1 SUBROUTINE DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
2 *
3 * -- LAPACK driver routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
10 * ..
11 * .. Array Arguments ..
12 INTEGER IPIV( * )
13 DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DGBSV computes the solution to a real system of linear equations
20 * A * X = B, where A is a band matrix of order N with KL subdiagonals
21 * and KU superdiagonals, and X and B are N-by-NRHS matrices.
22 *
23 * The LU decomposition with partial pivoting and row interchanges is
24 * used to factor A as A = L * U, where L is a product of permutation
25 * and unit lower triangular matrices with KL subdiagonals, and U is
26 * upper triangular with KL+KU superdiagonals. The factored form of A
27 * is then used to solve the system of equations A * X = B.
28 *
29 * Arguments
30 * =========
31 *
32 * N (input) INTEGER
33 * The number of linear equations, i.e., the order of the
34 * matrix A. N >= 0.
35 *
36 * KL (input) INTEGER
37 * The number of subdiagonals within the band of A. KL >= 0.
38 *
39 * KU (input) INTEGER
40 * The number of superdiagonals within the band of A. KU >= 0.
41 *
42 * NRHS (input) INTEGER
43 * The number of right hand sides, i.e., the number of columns
44 * of the matrix B. NRHS >= 0.
45 *
46 * AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
47 * On entry, the matrix A in band storage, in rows KL+1 to
48 * 2*KL+KU+1; rows 1 to KL of the array need not be set.
49 * The j-th column of A is stored in the j-th column of the
50 * array AB as follows:
51 * AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
52 * On exit, details of the factorization: U is stored as an
53 * upper triangular band matrix with KL+KU superdiagonals in
54 * rows 1 to KL+KU+1, and the multipliers used during the
55 * factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
56 * See below for further details.
57 *
58 * LDAB (input) INTEGER
59 * The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
60 *
61 * IPIV (output) INTEGER array, dimension (N)
62 * The pivot indices that define the permutation matrix P;
63 * row i of the matrix was interchanged with row IPIV(i).
64 *
65 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
66 * On entry, the N-by-NRHS right hand side matrix B.
67 * On exit, if INFO = 0, the N-by-NRHS solution matrix X.
68 *
69 * LDB (input) INTEGER
70 * The leading dimension of the array B. LDB >= max(1,N).
71 *
72 * INFO (output) INTEGER
73 * = 0: successful exit
74 * < 0: if INFO = -i, the i-th argument had an illegal value
75 * > 0: if INFO = i, U(i,i) is exactly zero. The factorization
76 * has been completed, but the factor U is exactly
77 * singular, and the solution has not been computed.
78 *
79 * Further Details
80 * ===============
81 *
82 * The band storage scheme is illustrated by the following example, when
83 * M = N = 6, KL = 2, KU = 1:
84 *
85 * On entry: On exit:
86 *
87 * * * * + + + * * * u14 u25 u36
88 * * * + + + + * * u13 u24 u35 u46
89 * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
90 * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
91 * a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
92 * a31 a42 a53 a64 * * m31 m42 m53 m64 * *
93 *
94 * Array elements marked * are not used by the routine; elements marked
95 * + need not be set on entry, but are required by the routine to store
96 * elements of U because of fill-in resulting from the row interchanges.
97 *
98 * =====================================================================
99 *
100 * .. External Subroutines ..
101 EXTERNAL DGBTRF, DGBTRS, XERBLA
102 * ..
103 * .. Intrinsic Functions ..
104 INTRINSIC MAX
105 * ..
106 * .. Executable Statements ..
107 *
108 * Test the input parameters.
109 *
110 INFO = 0
111 IF( N.LT.0 ) THEN
112 INFO = -1
113 ELSE IF( KL.LT.0 ) THEN
114 INFO = -2
115 ELSE IF( KU.LT.0 ) THEN
116 INFO = -3
117 ELSE IF( NRHS.LT.0 ) THEN
118 INFO = -4
119 ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
120 INFO = -6
121 ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
122 INFO = -9
123 END IF
124 IF( INFO.NE.0 ) THEN
125 CALL XERBLA( 'DGBSV ', -INFO )
126 RETURN
127 END IF
128 *
129 * Compute the LU factorization of the band matrix A.
130 *
131 CALL DGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
132 IF( INFO.EQ.0 ) THEN
133 *
134 * Solve the system A*X = B, overwriting B with X.
135 *
136 CALL DGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
137 $ B, LDB, INFO )
138 END IF
139 RETURN
140 *
141 * End of DGBSV
142 *
143 END
2 *
3 * -- LAPACK driver routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
10 * ..
11 * .. Array Arguments ..
12 INTEGER IPIV( * )
13 DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DGBSV computes the solution to a real system of linear equations
20 * A * X = B, where A is a band matrix of order N with KL subdiagonals
21 * and KU superdiagonals, and X and B are N-by-NRHS matrices.
22 *
23 * The LU decomposition with partial pivoting and row interchanges is
24 * used to factor A as A = L * U, where L is a product of permutation
25 * and unit lower triangular matrices with KL subdiagonals, and U is
26 * upper triangular with KL+KU superdiagonals. The factored form of A
27 * is then used to solve the system of equations A * X = B.
28 *
29 * Arguments
30 * =========
31 *
32 * N (input) INTEGER
33 * The number of linear equations, i.e., the order of the
34 * matrix A. N >= 0.
35 *
36 * KL (input) INTEGER
37 * The number of subdiagonals within the band of A. KL >= 0.
38 *
39 * KU (input) INTEGER
40 * The number of superdiagonals within the band of A. KU >= 0.
41 *
42 * NRHS (input) INTEGER
43 * The number of right hand sides, i.e., the number of columns
44 * of the matrix B. NRHS >= 0.
45 *
46 * AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
47 * On entry, the matrix A in band storage, in rows KL+1 to
48 * 2*KL+KU+1; rows 1 to KL of the array need not be set.
49 * The j-th column of A is stored in the j-th column of the
50 * array AB as follows:
51 * AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
52 * On exit, details of the factorization: U is stored as an
53 * upper triangular band matrix with KL+KU superdiagonals in
54 * rows 1 to KL+KU+1, and the multipliers used during the
55 * factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
56 * See below for further details.
57 *
58 * LDAB (input) INTEGER
59 * The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
60 *
61 * IPIV (output) INTEGER array, dimension (N)
62 * The pivot indices that define the permutation matrix P;
63 * row i of the matrix was interchanged with row IPIV(i).
64 *
65 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
66 * On entry, the N-by-NRHS right hand side matrix B.
67 * On exit, if INFO = 0, the N-by-NRHS solution matrix X.
68 *
69 * LDB (input) INTEGER
70 * The leading dimension of the array B. LDB >= max(1,N).
71 *
72 * INFO (output) INTEGER
73 * = 0: successful exit
74 * < 0: if INFO = -i, the i-th argument had an illegal value
75 * > 0: if INFO = i, U(i,i) is exactly zero. The factorization
76 * has been completed, but the factor U is exactly
77 * singular, and the solution has not been computed.
78 *
79 * Further Details
80 * ===============
81 *
82 * The band storage scheme is illustrated by the following example, when
83 * M = N = 6, KL = 2, KU = 1:
84 *
85 * On entry: On exit:
86 *
87 * * * * + + + * * * u14 u25 u36
88 * * * + + + + * * u13 u24 u35 u46
89 * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
90 * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
91 * a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
92 * a31 a42 a53 a64 * * m31 m42 m53 m64 * *
93 *
94 * Array elements marked * are not used by the routine; elements marked
95 * + need not be set on entry, but are required by the routine to store
96 * elements of U because of fill-in resulting from the row interchanges.
97 *
98 * =====================================================================
99 *
100 * .. External Subroutines ..
101 EXTERNAL DGBTRF, DGBTRS, XERBLA
102 * ..
103 * .. Intrinsic Functions ..
104 INTRINSIC MAX
105 * ..
106 * .. Executable Statements ..
107 *
108 * Test the input parameters.
109 *
110 INFO = 0
111 IF( N.LT.0 ) THEN
112 INFO = -1
113 ELSE IF( KL.LT.0 ) THEN
114 INFO = -2
115 ELSE IF( KU.LT.0 ) THEN
116 INFO = -3
117 ELSE IF( NRHS.LT.0 ) THEN
118 INFO = -4
119 ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
120 INFO = -6
121 ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
122 INFO = -9
123 END IF
124 IF( INFO.NE.0 ) THEN
125 CALL XERBLA( 'DGBSV ', -INFO )
126 RETURN
127 END IF
128 *
129 * Compute the LU factorization of the band matrix A.
130 *
131 CALL DGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
132 IF( INFO.EQ.0 ) THEN
133 *
134 * Solve the system A*X = B, overwriting B with X.
135 *
136 CALL DGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
137 $ B, LDB, INFO )
138 END IF
139 RETURN
140 *
141 * End of DGBSV
142 *
143 END