00001 SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, 00002 $ LDZ, WORK, INFO ) 00003 * 00004 * -- LAPACK driver routine (version 3.2) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * November 2006 00008 * 00009 * .. Scalar Arguments .. 00010 CHARACTER JOBZ, UPLO 00011 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N 00012 * .. 00013 * .. Array Arguments .. 00014 DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ), 00015 $ WORK( * ), Z( LDZ, * ) 00016 * .. 00017 * 00018 * Purpose 00019 * ======= 00020 * 00021 * DSBGV computes all the eigenvalues, and optionally, the eigenvectors 00022 * of a real generalized symmetric-definite banded eigenproblem, of 00023 * the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric 00024 * and banded, and B is also positive definite. 00025 * 00026 * Arguments 00027 * ========= 00028 * 00029 * JOBZ (input) CHARACTER*1 00030 * = 'N': Compute eigenvalues only; 00031 * = 'V': Compute eigenvalues and eigenvectors. 00032 * 00033 * UPLO (input) CHARACTER*1 00034 * = 'U': Upper triangles of A and B are stored; 00035 * = 'L': Lower triangles of A and B are stored. 00036 * 00037 * N (input) INTEGER 00038 * The order of the matrices A and B. N >= 0. 00039 * 00040 * KA (input) INTEGER 00041 * The number of superdiagonals of the matrix A if UPLO = 'U', 00042 * or the number of subdiagonals if UPLO = 'L'. KA >= 0. 00043 * 00044 * KB (input) INTEGER 00045 * The number of superdiagonals of the matrix B if UPLO = 'U', 00046 * or the number of subdiagonals if UPLO = 'L'. KB >= 0. 00047 * 00048 * AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N) 00049 * On entry, the upper or lower triangle of the symmetric band 00050 * matrix A, stored in the first ka+1 rows of the array. The 00051 * j-th column of A is stored in the j-th column of the array AB 00052 * as follows: 00053 * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; 00054 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). 00055 * 00056 * On exit, the contents of AB are destroyed. 00057 * 00058 * LDAB (input) INTEGER 00059 * The leading dimension of the array AB. LDAB >= KA+1. 00060 * 00061 * BB (input/output) DOUBLE PRECISION array, dimension (LDBB, N) 00062 * On entry, the upper or lower triangle of the symmetric band 00063 * matrix B, stored in the first kb+1 rows of the array. The 00064 * j-th column of B is stored in the j-th column of the array BB 00065 * as follows: 00066 * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; 00067 * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). 00068 * 00069 * On exit, the factor S from the split Cholesky factorization 00070 * B = S**T*S, as returned by DPBSTF. 00071 * 00072 * LDBB (input) INTEGER 00073 * The leading dimension of the array BB. LDBB >= KB+1. 00074 * 00075 * W (output) DOUBLE PRECISION array, dimension (N) 00076 * If INFO = 0, the eigenvalues in ascending order. 00077 * 00078 * Z (output) DOUBLE PRECISION array, dimension (LDZ, N) 00079 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 00080 * eigenvectors, with the i-th column of Z holding the 00081 * eigenvector associated with W(i). The eigenvectors are 00082 * normalized so that Z**T*B*Z = I. 00083 * If JOBZ = 'N', then Z is not referenced. 00084 * 00085 * LDZ (input) INTEGER 00086 * The leading dimension of the array Z. LDZ >= 1, and if 00087 * JOBZ = 'V', LDZ >= N. 00088 * 00089 * WORK (workspace) DOUBLE PRECISION array, dimension (3*N) 00090 * 00091 * INFO (output) INTEGER 00092 * = 0: successful exit 00093 * < 0: if INFO = -i, the i-th argument had an illegal value 00094 * > 0: if INFO = i, and i is: 00095 * <= N: the algorithm failed to converge: 00096 * i off-diagonal elements of an intermediate 00097 * tridiagonal form did not converge to zero; 00098 * > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF 00099 * returned INFO = i: B is not positive definite. 00100 * The factorization of B could not be completed and 00101 * no eigenvalues or eigenvectors were computed. 00102 * 00103 * ===================================================================== 00104 * 00105 * .. Local Scalars .. 00106 LOGICAL UPPER, WANTZ 00107 CHARACTER VECT 00108 INTEGER IINFO, INDE, INDWRK 00109 * .. 00110 * .. External Functions .. 00111 LOGICAL LSAME 00112 EXTERNAL LSAME 00113 * .. 00114 * .. External Subroutines .. 00115 EXTERNAL DPBSTF, DSBGST, DSBTRD, DSTEQR, DSTERF, XERBLA 00116 * .. 00117 * .. Executable Statements .. 00118 * 00119 * Test the input parameters. 00120 * 00121 WANTZ = LSAME( JOBZ, 'V' ) 00122 UPPER = LSAME( UPLO, 'U' ) 00123 * 00124 INFO = 0 00125 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00126 INFO = -1 00127 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 00128 INFO = -2 00129 ELSE IF( N.LT.0 ) THEN 00130 INFO = -3 00131 ELSE IF( KA.LT.0 ) THEN 00132 INFO = -4 00133 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN 00134 INFO = -5 00135 ELSE IF( LDAB.LT.KA+1 ) THEN 00136 INFO = -7 00137 ELSE IF( LDBB.LT.KB+1 ) THEN 00138 INFO = -9 00139 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00140 INFO = -12 00141 END IF 00142 IF( INFO.NE.0 ) THEN 00143 CALL XERBLA( 'DSBGV ', -INFO ) 00144 RETURN 00145 END IF 00146 * 00147 * Quick return if possible 00148 * 00149 IF( N.EQ.0 ) 00150 $ RETURN 00151 * 00152 * Form a split Cholesky factorization of B. 00153 * 00154 CALL DPBSTF( UPLO, N, KB, BB, LDBB, INFO ) 00155 IF( INFO.NE.0 ) THEN 00156 INFO = N + INFO 00157 RETURN 00158 END IF 00159 * 00160 * Transform problem to standard eigenvalue problem. 00161 * 00162 INDE = 1 00163 INDWRK = INDE + N 00164 CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ, 00165 $ WORK( INDWRK ), IINFO ) 00166 * 00167 * Reduce to tridiagonal form. 00168 * 00169 IF( WANTZ ) THEN 00170 VECT = 'U' 00171 ELSE 00172 VECT = 'N' 00173 END IF 00174 CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ, 00175 $ WORK( INDWRK ), IINFO ) 00176 * 00177 * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEQR. 00178 * 00179 IF( .NOT.WANTZ ) THEN 00180 CALL DSTERF( N, W, WORK( INDE ), INFO ) 00181 ELSE 00182 CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ), 00183 $ INFO ) 00184 END IF 00185 RETURN 00186 * 00187 * End of DSBGV 00188 * 00189 END
1.7.2