00001 SUBROUTINE CHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, 00002 $ LDZ, WORK, RWORK, 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 REAL RWORK( * ), W( * ) 00015 COMPLEX AB( LDAB, * ), BB( LDBB, * ), WORK( * ), 00016 $ Z( LDZ, * ) 00017 * .. 00018 * 00019 * Purpose 00020 * ======= 00021 * 00022 * CHBGV computes all the eigenvalues, and optionally, the eigenvectors 00023 * of a complex generalized Hermitian-definite banded eigenproblem, of 00024 * the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian 00025 * and banded, and B is also positive definite. 00026 * 00027 * Arguments 00028 * ========= 00029 * 00030 * JOBZ (input) CHARACTER*1 00031 * = 'N': Compute eigenvalues only; 00032 * = 'V': Compute eigenvalues and eigenvectors. 00033 * 00034 * UPLO (input) CHARACTER*1 00035 * = 'U': Upper triangles of A and B are stored; 00036 * = 'L': Lower triangles of A and B are stored. 00037 * 00038 * N (input) INTEGER 00039 * The order of the matrices A and B. N >= 0. 00040 * 00041 * KA (input) INTEGER 00042 * The number of superdiagonals of the matrix A if UPLO = 'U', 00043 * or the number of subdiagonals if UPLO = 'L'. KA >= 0. 00044 * 00045 * KB (input) INTEGER 00046 * The number of superdiagonals of the matrix B if UPLO = 'U', 00047 * or the number of subdiagonals if UPLO = 'L'. KB >= 0. 00048 * 00049 * AB (input/output) COMPLEX array, dimension (LDAB, N) 00050 * On entry, the upper or lower triangle of the Hermitian band 00051 * matrix A, stored in the first ka+1 rows of the array. The 00052 * j-th column of A is stored in the j-th column of the array AB 00053 * as follows: 00054 * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; 00055 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). 00056 * 00057 * On exit, the contents of AB are destroyed. 00058 * 00059 * LDAB (input) INTEGER 00060 * The leading dimension of the array AB. LDAB >= KA+1. 00061 * 00062 * BB (input/output) COMPLEX array, dimension (LDBB, N) 00063 * On entry, the upper or lower triangle of the Hermitian band 00064 * matrix B, stored in the first kb+1 rows of the array. The 00065 * j-th column of B is stored in the j-th column of the array BB 00066 * as follows: 00067 * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; 00068 * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). 00069 * 00070 * On exit, the factor S from the split Cholesky factorization 00071 * B = S**H*S, as returned by CPBSTF. 00072 * 00073 * LDBB (input) INTEGER 00074 * The leading dimension of the array BB. LDBB >= KB+1. 00075 * 00076 * W (output) REAL array, dimension (N) 00077 * If INFO = 0, the eigenvalues in ascending order. 00078 * 00079 * Z (output) COMPLEX array, dimension (LDZ, N) 00080 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 00081 * eigenvectors, with the i-th column of Z holding the 00082 * eigenvector associated with W(i). The eigenvectors are 00083 * normalized so that Z**H*B*Z = I. 00084 * If JOBZ = 'N', then Z is not referenced. 00085 * 00086 * LDZ (input) INTEGER 00087 * The leading dimension of the array Z. LDZ >= 1, and if 00088 * JOBZ = 'V', LDZ >= N. 00089 * 00090 * WORK (workspace) COMPLEX array, dimension (N) 00091 * 00092 * RWORK (workspace) REAL array, dimension (3*N) 00093 * 00094 * INFO (output) INTEGER 00095 * = 0: successful exit 00096 * < 0: if INFO = -i, the i-th argument had an illegal value 00097 * > 0: if INFO = i, and i is: 00098 * <= N: the algorithm failed to converge: 00099 * i off-diagonal elements of an intermediate 00100 * tridiagonal form did not converge to zero; 00101 * > N: if INFO = N + i, for 1 <= i <= N, then CPBSTF 00102 * returned INFO = i: B is not positive definite. 00103 * The factorization of B could not be completed and 00104 * no eigenvalues or eigenvectors were computed. 00105 * 00106 * ===================================================================== 00107 * 00108 * .. Local Scalars .. 00109 LOGICAL UPPER, WANTZ 00110 CHARACTER VECT 00111 INTEGER IINFO, INDE, INDWRK 00112 * .. 00113 * .. External Functions .. 00114 LOGICAL LSAME 00115 EXTERNAL LSAME 00116 * .. 00117 * .. External Subroutines .. 00118 EXTERNAL CHBGST, CHBTRD, CPBSTF, CSTEQR, SSTERF, XERBLA 00119 * .. 00120 * .. Executable Statements .. 00121 * 00122 * Test the input parameters. 00123 * 00124 WANTZ = LSAME( JOBZ, 'V' ) 00125 UPPER = LSAME( UPLO, 'U' ) 00126 * 00127 INFO = 0 00128 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00129 INFO = -1 00130 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 00131 INFO = -2 00132 ELSE IF( N.LT.0 ) THEN 00133 INFO = -3 00134 ELSE IF( KA.LT.0 ) THEN 00135 INFO = -4 00136 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN 00137 INFO = -5 00138 ELSE IF( LDAB.LT.KA+1 ) THEN 00139 INFO = -7 00140 ELSE IF( LDBB.LT.KB+1 ) THEN 00141 INFO = -9 00142 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00143 INFO = -12 00144 END IF 00145 IF( INFO.NE.0 ) THEN 00146 CALL XERBLA( 'CHBGV ', -INFO ) 00147 RETURN 00148 END IF 00149 * 00150 * Quick return if possible 00151 * 00152 IF( N.EQ.0 ) 00153 $ RETURN 00154 * 00155 * Form a split Cholesky factorization of B. 00156 * 00157 CALL CPBSTF( UPLO, N, KB, BB, LDBB, INFO ) 00158 IF( INFO.NE.0 ) THEN 00159 INFO = N + INFO 00160 RETURN 00161 END IF 00162 * 00163 * Transform problem to standard eigenvalue problem. 00164 * 00165 INDE = 1 00166 INDWRK = INDE + N 00167 CALL CHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ, 00168 $ WORK, RWORK( INDWRK ), IINFO ) 00169 * 00170 * Reduce to tridiagonal form. 00171 * 00172 IF( WANTZ ) THEN 00173 VECT = 'U' 00174 ELSE 00175 VECT = 'N' 00176 END IF 00177 CALL CHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z, 00178 $ LDZ, WORK, IINFO ) 00179 * 00180 * For eigenvalues only, call SSTERF. For eigenvectors, call CSTEQR. 00181 * 00182 IF( .NOT.WANTZ ) THEN 00183 CALL SSTERF( N, W, RWORK( INDE ), INFO ) 00184 ELSE 00185 CALL CSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ, 00186 $ RWORK( INDWRK ), INFO ) 00187 END IF 00188 RETURN 00189 * 00190 * End of CHBGV 00191 * 00192 END
1.7.2