00001 SUBROUTINE DLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK ) 00002 * 00003 * -- LAPACK auxiliary test routine (version 3.1) -- 00004 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00005 * November 2006 00006 * 00007 * .. Scalar Arguments .. 00008 CHARACTER UPLO 00009 INTEGER INCV, LDC, N 00010 DOUBLE PRECISION TAU 00011 * .. 00012 * .. Array Arguments .. 00013 DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * DLARFY applies an elementary reflector, or Householder matrix, H, 00020 * to an n x n symmetric matrix C, from both the left and the right. 00021 * 00022 * H is represented in the form 00023 * 00024 * H = I - tau * v * v' 00025 * 00026 * where tau is a scalar and v is a vector. 00027 * 00028 * If tau is zero, then H is taken to be the unit matrix. 00029 * 00030 * Arguments 00031 * ========= 00032 * 00033 * UPLO (input) CHARACTER*1 00034 * Specifies whether the upper or lower triangular part of the 00035 * symmetric matrix C is stored. 00036 * = 'U': Upper triangle 00037 * = 'L': Lower triangle 00038 * 00039 * N (input) INTEGER 00040 * The number of rows and columns of the matrix C. N >= 0. 00041 * 00042 * V (input) DOUBLE PRECISION array, dimension 00043 * (1 + (N-1)*abs(INCV)) 00044 * The vector v as described above. 00045 * 00046 * INCV (input) INTEGER 00047 * The increment between successive elements of v. INCV must 00048 * not be zero. 00049 * 00050 * TAU (input) DOUBLE PRECISION 00051 * The value tau as described above. 00052 * 00053 * C (input/output) DOUBLE PRECISION array, dimension (LDC, N) 00054 * On entry, the matrix C. 00055 * On exit, C is overwritten by H * C * H'. 00056 * 00057 * LDC (input) INTEGER 00058 * The leading dimension of the array C. LDC >= max( 1, N ). 00059 * 00060 * WORK (workspace) DOUBLE PRECISION array, dimension (N) 00061 * 00062 * ===================================================================== 00063 * 00064 * .. Parameters .. 00065 DOUBLE PRECISION ONE, ZERO, HALF 00066 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0, HALF = 0.5D+0 ) 00067 * .. 00068 * .. Local Scalars .. 00069 DOUBLE PRECISION ALPHA 00070 * .. 00071 * .. External Subroutines .. 00072 EXTERNAL DAXPY, DSYMV, DSYR2 00073 * .. 00074 * .. External Functions .. 00075 DOUBLE PRECISION DDOT 00076 EXTERNAL DDOT 00077 * .. 00078 * .. Executable Statements .. 00079 * 00080 IF( TAU.EQ.ZERO ) 00081 $ RETURN 00082 * 00083 * Form w:= C * v 00084 * 00085 CALL DSYMV( UPLO, N, ONE, C, LDC, V, INCV, ZERO, WORK, 1 ) 00086 * 00087 ALPHA = -HALF*TAU*DDOT( N, WORK, 1, V, INCV ) 00088 CALL DAXPY( N, ALPHA, V, INCV, WORK, 1 ) 00089 * 00090 * C := C - v * w' - w * v' 00091 * 00092 CALL DSYR2( UPLO, N, -TAU, V, INCV, WORK, 1, C, LDC ) 00093 * 00094 RETURN 00095 * 00096 * End of DLARFY 00097 * 00098 END
1.7.2