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1.1 bertrand 1: SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
2: $ WORK, INFO )
3: *
4: * -- LAPACK routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * .. Scalar Arguments ..
10: CHARACTER SIDE, TRANS
11: INTEGER INFO, K, L, LDA, LDC, M, N
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * DORMR3 overwrites the general real m by n matrix C with
21: *
22: * Q * C if SIDE = 'L' and TRANS = 'N', or
23: *
24: * Q'* C if SIDE = 'L' and TRANS = 'T', or
25: *
26: * C * Q if SIDE = 'R' and TRANS = 'N', or
27: *
28: * C * Q' if SIDE = 'R' and TRANS = 'T',
29: *
30: * where Q is a real orthogonal matrix defined as the product of k
31: * elementary reflectors
32: *
33: * Q = H(1) H(2) . . . H(k)
34: *
35: * as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n
36: * if SIDE = 'R'.
37: *
38: * Arguments
39: * =========
40: *
41: * SIDE (input) CHARACTER*1
42: * = 'L': apply Q or Q' from the Left
43: * = 'R': apply Q or Q' from the Right
44: *
45: * TRANS (input) CHARACTER*1
46: * = 'N': apply Q (No transpose)
47: * = 'T': apply Q' (Transpose)
48: *
49: * M (input) INTEGER
50: * The number of rows of the matrix C. M >= 0.
51: *
52: * N (input) INTEGER
53: * The number of columns of the matrix C. N >= 0.
54: *
55: * K (input) INTEGER
56: * The number of elementary reflectors whose product defines
57: * the matrix Q.
58: * If SIDE = 'L', M >= K >= 0;
59: * if SIDE = 'R', N >= K >= 0.
60: *
61: * L (input) INTEGER
62: * The number of columns of the matrix A containing
63: * the meaningful part of the Householder reflectors.
64: * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
65: *
66: * A (input) DOUBLE PRECISION array, dimension
67: * (LDA,M) if SIDE = 'L',
68: * (LDA,N) if SIDE = 'R'
69: * The i-th row must contain the vector which defines the
70: * elementary reflector H(i), for i = 1,2,...,k, as returned by
71: * DTZRZF in the last k rows of its array argument A.
72: * A is modified by the routine but restored on exit.
73: *
74: * LDA (input) INTEGER
75: * The leading dimension of the array A. LDA >= max(1,K).
76: *
77: * TAU (input) DOUBLE PRECISION array, dimension (K)
78: * TAU(i) must contain the scalar factor of the elementary
79: * reflector H(i), as returned by DTZRZF.
80: *
81: * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
82: * On entry, the m-by-n matrix C.
83: * On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
84: *
85: * LDC (input) INTEGER
86: * The leading dimension of the array C. LDC >= max(1,M).
87: *
88: * WORK (workspace) DOUBLE PRECISION array, dimension
89: * (N) if SIDE = 'L',
90: * (M) if SIDE = 'R'
91: *
92: * INFO (output) INTEGER
93: * = 0: successful exit
94: * < 0: if INFO = -i, the i-th argument had an illegal value
95: *
96: * Further Details
97: * ===============
98: *
99: * Based on contributions by
100: * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
101: *
102: * =====================================================================
103: *
104: * .. Local Scalars ..
105: LOGICAL LEFT, NOTRAN
106: INTEGER I, I1, I2, I3, IC, JA, JC, MI, NI, NQ
107: * ..
108: * .. External Functions ..
109: LOGICAL LSAME
110: EXTERNAL LSAME
111: * ..
112: * .. External Subroutines ..
113: EXTERNAL DLARZ, XERBLA
114: * ..
115: * .. Intrinsic Functions ..
116: INTRINSIC MAX
117: * ..
118: * .. Executable Statements ..
119: *
120: * Test the input arguments
121: *
122: INFO = 0
123: LEFT = LSAME( SIDE, 'L' )
124: NOTRAN = LSAME( TRANS, 'N' )
125: *
126: * NQ is the order of Q
127: *
128: IF( LEFT ) THEN
129: NQ = M
130: ELSE
131: NQ = N
132: END IF
133: IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
134: INFO = -1
135: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
136: INFO = -2
137: ELSE IF( M.LT.0 ) THEN
138: INFO = -3
139: ELSE IF( N.LT.0 ) THEN
140: INFO = -4
141: ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
142: INFO = -5
143: ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
144: $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
145: INFO = -6
146: ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
147: INFO = -8
148: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
149: INFO = -11
150: END IF
151: IF( INFO.NE.0 ) THEN
152: CALL XERBLA( 'DORMR3', -INFO )
153: RETURN
154: END IF
155: *
156: * Quick return if possible
157: *
158: IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
159: $ RETURN
160: *
161: IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN
162: I1 = 1
163: I2 = K
164: I3 = 1
165: ELSE
166: I1 = K
167: I2 = 1
168: I3 = -1
169: END IF
170: *
171: IF( LEFT ) THEN
172: NI = N
173: JA = M - L + 1
174: JC = 1
175: ELSE
176: MI = M
177: JA = N - L + 1
178: IC = 1
179: END IF
180: *
181: DO 10 I = I1, I2, I3
182: IF( LEFT ) THEN
183: *
184: * H(i) or H(i)' is applied to C(i:m,1:n)
185: *
186: MI = M - I + 1
187: IC = I
188: ELSE
189: *
190: * H(i) or H(i)' is applied to C(1:m,i:n)
191: *
192: NI = N - I + 1
193: JC = I
194: END IF
195: *
196: * Apply H(i) or H(i)'
197: *
198: CALL DLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ),
199: $ C( IC, JC ), LDC, WORK )
200: *
201: 10 CONTINUE
202: *
203: RETURN
204: *
205: * End of DORMR3
206: *
207: END