1DLASR(1) LAPACK auxiliary routine (version 3.2) DLASR(1)
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6 DLASR - applies a sequence of plane rotations to a real matrix A,
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9 SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
10 CHARACTER DIRECT, PIVOT, SIDE
12 INTEGER LDA, M, N
14 DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
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18 DLASR applies a sequence of plane rotations to a real matrix A, from
19 either the left or the right.
20 When SIDE = 'L', the transformation takes the form
21 A := P*A
22 and when SIDE = 'R', the transformation takes the form
23 A := A*P**T
24 where P is an orthogonal matrix consisting of a sequence of z plane
25 rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', and
26 P**T is the transpose of P.
27 When DIRECT = 'F' (Forward sequence), then
28 P = P(z-1) * ... * P(2) * P(1)
29 and when DIRECT = 'B' (Backward sequence), then
30 P = P(1) * P(2) * ... * P(z-1)
31 where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
32 R(k) = ( c(k) s(k) )
33 = ( -s(k) c(k) ).
34 When PIVOT = 'V' (Variable pivot), the rotation is performed for the
35 plane (k,k+1), i.e., P(k) has the form
36 P(k) = ( 1 )
37 ( ... )
38 ( 1 )
39 ( c(k) s(k) )
40 ( -s(k) c(k) )
41 ( 1 )
42 ( ... )
43 ( 1 )
44 where R(k) appears as a rank-2 modification to the identity matrix in
45 rows and columns k and k+1.
46 When PIVOT = 'T' (Top pivot), the rotation is performed for the plane
47 (1,k+1), so P(k) has the form
48 P(k) = ( c(k) s(k) )
49 ( 1 )
50 ( ... )
51 ( 1 )
52 ( -s(k) c(k) )
53 ( 1 )
54 ( ... )
55 ( 1 )
56 where R(k) appears in rows and columns 1 and k+1.
57 Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is performed
58 for the plane (k,z), giving P(k) the form
59 P(k) = ( 1 )
60 ( ... )
61 ( 1 )
62 ( c(k) s(k) )
63 ( 1 )
64 ( ... )
65 ( 1 )
66 ( -s(k) c(k) )
67 where R(k) appears in rows and columns k and z. The rotations are per‐
68 formed without ever forming P(k) explicitly.
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71 SIDE (input) CHARACTER*1
72 Specifies whether the plane rotation matrix P is applied to A
73 on the left or the right. = 'L': Left, compute A := P*A
74 = 'R': Right, compute A:= A*P**T
75 PIVOT (input) CHARACTER*1
77 Specifies the plane for which P(k) is a plane rotation matrix.
78 = 'V': Variable pivot, the plane (k,k+1)
79 = 'T': Top pivot, the plane (1,k+1)
80 = 'B': Bottom pivot, the plane (k,z)
81 DIRECT (input) CHARACTER*1
83 Specifies whether P is a forward or backward sequence of plane
84 rotations. = 'F': Forward, P = P(z-1)*...*P(2)*P(1)
85 = 'B': Backward, P = P(1)*P(2)*...*P(z-1)
86 M (input) INTEGER
88 The number of rows of the matrix A. If m <= 1, an immediate
89 return is effected.
90 N (input) INTEGER
92 The number of columns of the matrix A. If n <= 1, an immediate
93 return is effected.
94 C (input) DOUBLE PRECISION array, dimension
96 (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' The cosines c(k) of the
97 plane rotations.
98 S (input) DOUBLE PRECISION array, dimension
100 (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' The sines s(k) of the
101 plane rotations. The 2-by-2 plane rotation part of the matrix
102 P(k), R(k), has the form R(k) = ( c(k) s(k) ) ( -s(k) c(k)
103 ).
104 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
106 The M-by-N matrix A. On exit, A is overwritten by P*A if SIDE
107 = 'R' or by A*P**T if SIDE = 'L'.
108 LDA (input) INTEGER
110 The leading dimension of the array A. LDA >= max(1,M).
111 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008 DLASR(1)