1DPBSV(1) LAPACK driver routine (version 3.1) DPBSV(1)
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6 DPBSV - the solution to a real system of linear equations A * X = B,
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9 SUBROUTINE DPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
10 CHARACTER UPLO
12 INTEGER INFO, KD, LDAB, LDB, N, NRHS
14 DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
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18 DPBSV computes the solution to a real system of linear equations
19 A * X = B, where A is an N-by-N symmetric positive definite band
20 matrix and X and B are N-by-NRHS matrices.
21 The Cholesky decomposition is used to factor A as
23 A = U**T * U, if UPLO = 'U', or
24 A = L * L**T, if UPLO = 'L',
25 where U is an upper triangular band matrix, and L is a lower triangular
26 band matrix, with the same number of superdiagonals or subdiagonals as
27 A. The factored form of A is then used to solve the system of equa‐
28 tions A * X = B.
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32 UPLO (input) CHARACTER*1
33 = 'U': Upper triangle of A is stored;
34 = 'L': Lower triangle of A is stored.
35 N (input) INTEGER
37 The number of linear equations, i.e., the order of the matrix
38 A. N >= 0.
39 KD (input) INTEGER
41 The number of superdiagonals of the matrix A if UPLO = 'U', or
42 the number of subdiagonals if UPLO = 'L'. KD >= 0.
43 NRHS (input) INTEGER
45 The number of right hand sides, i.e., the number of columns of
46 the matrix B. NRHS >= 0.
47 AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
49 On entry, the upper or lower triangle of the symmetric band
50 matrix A, stored in the first KD+1 rows of the array. The j-th
51 column of A is stored in the j-th column of the array AB as
52 follows: if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-
53 KD)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
54 j<=i<=min(N,j+KD). See below for further details.
55 On exit, if INFO = 0, the triangular factor U or L from the
57 Cholesky factorization A = U**T*U or A = L*L**T of the band
58 matrix A, in the same storage format as A.
59 LDAB (input) INTEGER
61 The leading dimension of the array AB. LDAB >= KD+1.
62 B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
64 On entry, the N-by-NRHS right hand side matrix B. On exit, if
65 INFO = 0, the N-by-NRHS solution matrix X.
66 LDB (input) INTEGER
68 The leading dimension of the array B. LDB >= max(1,N).
69 INFO (output) INTEGER
71 = 0: successful exit
72 < 0: if INFO = -i, the i-th argument had an illegal value
73 > 0: if INFO = i, the leading minor of order i of A is not
74 positive definite, so the factorization could not be completed,
75 and the solution has not been computed.
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78 The band storage scheme is illustrated by the following example, when N
79 = 6, KD = 2, and UPLO = 'U':
80 On entry: On exit:
82 * * a13 a24 a35 a46 * * u13 u24 u35 u46
84 * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
85 a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
86 Similarly, if UPLO = 'L' the format of A is as follows:
88 On entry: On exit:
90 a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
92 a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
93 a31 a42 a53 a64 * * l31 l42 l53 l64 * *
94 Array elements marked * are not used by the routine.
96 LAPACK driver routine (version 3.N1o)vember 2006 DPBSV(1)