00001 SUBROUTINE CPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) 00002 * 00003 * -- LAPACK driver routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER UPLO 00010 INTEGER INFO, KD, LDAB, LDB, N, NRHS 00011 * .. 00012 * .. Array Arguments .. 00013 COMPLEX AB( LDAB, * ), B( LDB, * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * CPBSV computes the solution to a complex system of linear equations 00020 * A * X = B, 00021 * where A is an N-by-N Hermitian positive definite band matrix and X 00022 * and B are N-by-NRHS matrices. 00023 * 00024 * The Cholesky decomposition is used to factor A as 00025 * A = U**H * U, if UPLO = 'U', or 00026 * A = L * L**H, if UPLO = 'L', 00027 * where U is an upper triangular band matrix, and L is a lower 00028 * triangular band matrix, with the same number of superdiagonals or 00029 * subdiagonals as A. The factored form of A is then used to solve the 00030 * system of equations A * X = B. 00031 * 00032 * Arguments 00033 * ========= 00034 * 00035 * UPLO (input) CHARACTER*1 00036 * = 'U': Upper triangle of A is stored; 00037 * = 'L': Lower triangle of A is stored. 00038 * 00039 * N (input) INTEGER 00040 * The number of linear equations, i.e., the order of the 00041 * matrix A. N >= 0. 00042 * 00043 * KD (input) INTEGER 00044 * The number of superdiagonals of the matrix A if UPLO = 'U', 00045 * or the number of subdiagonals if UPLO = 'L'. KD >= 0. 00046 * 00047 * NRHS (input) INTEGER 00048 * The number of right hand sides, i.e., the number of columns 00049 * of the matrix B. NRHS >= 0. 00050 * 00051 * AB (input/output) COMPLEX array, dimension (LDAB,N) 00052 * On entry, the upper or lower triangle of the Hermitian band 00053 * matrix A, stored in the first KD+1 rows of the array. The 00054 * j-th column of A is stored in the j-th column of the array AB 00055 * as follows: 00056 * if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; 00057 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). 00058 * See below for further details. 00059 * 00060 * On exit, if INFO = 0, the triangular factor U or L from the 00061 * Cholesky factorization A = U**H*U or A = L*L**H of the band 00062 * matrix A, in the same storage format as A. 00063 * 00064 * LDAB (input) INTEGER 00065 * The leading dimension of the array AB. LDAB >= KD+1. 00066 * 00067 * B (input/output) COMPLEX array, dimension (LDB,NRHS) 00068 * On entry, the N-by-NRHS right hand side matrix B. 00069 * On exit, if INFO = 0, the N-by-NRHS solution matrix X. 00070 * 00071 * LDB (input) INTEGER 00072 * The leading dimension of the array B. LDB >= max(1,N). 00073 * 00074 * INFO (output) INTEGER 00075 * = 0: successful exit 00076 * < 0: if INFO = -i, the i-th argument had an illegal value 00077 * > 0: if INFO = i, the leading minor of order i of A is not 00078 * positive definite, so the factorization could not be 00079 * completed, and the solution has not been computed. 00080 * 00081 * Further Details 00082 * =============== 00083 * 00084 * The band storage scheme is illustrated by the following example, when 00085 * N = 6, KD = 2, and UPLO = 'U': 00086 * 00087 * On entry: On exit: 00088 * 00089 * * * a13 a24 a35 a46 * * u13 u24 u35 u46 00090 * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 00091 * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 00092 * 00093 * Similarly, if UPLO = 'L' the format of A is as follows: 00094 * 00095 * On entry: On exit: 00096 * 00097 * a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 00098 * a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * 00099 * a31 a42 a53 a64 * * l31 l42 l53 l64 * * 00100 * 00101 * Array elements marked * are not used by the routine. 00102 * 00103 * ===================================================================== 00104 * 00105 * .. External Functions .. 00106 LOGICAL LSAME 00107 EXTERNAL LSAME 00108 * .. 00109 * .. External Subroutines .. 00110 EXTERNAL CPBTRF, CPBTRS, XERBLA 00111 * .. 00112 * .. Intrinsic Functions .. 00113 INTRINSIC MAX 00114 * .. 00115 * .. Executable Statements .. 00116 * 00117 * Test the input parameters. 00118 * 00119 INFO = 0 00120 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00121 INFO = -1 00122 ELSE IF( N.LT.0 ) THEN 00123 INFO = -2 00124 ELSE IF( KD.LT.0 ) THEN 00125 INFO = -3 00126 ELSE IF( NRHS.LT.0 ) THEN 00127 INFO = -4 00128 ELSE IF( LDAB.LT.KD+1 ) THEN 00129 INFO = -6 00130 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00131 INFO = -8 00132 END IF 00133 IF( INFO.NE.0 ) THEN 00134 CALL XERBLA( 'CPBSV ', -INFO ) 00135 RETURN 00136 END IF 00137 * 00138 * Compute the Cholesky factorization A = U'*U or A = L*L'. 00139 * 00140 CALL CPBTRF( UPLO, N, KD, AB, LDAB, INFO ) 00141 IF( INFO.EQ.0 ) THEN 00142 * 00143 * Solve the system A*X = B, overwriting B with X. 00144 * 00145 CALL CPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) 00146 * 00147 END IF 00148 RETURN 00149 * 00150 * End of CPBSV 00151 * 00152 END
1.7.2