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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE CGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, 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 INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS 00010 * .. 00011 * .. Array Arguments .. 00012 INTEGER IPIV( * ) 00013 COMPLEX AB( LDAB, * ), B( LDB, * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * CGBSV computes the solution to a complex system of linear equations 00020 * A * X = B, where A is a band matrix of order N with KL subdiagonals 00021 * and KU superdiagonals, and X and B are N-by-NRHS matrices. 00022 * 00023 * The LU decomposition with partial pivoting and row interchanges is 00024 * used to factor A as A = L * U, where L is a product of permutation 00025 * and unit lower triangular matrices with KL subdiagonals, and U is 00026 * upper triangular with KL+KU superdiagonals. The factored form of A 00027 * is then used to solve the system of equations A * X = B. 00028 * 00029 * Arguments 00030 * ========= 00031 * 00032 * N (input) INTEGER 00033 * The number of linear equations, i.e., the order of the 00034 * matrix A. N >= 0. 00035 * 00036 * KL (input) INTEGER 00037 * The number of subdiagonals within the band of A. KL >= 0. 00038 * 00039 * KU (input) INTEGER 00040 * The number of superdiagonals within the band of A. KU >= 0. 00041 * 00042 * NRHS (input) INTEGER 00043 * The number of right hand sides, i.e., the number of columns 00044 * of the matrix B. NRHS >= 0. 00045 * 00046 * AB (input/output) COMPLEX array, dimension (LDAB,N) 00047 * On entry, the matrix A in band storage, in rows KL+1 to 00048 * 2*KL+KU+1; rows 1 to KL of the array need not be set. 00049 * The j-th column of A is stored in the j-th column of the 00050 * array AB as follows: 00051 * AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL) 00052 * On exit, details of the factorization: U is stored as an 00053 * upper triangular band matrix with KL+KU superdiagonals in 00054 * rows 1 to KL+KU+1, and the multipliers used during the 00055 * factorization are stored in rows KL+KU+2 to 2*KL+KU+1. 00056 * See below for further details. 00057 * 00058 * LDAB (input) INTEGER 00059 * The leading dimension of the array AB. LDAB >= 2*KL+KU+1. 00060 * 00061 * IPIV (output) INTEGER array, dimension (N) 00062 * The pivot indices that define the permutation matrix P; 00063 * row i of the matrix was interchanged with row IPIV(i). 00064 * 00065 * B (input/output) COMPLEX array, dimension (LDB,NRHS) 00066 * On entry, the N-by-NRHS right hand side matrix B. 00067 * On exit, if INFO = 0, the N-by-NRHS solution matrix X. 00068 * 00069 * LDB (input) INTEGER 00070 * The leading dimension of the array B. LDB >= max(1,N). 00071 * 00072 * INFO (output) INTEGER 00073 * = 0: successful exit 00074 * < 0: if INFO = -i, the i-th argument had an illegal value 00075 * > 0: if INFO = i, U(i,i) is exactly zero. The factorization 00076 * has been completed, but the factor U is exactly 00077 * singular, and the solution has not been computed. 00078 * 00079 * Further Details 00080 * =============== 00081 * 00082 * The band storage scheme is illustrated by the following example, when 00083 * M = N = 6, KL = 2, KU = 1: 00084 * 00085 * On entry: On exit: 00086 * 00087 * * * * + + + * * * u14 u25 u36 00088 * * * + + + + * * u13 u24 u35 u46 00089 * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 00090 * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 00091 * a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * 00092 * a31 a42 a53 a64 * * m31 m42 m53 m64 * * 00093 * 00094 * Array elements marked * are not used by the routine; elements marked 00095 * + need not be set on entry, but are required by the routine to store 00096 * elements of U because of fill-in resulting from the row interchanges. 00097 * 00098 * ===================================================================== 00099 * 00100 * .. External Subroutines .. 00101 EXTERNAL CGBTRF, CGBTRS, XERBLA 00102 * .. 00103 * .. Intrinsic Functions .. 00104 INTRINSIC MAX 00105 * .. 00106 * .. Executable Statements .. 00107 * 00108 * Test the input parameters. 00109 * 00110 INFO = 0 00111 IF( N.LT.0 ) THEN 00112 INFO = -1 00113 ELSE IF( KL.LT.0 ) THEN 00114 INFO = -2 00115 ELSE IF( KU.LT.0 ) THEN 00116 INFO = -3 00117 ELSE IF( NRHS.LT.0 ) THEN 00118 INFO = -4 00119 ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN 00120 INFO = -6 00121 ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN 00122 INFO = -9 00123 END IF 00124 IF( INFO.NE.0 ) THEN 00125 CALL XERBLA( 'CGBSV ', -INFO ) 00126 RETURN 00127 END IF 00128 * 00129 * Compute the LU factorization of the band matrix A. 00130 * 00131 CALL CGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO ) 00132 IF( INFO.EQ.0 ) THEN 00133 * 00134 * Solve the system A*X = B, overwriting B with X. 00135 * 00136 CALL CGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV, 00137 $ B, LDB, INFO ) 00138 END IF 00139 RETURN 00140 * 00141 * End of CGBSV 00142 * 00143 END