Annotation of rpl/lapack/lapack/zlatzm.f, revision 1.8
1.1 bertrand 1: SUBROUTINE ZLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
2: *
1.8 ! bertrand 3: * -- LAPACK routine (version 3.3.1) --
1.1 bertrand 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 6: * -- April 2011 --
1.1 bertrand 7: *
8: * .. Scalar Arguments ..
9: CHARACTER SIDE
10: INTEGER INCV, LDC, M, N
11: COMPLEX*16 TAU
12: * ..
13: * .. Array Arguments ..
14: COMPLEX*16 C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * This routine is deprecated and has been replaced by routine ZUNMRZ.
21: *
22: * ZLATZM applies a Householder matrix generated by ZTZRQF to a matrix.
23: *
1.8 ! bertrand 24: * Let P = I - tau*u*u**H, u = ( 1 ),
! 25: * ( v )
1.1 bertrand 26: * where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
27: * SIDE = 'R'.
28: *
29: * If SIDE equals 'L', let
30: * C = [ C1 ] 1
31: * [ C2 ] m-1
32: * n
33: * Then C is overwritten by P*C.
34: *
35: * If SIDE equals 'R', let
36: * C = [ C1, C2 ] m
37: * 1 n-1
38: * Then C is overwritten by C*P.
39: *
40: * Arguments
41: * =========
42: *
43: * SIDE (input) CHARACTER*1
44: * = 'L': form P * C
45: * = 'R': form C * P
46: *
47: * M (input) INTEGER
48: * The number of rows of the matrix C.
49: *
50: * N (input) INTEGER
51: * The number of columns of the matrix C.
52: *
53: * V (input) COMPLEX*16 array, dimension
54: * (1 + (M-1)*abs(INCV)) if SIDE = 'L'
55: * (1 + (N-1)*abs(INCV)) if SIDE = 'R'
56: * The vector v in the representation of P. V is not used
57: * if TAU = 0.
58: *
59: * INCV (input) INTEGER
60: * The increment between elements of v. INCV <> 0
61: *
62: * TAU (input) COMPLEX*16
63: * The value tau in the representation of P.
64: *
65: * C1 (input/output) COMPLEX*16 array, dimension
66: * (LDC,N) if SIDE = 'L'
67: * (M,1) if SIDE = 'R'
68: * On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
69: * if SIDE = 'R'.
70: *
71: * On exit, the first row of P*C if SIDE = 'L', or the first
72: * column of C*P if SIDE = 'R'.
73: *
74: * C2 (input/output) COMPLEX*16 array, dimension
75: * (LDC, N) if SIDE = 'L'
76: * (LDC, N-1) if SIDE = 'R'
77: * On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
78: * m x (n - 1) matrix C2 if SIDE = 'R'.
79: *
80: * On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
81: * if SIDE = 'R'.
82: *
83: * LDC (input) INTEGER
84: * The leading dimension of the arrays C1 and C2.
85: * LDC >= max(1,M).
86: *
87: * WORK (workspace) COMPLEX*16 array, dimension
88: * (N) if SIDE = 'L'
89: * (M) if SIDE = 'R'
90: *
91: * =====================================================================
92: *
93: * .. Parameters ..
94: COMPLEX*16 ONE, ZERO
95: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
96: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
97: * ..
98: * .. External Subroutines ..
99: EXTERNAL ZAXPY, ZCOPY, ZGEMV, ZGERC, ZGERU, ZLACGV
100: * ..
101: * .. External Functions ..
102: LOGICAL LSAME
103: EXTERNAL LSAME
104: * ..
105: * .. Intrinsic Functions ..
106: INTRINSIC MIN
107: * ..
108: * .. Executable Statements ..
109: *
110: IF( ( MIN( M, N ).EQ.0 ) .OR. ( TAU.EQ.ZERO ) )
111: $ RETURN
112: *
113: IF( LSAME( SIDE, 'L' ) ) THEN
114: *
1.8 ! bertrand 115: * w := ( C1 + v**H * C2 )**H
1.1 bertrand 116: *
117: CALL ZCOPY( N, C1, LDC, WORK, 1 )
118: CALL ZLACGV( N, WORK, 1 )
119: CALL ZGEMV( 'Conjugate transpose', M-1, N, ONE, C2, LDC, V,
120: $ INCV, ONE, WORK, 1 )
121: *
1.8 ! bertrand 122: * [ C1 ] := [ C1 ] - tau* [ 1 ] * w**H
1.1 bertrand 123: * [ C2 ] [ C2 ] [ v ]
124: *
125: CALL ZLACGV( N, WORK, 1 )
126: CALL ZAXPY( N, -TAU, WORK, 1, C1, LDC )
127: CALL ZGERU( M-1, N, -TAU, V, INCV, WORK, 1, C2, LDC )
128: *
129: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
130: *
131: * w := C1 + C2 * v
132: *
133: CALL ZCOPY( M, C1, 1, WORK, 1 )
134: CALL ZGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
135: $ WORK, 1 )
136: *
1.8 ! bertrand 137: * [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**H]
1.1 bertrand 138: *
139: CALL ZAXPY( M, -TAU, WORK, 1, C1, 1 )
140: CALL ZGERC( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
141: END IF
142: *
143: RETURN
144: *
145: * End of ZLATZM
146: *
147: END
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