1 SUBROUTINE ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER INFO, KD, LDAB, LDB, N, NRHS
11 * ..
12 * .. Array Arguments ..
13 COMPLEX*16 AB( LDAB, * ), B( LDB, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZPBTRS solves a system of linear equations A*X = B with a Hermitian
20 * positive definite band matrix A using the Cholesky factorization
21 * A = U**H *U or A = L*L**H computed by ZPBTRF.
22 *
23 * Arguments
24 * =========
25 *
26 * UPLO (input) CHARACTER*1
27 * = 'U': Upper triangular factor stored in AB;
28 * = 'L': Lower triangular factor stored in AB.
29 *
30 * N (input) INTEGER
31 * The order of the matrix A. N >= 0.
32 *
33 * KD (input) INTEGER
34 * The number of superdiagonals of the matrix A if UPLO = 'U',
35 * or the number of subdiagonals if UPLO = 'L'. KD >= 0.
36 *
37 * NRHS (input) INTEGER
38 * The number of right hand sides, i.e., the number of columns
39 * of the matrix B. NRHS >= 0.
40 *
41 * AB (input) COMPLEX*16 array, dimension (LDAB,N)
42 * The triangular factor U or L from the Cholesky factorization
43 * A = U**H *U or A = L*L**H of the band matrix A, stored in the
44 * first KD+1 rows of the array. The j-th column of U or L is
45 * stored in the j-th column of the array AB as follows:
46 * if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
47 * if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
48 *
49 * LDAB (input) INTEGER
50 * The leading dimension of the array AB. LDAB >= KD+1.
51 *
52 * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
53 * On entry, the right hand side matrix B.
54 * On exit, the solution matrix X.
55 *
56 * LDB (input) INTEGER
57 * The leading dimension of the array B. LDB >= max(1,N).
58 *
59 * INFO (output) INTEGER
60 * = 0: successful exit
61 * < 0: if INFO = -i, the i-th argument had an illegal value
62 *
63 * =====================================================================
64 *
65 * .. Local Scalars ..
66 LOGICAL UPPER
67 INTEGER J
68 * ..
69 * .. External Functions ..
70 LOGICAL LSAME
71 EXTERNAL LSAME
72 * ..
73 * .. External Subroutines ..
74 EXTERNAL XERBLA, ZTBSV
75 * ..
76 * .. Intrinsic Functions ..
77 INTRINSIC MAX
78 * ..
79 * .. Executable Statements ..
80 *
81 * Test the input parameters.
82 *
83 INFO = 0
84 UPPER = LSAME( UPLO, 'U' )
85 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
86 INFO = -1
87 ELSE IF( N.LT.0 ) THEN
88 INFO = -2
89 ELSE IF( KD.LT.0 ) THEN
90 INFO = -3
91 ELSE IF( NRHS.LT.0 ) THEN
92 INFO = -4
93 ELSE IF( LDAB.LT.KD+1 ) THEN
94 INFO = -6
95 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
96 INFO = -8
97 END IF
98 IF( INFO.NE.0 ) THEN
99 CALL XERBLA( 'ZPBTRS', -INFO )
100 RETURN
101 END IF
102 *
103 * Quick return if possible
104 *
105 IF( N.EQ.0 .OR. NRHS.EQ.0 )
106 $ RETURN
107 *
108 IF( UPPER ) THEN
109 *
110 * Solve A*X = B where A = U**H *U.
111 *
112 DO 10 J = 1, NRHS
113 *
114 * Solve U**H *X = B, overwriting B with X.
115 *
116 CALL ZTBSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
117 $ KD, AB, LDAB, B( 1, J ), 1 )
118 *
119 * Solve U*X = B, overwriting B with X.
120 *
121 CALL ZTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
122 $ LDAB, B( 1, J ), 1 )
123 10 CONTINUE
124 ELSE
125 *
126 * Solve A*X = B where A = L*L**H.
127 *
128 DO 20 J = 1, NRHS
129 *
130 * Solve L*X = B, overwriting B with X.
131 *
132 CALL ZTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
133 $ LDAB, B( 1, J ), 1 )
134 *
135 * Solve L**H *X = B, overwriting B with X.
136 *
137 CALL ZTBSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
138 $ KD, AB, LDAB, B( 1, J ), 1 )
139 20 CONTINUE
140 END IF
141 *
142 RETURN
143 *
144 * End of ZPBTRS
145 *
146 END
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER INFO, KD, LDAB, LDB, N, NRHS
11 * ..
12 * .. Array Arguments ..
13 COMPLEX*16 AB( LDAB, * ), B( LDB, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZPBTRS solves a system of linear equations A*X = B with a Hermitian
20 * positive definite band matrix A using the Cholesky factorization
21 * A = U**H *U or A = L*L**H computed by ZPBTRF.
22 *
23 * Arguments
24 * =========
25 *
26 * UPLO (input) CHARACTER*1
27 * = 'U': Upper triangular factor stored in AB;
28 * = 'L': Lower triangular factor stored in AB.
29 *
30 * N (input) INTEGER
31 * The order of the matrix A. N >= 0.
32 *
33 * KD (input) INTEGER
34 * The number of superdiagonals of the matrix A if UPLO = 'U',
35 * or the number of subdiagonals if UPLO = 'L'. KD >= 0.
36 *
37 * NRHS (input) INTEGER
38 * The number of right hand sides, i.e., the number of columns
39 * of the matrix B. NRHS >= 0.
40 *
41 * AB (input) COMPLEX*16 array, dimension (LDAB,N)
42 * The triangular factor U or L from the Cholesky factorization
43 * A = U**H *U or A = L*L**H of the band matrix A, stored in the
44 * first KD+1 rows of the array. The j-th column of U or L is
45 * stored in the j-th column of the array AB as follows:
46 * if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
47 * if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
48 *
49 * LDAB (input) INTEGER
50 * The leading dimension of the array AB. LDAB >= KD+1.
51 *
52 * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
53 * On entry, the right hand side matrix B.
54 * On exit, the solution matrix X.
55 *
56 * LDB (input) INTEGER
57 * The leading dimension of the array B. LDB >= max(1,N).
58 *
59 * INFO (output) INTEGER
60 * = 0: successful exit
61 * < 0: if INFO = -i, the i-th argument had an illegal value
62 *
63 * =====================================================================
64 *
65 * .. Local Scalars ..
66 LOGICAL UPPER
67 INTEGER J
68 * ..
69 * .. External Functions ..
70 LOGICAL LSAME
71 EXTERNAL LSAME
72 * ..
73 * .. External Subroutines ..
74 EXTERNAL XERBLA, ZTBSV
75 * ..
76 * .. Intrinsic Functions ..
77 INTRINSIC MAX
78 * ..
79 * .. Executable Statements ..
80 *
81 * Test the input parameters.
82 *
83 INFO = 0
84 UPPER = LSAME( UPLO, 'U' )
85 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
86 INFO = -1
87 ELSE IF( N.LT.0 ) THEN
88 INFO = -2
89 ELSE IF( KD.LT.0 ) THEN
90 INFO = -3
91 ELSE IF( NRHS.LT.0 ) THEN
92 INFO = -4
93 ELSE IF( LDAB.LT.KD+1 ) THEN
94 INFO = -6
95 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
96 INFO = -8
97 END IF
98 IF( INFO.NE.0 ) THEN
99 CALL XERBLA( 'ZPBTRS', -INFO )
100 RETURN
101 END IF
102 *
103 * Quick return if possible
104 *
105 IF( N.EQ.0 .OR. NRHS.EQ.0 )
106 $ RETURN
107 *
108 IF( UPPER ) THEN
109 *
110 * Solve A*X = B where A = U**H *U.
111 *
112 DO 10 J = 1, NRHS
113 *
114 * Solve U**H *X = B, overwriting B with X.
115 *
116 CALL ZTBSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
117 $ KD, AB, LDAB, B( 1, J ), 1 )
118 *
119 * Solve U*X = B, overwriting B with X.
120 *
121 CALL ZTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
122 $ LDAB, B( 1, J ), 1 )
123 10 CONTINUE
124 ELSE
125 *
126 * Solve A*X = B where A = L*L**H.
127 *
128 DO 20 J = 1, NRHS
129 *
130 * Solve L*X = B, overwriting B with X.
131 *
132 CALL ZTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
133 $ LDAB, B( 1, J ), 1 )
134 *
135 * Solve L**H *X = B, overwriting B with X.
136 *
137 CALL ZTBSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
138 $ KD, AB, LDAB, B( 1, J ), 1 )
139 20 CONTINUE
140 END IF
141 *
142 RETURN
143 *
144 * End of ZPBTRS
145 *
146 END