1 SUBROUTINE SLAPTM( N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB )
2 *
3 * -- LAPACK auxiliary routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 INTEGER LDB, LDX, N, NRHS
9 REAL ALPHA, BETA
10 * ..
11 * .. Array Arguments ..
12 REAL B( LDB, * ), D( * ), E( * ), X( LDX, * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * SLAPTM multiplies an N by NRHS matrix X by a symmetric tridiagonal
19 * matrix A and stores the result in a matrix B. The operation has the
20 * form
21 *
22 * B := alpha * A * X + beta * B
23 *
24 * where alpha may be either 1. or -1. and beta may be 0., 1., or -1.
25 *
26 * Arguments
27 * =========
28 *
29 * N (input) INTEGER
30 * The order of the matrix A. N >= 0.
31 *
32 * NRHS (input) INTEGER
33 * The number of right hand sides, i.e., the number of columns
34 * of the matrices X and B.
35 *
36 * ALPHA (input) REAL
37 * The scalar alpha. ALPHA must be 1. or -1.; otherwise,
38 * it is assumed to be 0.
39 *
40 * D (input) REAL array, dimension (N)
41 * The n diagonal elements of the tridiagonal matrix A.
42 *
43 * E (input) REAL array, dimension (N-1)
44 * The (n-1) subdiagonal or superdiagonal elements of A.
45 *
46 * X (input) REAL array, dimension (LDX,NRHS)
47 * The N by NRHS matrix X.
48 *
49 * LDX (input) INTEGER
50 * The leading dimension of the array X. LDX >= max(N,1).
51 *
52 * BETA (input) REAL
53 * The scalar beta. BETA must be 0., 1., or -1.; otherwise,
54 * it is assumed to be 1.
55 *
56 * B (input/output) REAL array, dimension (LDB,NRHS)
57 * On entry, the N by NRHS matrix B.
58 * On exit, B is overwritten by the matrix expression
59 * B := alpha * A * X + beta * B.
60 *
61 * LDB (input) INTEGER
62 * The leading dimension of the array B. LDB >= max(N,1).
63 *
64 * =====================================================================
65 *
66 * .. Parameters ..
67 REAL ONE, ZERO
68 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
69 * ..
70 * .. Local Scalars ..
71 INTEGER I, J
72 * ..
73 * .. Executable Statements ..
74 *
75 IF( N.EQ.0 )
76 $ RETURN
77 *
78 * Multiply B by BETA if BETA.NE.1.
79 *
80 IF( BETA.EQ.ZERO ) THEN
81 DO 20 J = 1, NRHS
82 DO 10 I = 1, N
83 B( I, J ) = ZERO
84 10 CONTINUE
85 20 CONTINUE
86 ELSE IF( BETA.EQ.-ONE ) THEN
87 DO 40 J = 1, NRHS
88 DO 30 I = 1, N
89 B( I, J ) = -B( I, J )
90 30 CONTINUE
91 40 CONTINUE
92 END IF
93 *
94 IF( ALPHA.EQ.ONE ) THEN
95 *
96 * Compute B := B + A*X
97 *
98 DO 60 J = 1, NRHS
99 IF( N.EQ.1 ) THEN
100 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
101 ELSE
102 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
103 $ E( 1 )*X( 2, J )
104 B( N, J ) = B( N, J ) + E( N-1 )*X( N-1, J ) +
105 $ D( N )*X( N, J )
106 DO 50 I = 2, N - 1
107 B( I, J ) = B( I, J ) + E( I-1 )*X( I-1, J ) +
108 $ D( I )*X( I, J ) + E( I )*X( I+1, J )
109 50 CONTINUE
110 END IF
111 60 CONTINUE
112 ELSE IF( ALPHA.EQ.-ONE ) THEN
113 *
114 * Compute B := B - A*X
115 *
116 DO 80 J = 1, NRHS
117 IF( N.EQ.1 ) THEN
118 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
119 ELSE
120 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
121 $ E( 1 )*X( 2, J )
122 B( N, J ) = B( N, J ) - E( N-1 )*X( N-1, J ) -
123 $ D( N )*X( N, J )
124 DO 70 I = 2, N - 1
125 B( I, J ) = B( I, J ) - E( I-1 )*X( I-1, J ) -
126 $ D( I )*X( I, J ) - E( I )*X( I+1, J )
127 70 CONTINUE
128 END IF
129 80 CONTINUE
130 END IF
131 RETURN
132 *
133 * End of SLAPTM
134 *
135 END
2 *
3 * -- LAPACK auxiliary routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 INTEGER LDB, LDX, N, NRHS
9 REAL ALPHA, BETA
10 * ..
11 * .. Array Arguments ..
12 REAL B( LDB, * ), D( * ), E( * ), X( LDX, * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * SLAPTM multiplies an N by NRHS matrix X by a symmetric tridiagonal
19 * matrix A and stores the result in a matrix B. The operation has the
20 * form
21 *
22 * B := alpha * A * X + beta * B
23 *
24 * where alpha may be either 1. or -1. and beta may be 0., 1., or -1.
25 *
26 * Arguments
27 * =========
28 *
29 * N (input) INTEGER
30 * The order of the matrix A. N >= 0.
31 *
32 * NRHS (input) INTEGER
33 * The number of right hand sides, i.e., the number of columns
34 * of the matrices X and B.
35 *
36 * ALPHA (input) REAL
37 * The scalar alpha. ALPHA must be 1. or -1.; otherwise,
38 * it is assumed to be 0.
39 *
40 * D (input) REAL array, dimension (N)
41 * The n diagonal elements of the tridiagonal matrix A.
42 *
43 * E (input) REAL array, dimension (N-1)
44 * The (n-1) subdiagonal or superdiagonal elements of A.
45 *
46 * X (input) REAL array, dimension (LDX,NRHS)
47 * The N by NRHS matrix X.
48 *
49 * LDX (input) INTEGER
50 * The leading dimension of the array X. LDX >= max(N,1).
51 *
52 * BETA (input) REAL
53 * The scalar beta. BETA must be 0., 1., or -1.; otherwise,
54 * it is assumed to be 1.
55 *
56 * B (input/output) REAL array, dimension (LDB,NRHS)
57 * On entry, the N by NRHS matrix B.
58 * On exit, B is overwritten by the matrix expression
59 * B := alpha * A * X + beta * B.
60 *
61 * LDB (input) INTEGER
62 * The leading dimension of the array B. LDB >= max(N,1).
63 *
64 * =====================================================================
65 *
66 * .. Parameters ..
67 REAL ONE, ZERO
68 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
69 * ..
70 * .. Local Scalars ..
71 INTEGER I, J
72 * ..
73 * .. Executable Statements ..
74 *
75 IF( N.EQ.0 )
76 $ RETURN
77 *
78 * Multiply B by BETA if BETA.NE.1.
79 *
80 IF( BETA.EQ.ZERO ) THEN
81 DO 20 J = 1, NRHS
82 DO 10 I = 1, N
83 B( I, J ) = ZERO
84 10 CONTINUE
85 20 CONTINUE
86 ELSE IF( BETA.EQ.-ONE ) THEN
87 DO 40 J = 1, NRHS
88 DO 30 I = 1, N
89 B( I, J ) = -B( I, J )
90 30 CONTINUE
91 40 CONTINUE
92 END IF
93 *
94 IF( ALPHA.EQ.ONE ) THEN
95 *
96 * Compute B := B + A*X
97 *
98 DO 60 J = 1, NRHS
99 IF( N.EQ.1 ) THEN
100 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
101 ELSE
102 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
103 $ E( 1 )*X( 2, J )
104 B( N, J ) = B( N, J ) + E( N-1 )*X( N-1, J ) +
105 $ D( N )*X( N, J )
106 DO 50 I = 2, N - 1
107 B( I, J ) = B( I, J ) + E( I-1 )*X( I-1, J ) +
108 $ D( I )*X( I, J ) + E( I )*X( I+1, J )
109 50 CONTINUE
110 END IF
111 60 CONTINUE
112 ELSE IF( ALPHA.EQ.-ONE ) THEN
113 *
114 * Compute B := B - A*X
115 *
116 DO 80 J = 1, NRHS
117 IF( N.EQ.1 ) THEN
118 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
119 ELSE
120 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
121 $ E( 1 )*X( 2, J )
122 B( N, J ) = B( N, J ) - E( N-1 )*X( N-1, J ) -
123 $ D( N )*X( N, J )
124 DO 70 I = 2, N - 1
125 B( I, J ) = B( I, J ) - E( I-1 )*X( I-1, J ) -
126 $ D( I )*X( I, J ) - E( I )*X( I+1, J )
127 70 CONTINUE
128 END IF
129 80 CONTINUE
130 END IF
131 RETURN
132 *
133 * End of SLAPTM
134 *
135 END