LAPACK 3.3.1 Linear Algebra PACKage

# dspgv.f

Go to the documentation of this file.
```00001       SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
00002      \$                  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, LDZ, N
00012 *     ..
00013 *     .. Array Arguments ..
00014       DOUBLE PRECISION   AP( * ), BP( * ), W( * ), WORK( * ),
00015      \$                   Z( LDZ, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  DSPGV 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.
00024 *  Here A and B are assumed to be symmetric, stored in packed format,
00025 *  and B is also positive definite.
00026 *
00027 *  Arguments
00028 *  =========
00029 *
00030 *  ITYPE   (input) INTEGER
00031 *          Specifies the problem type to be solved:
00032 *          = 1:  A*x = (lambda)*B*x
00033 *          = 2:  A*B*x = (lambda)*x
00034 *          = 3:  B*A*x = (lambda)*x
00035 *
00036 *  JOBZ    (input) CHARACTER*1
00037 *          = 'N':  Compute eigenvalues only;
00038 *          = 'V':  Compute eigenvalues and eigenvectors.
00039 *
00040 *  UPLO    (input) CHARACTER*1
00041 *          = 'U':  Upper triangles of A and B are stored;
00042 *          = 'L':  Lower triangles of A and B are stored.
00043 *
00044 *  N       (input) INTEGER
00045 *          The order of the matrices A and B.  N >= 0.
00046 *
00047 *  AP      (input/output) DOUBLE PRECISION array, dimension
00048 *                            (N*(N+1)/2)
00049 *          On entry, the upper or lower triangle of the symmetric matrix
00050 *          A, packed columnwise in a linear array.  The j-th column of A
00051 *          is stored in the array AP as follows:
00052 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00053 *          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
00054 *
00055 *          On exit, the contents of AP are destroyed.
00056 *
00057 *  BP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
00058 *          On entry, the upper or lower triangle of the symmetric matrix
00059 *          B, packed columnwise in a linear array.  The j-th column of B
00060 *          is stored in the array BP as follows:
00061 *          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
00062 *          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
00063 *
00064 *          On exit, the triangular factor U or L from the Cholesky
00065 *          factorization B = U**T*U or B = L*L**T, in the same storage
00066 *          format as B.
00067 *
00068 *  W       (output) DOUBLE PRECISION array, dimension (N)
00069 *          If INFO = 0, the eigenvalues in ascending order.
00070 *
00071 *  Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
00072 *          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
00073 *          eigenvectors.  The eigenvectors are normalized as follows:
00074 *          if ITYPE = 1 or 2, Z**T*B*Z = I;
00075 *          if ITYPE = 3, Z**T*inv(B)*Z = I.
00076 *          If JOBZ = 'N', then Z is not referenced.
00077 *
00078 *  LDZ     (input) INTEGER
00079 *          The leading dimension of the array Z.  LDZ >= 1, and if
00080 *          JOBZ = 'V', LDZ >= max(1,N).
00081 *
00082 *  WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)
00083 *
00084 *  INFO    (output) INTEGER
00085 *          = 0:  successful exit
00086 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00087 *          > 0:  DPPTRF or DSPEV returned an error code:
00088 *             <= N:  if INFO = i, DSPEV failed to converge;
00089 *                    i off-diagonal elements of an intermediate
00090 *                    tridiagonal form did not converge to zero.
00091 *             > N:   if INFO = n + i, for 1 <= i <= n, then the leading
00092 *                    minor of order i of B is not positive definite.
00093 *                    The factorization of B could not be completed and
00094 *                    no eigenvalues or eigenvectors were computed.
00095 *
00096 *  =====================================================================
00097 *
00098 *     .. Local Scalars ..
00099       LOGICAL            UPPER, WANTZ
00100       CHARACTER          TRANS
00101       INTEGER            J, NEIG
00102 *     ..
00103 *     .. External Functions ..
00104       LOGICAL            LSAME
00105       EXTERNAL           LSAME
00106 *     ..
00107 *     .. External Subroutines ..
00108       EXTERNAL           DPPTRF, DSPEV, DSPGST, DTPMV, DTPSV, XERBLA
00109 *     ..
00110 *     .. Executable Statements ..
00111 *
00112 *     Test the input parameters.
00113 *
00114       WANTZ = LSAME( JOBZ, 'V' )
00115       UPPER = LSAME( UPLO, 'U' )
00116 *
00117       INFO = 0
00118       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
00119          INFO = -1
00120       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00121          INFO = -2
00122       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
00123          INFO = -3
00124       ELSE IF( N.LT.0 ) THEN
00125          INFO = -4
00126       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
00127          INFO = -9
00128       END IF
00129       IF( INFO.NE.0 ) THEN
00130          CALL XERBLA( 'DSPGV ', -INFO )
00131          RETURN
00132       END IF
00133 *
00134 *     Quick return if possible
00135 *
00136       IF( N.EQ.0 )
00137      \$   RETURN
00138 *
00139 *     Form a Cholesky factorization of B.
00140 *
00141       CALL DPPTRF( UPLO, N, BP, INFO )
00142       IF( INFO.NE.0 ) THEN
00143          INFO = N + INFO
00144          RETURN
00145       END IF
00146 *
00147 *     Transform problem to standard eigenvalue problem and solve.
00148 *
00149       CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
00150       CALL DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
00151 *
00152       IF( WANTZ ) THEN
00153 *
00154 *        Backtransform eigenvectors to the original problem.
00155 *
00156          NEIG = N
00157          IF( INFO.GT.0 )
00158      \$      NEIG = INFO - 1
00159          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
00160 *
00161 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
00162 *           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
00163 *
00164             IF( UPPER ) THEN
00165                TRANS = 'N'
00166             ELSE
00167                TRANS = 'T'
00168             END IF
00169 *
00170             DO 10 J = 1, NEIG
00171                CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
00172      \$                     1 )
00173    10       CONTINUE
00174 *
00175          ELSE IF( ITYPE.EQ.3 ) THEN
00176 *
00177 *           For B*A*x=(lambda)*x;
00178 *           backtransform eigenvectors: x = L*y or U**T*y
00179 *
00180             IF( UPPER ) THEN
00181                TRANS = 'T'
00182             ELSE
00183                TRANS = 'N'
00184             END IF
00185 *
00186             DO 20 J = 1, NEIG
00187                CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
00188      \$                     1 )
00189    20       CONTINUE
00190          END IF
00191       END IF
00192       RETURN
00193 *
00194 *     End of DSPGV
00195 *
00196       END
```