE
00050 *> \verbatim
00051 *>          ITYPE is INTEGER
00052 *>          Specifies the problem type to be solved:
00053 *>          = 1:  A*x = (lambda)*B*x
00054 *>          = 2:  A*B*x = (lambda)*x
00055 *>          = 3:  B*A*x = (lambda)*x
00056 *> \endverbatim
00057 *>
00058 *> \param[in] JOBZ
00059 *> \verbatim
00060 *>          JOBZ is CHARACTER*1
00061 *>          = 'N':  Compute eigenvalues only;
00062 *>          = 'V':  Compute eigenvalues and eigenvectors.
00063 *> \endverbatim
00064 *>
00065 *> \param[in] UPLO
00066 *> \verbatim
00067 *>          UPLO is CHARACTER*1
00068 *>          = 'U':  Upper triangles of A and B are stored;
00069 *>          = 'L':  Lower triangles of A and B are stored.
00070 *> \endverbatim
00071 *>
00072 *> \param[in] N
00073 *> \verbatim
00074 *>          N is INTEGER
00075 *>          The order of the matrices A and B.  N >= 0.
00076 *> \endverbatim
00077 *>
00078 *> \param[in,out] AP
00079 *> \verbatim
00080 *>          AP is REAL array, dimension
00081 *>                            (N*(N+1)/2)
00082 *>          On entry, the upper or lower triangle of the symmetric matrix
00083 *>          A, packed columnwise in a linear array.  The j-th column of A
00084 *>          is stored in the array AP as follows:
00085 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00086 *>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
00087 *>
00088 *>          On exit, the contents of AP are destroyed.
00089 *> \endverbatim
00090 *>
00091 *> \param[in,out] BP
00092 *> \verbatim
00093 *>          BP is REAL array, dimension (N*(N+1)/2)
00094 *>          On entry, the upper or lower triangle of the symmetric matrix
00095 *>          B, packed columnwise in a linear array.  The j-th column of B
00096 *>          is stored in the array BP as follows:
00097 *>          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
00098 *>          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
00099 *>
00100 *>          On exit, the triangular factor U or L from the Cholesky
00101 *>          factorization B = U**T*U or B = L*L**T, in the same storage
00102 *>          format as B.
00103 *> \endverbatim
00104 *>
00105 *> \param[out] W
00106 *> \verbatim
00107 *>          W is REAL array, dimension (N)
00108 *>          If INFO = 0, the eigenvalues in ascending order.
00109 *> \endverbatim
00110 *>
00111 *> \param[out] Z
00112 *> \verbatim
00113 *>          Z is REAL array, dimension (LDZ, N)
00114 *>          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
00115 *>          eigenvectors.  The eigenvectors are normalized as follows:
00116 *>          if ITYPE = 1 or 2, Z**T*B*Z = I;
00117 *>          if ITYPE = 3, Z**T*inv(B)*Z = I.
00118 *>          If JOBZ = 'N', then Z is not referenced.
00119 *> \endverbatim
00120 *>
00121 *> \param[in] LDZ
00122 *> \verbatim
00123 *>          LDZ is INTEGER
00124 *>          The leading dimension of the array Z.  LDZ >= 1, and if
00125 *>          JOBZ = 'V', LDZ >= max(1,N).
00126 *> \endverbatim
00127 *>
00128 *> \param[out] WORK
00129 *> \verbatim
00130 *>          WORK is REAL array, dimension (3*N)
00131 *> \endverbatim
00132 *>
00133 *> \param[out] INFO
00134 *> \verbatim
00135 *>          INFO is INTEGER
00136 *>          = 0:  successful exit
00137 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00138 *>          > 0:  SPPTRF or SSPEV returned an error code:
00139 *>             <= N:  if INFO = i, SSPEV failed to converge;
00140 *>                    i off-diagonal elements of an intermediate
00141 *>                    tridiagonal form did not converge to zero.
00142 *>             > N:   if INFO = n + i, for 1 <= i <= n, then the leading
00143 *>                    minor of order i of B is not positive definite.
00144 *>                    The factorization of B could not be completed and
00145 *>                    no eigenvalues or eigenvectors were computed.
00146 *> \endverbatim
00147 *
00148 *  Authors:
00149 *  ========
00150 *
00151 *> \author Univ. of Tennessee 
00152 *> \author Univ. of California Berkeley 
00153 *> \author Univ. of Colorado Denver 
00154 *> \author NAG Ltd. 
00155 *
00156 *> \date November 2011
00157 *
00158 *> \ingroup realOTHEReigen
00159 *
00160 *  =====================================================================
00161       SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
00162      $                  INFO )
00163 *
00164 *  -- LAPACK driver routine (version 3.4.0) --
00165 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00166 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00167 *     November 2011
00168 *
00169 *     .. Scalar Arguments ..
00170       CHARACTER          JOBZ, UPLO
00171       INTEGER            INFO, ITYPE, LDZ, N
00172 *     ..
00173 *     .. Array Arguments ..
00174       REAL               AP( * ), BP( * ), W( * ), WORK( * ),
00175      $                   Z( LDZ, * )
00176 *     ..
00177 *
00178 *  =====================================================================
00179 *
00180 *     .. Local Scalars ..
00181       LOGICAL            UPPER, WANTZ
00182       CHARACTER          TRANS
00183       INTEGER            J, NEIG
00184 *     ..
00185 *     .. External Functions ..
00186       LOGICAL            LSAME
00187       EXTERNAL           LSAME
00188 *     ..
00189 *     .. External Subroutines ..
00190       EXTERNAL           SPPTRF, SSPEV, SSPGST, STPMV, STPSV, XERBLA
00191 *     ..
00192 *     .. Executable Statements ..
00193 *
00194 *     Test the input parameters.
00195 *
00196       WANTZ = LSAME( JOBZ, 'V' )
00197       UPPER = LSAME( UPLO, 'U' )
00198 *
00199       INFO = 0
00200       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
00201          INFO = -1
00202       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00203          INFO = -2
00204       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
00205          INFO = -3
00206       ELSE IF( N.LT.0 ) THEN
00207          INFO = -4
00208       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
00209          INFO = -9
00210       END IF
00211       IF( INFO.NE.0 ) THEN
00212          CALL XERBLA( 'SSPGV ', -INFO )
00213          RETURN
00214       END IF
00215 *
00216 *     Quick return if possible
00217 *
00218       IF( N.EQ.0 )
00219      $   RETURN
00220 *
00221 *     Form a Cholesky factorization of B.
00222 *
00223       CALL SPPTRF( UPLO, N, BP, INFO )
00224       IF( INFO.NE.0 ) THEN
00225          INFO = N + INFO
00226          RETURN
00227       END IF
00228 *
00229 *     Transform problem to standard eigenvalue problem and solve.
00230 *
00231       CALL SSPGST( ITYPE, UPLO, N, AP, BP, INFO )
00232       CALL SSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
00233 *
00234       IF( WANTZ ) THEN
00235 *
00236 *        Backtransform eigenvectors to the original problem.
00237 *
00238          NEIG = N
00239          IF( INFO.GT.0 )
00240      $      NEIG = INFO - 1
00241          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
00242 *
00243 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
00244 *           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
00245 *
00246             IF( UPPER ) THEN
00247                TRANS = 'N'
00248             ELSE
00249                TRANS = 'T'
00250             END IF
00251 *
00252             DO 10 J = 1, NEIG
00253                CALL STPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
00254      $                     1 )
00255    10       CONTINUE
00256 *
00257          ELSE IF( ITYPE.EQ.3 ) THEN
00258 *
00259 *           For B*A*x=(lambda)*x;
00260 *           backtransform eigenvectors: x = L*y or U**T*y
00261 *
00262             IF( UPPER ) THEN
00263                TRANS = 'T'
00264             ELSE
00265                TRANS = 'N'
00266             END IF
00267 *
00268             DO 20 J = 1, NEIG
00269                CALL STPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
00270      $                     1 )
00271    20       CONTINUE
00272          END IF
00273       END IF
00274       RETURN
00275 *
00276 *     End of SSPGV
00277 *
00278       END
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