00001 SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, 00002 $ WORK, INFO ) 00003 * 00004 * -- LAPACK routine (version 3.2) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * November 2006 00008 * 00009 * .. Scalar Arguments .. 00010 CHARACTER SIDE, TRANS 00011 INTEGER INFO, K, LDA, LDC, M, N 00012 * .. 00013 * .. Array Arguments .. 00014 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * DORM2L overwrites the general real m by n matrix C with 00021 * 00022 * Q * C if SIDE = 'L' and TRANS = 'N', or 00023 * 00024 * Q'* C if SIDE = 'L' and TRANS = 'T', or 00025 * 00026 * C * Q if SIDE = 'R' and TRANS = 'N', or 00027 * 00028 * C * Q' if SIDE = 'R' and TRANS = 'T', 00029 * 00030 * where Q is a real orthogonal matrix defined as the product of k 00031 * elementary reflectors 00032 * 00033 * Q = H(k) . . . H(2) H(1) 00034 * 00035 * as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n 00036 * if SIDE = 'R'. 00037 * 00038 * Arguments 00039 * ========= 00040 * 00041 * SIDE (input) CHARACTER*1 00042 * = 'L': apply Q or Q' from the Left 00043 * = 'R': apply Q or Q' from the Right 00044 * 00045 * TRANS (input) CHARACTER*1 00046 * = 'N': apply Q (No transpose) 00047 * = 'T': apply Q' (Transpose) 00048 * 00049 * M (input) INTEGER 00050 * The number of rows of the matrix C. M >= 0. 00051 * 00052 * N (input) INTEGER 00053 * The number of columns of the matrix C. N >= 0. 00054 * 00055 * K (input) INTEGER 00056 * The number of elementary reflectors whose product defines 00057 * the matrix Q. 00058 * If SIDE = 'L', M >= K >= 0; 00059 * if SIDE = 'R', N >= K >= 0. 00060 * 00061 * A (input) DOUBLE PRECISION array, dimension (LDA,K) 00062 * The i-th column must contain the vector which defines the 00063 * elementary reflector H(i), for i = 1,2,...,k, as returned by 00064 * DGEQLF in the last k columns of its array argument A. 00065 * A is modified by the routine but restored on exit. 00066 * 00067 * LDA (input) INTEGER 00068 * The leading dimension of the array A. 00069 * If SIDE = 'L', LDA >= max(1,M); 00070 * if SIDE = 'R', LDA >= max(1,N). 00071 * 00072 * TAU (input) DOUBLE PRECISION array, dimension (K) 00073 * TAU(i) must contain the scalar factor of the elementary 00074 * reflector H(i), as returned by DGEQLF. 00075 * 00076 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) 00077 * On entry, the m by n matrix C. 00078 * On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q. 00079 * 00080 * LDC (input) INTEGER 00081 * The leading dimension of the array C. LDC >= max(1,M). 00082 * 00083 * WORK (workspace) DOUBLE PRECISION array, dimension 00084 * (N) if SIDE = 'L', 00085 * (M) if SIDE = 'R' 00086 * 00087 * INFO (output) INTEGER 00088 * = 0: successful exit 00089 * < 0: if INFO = -i, the i-th argument had an illegal value 00090 * 00091 * ===================================================================== 00092 * 00093 * .. Parameters .. 00094 DOUBLE PRECISION ONE 00095 PARAMETER ( ONE = 1.0D+0 ) 00096 * .. 00097 * .. Local Scalars .. 00098 LOGICAL LEFT, NOTRAN 00099 INTEGER I, I1, I2, I3, MI, NI, NQ 00100 DOUBLE PRECISION AII 00101 * .. 00102 * .. External Functions .. 00103 LOGICAL LSAME 00104 EXTERNAL LSAME 00105 * .. 00106 * .. External Subroutines .. 00107 EXTERNAL DLARF, XERBLA 00108 * .. 00109 * .. Intrinsic Functions .. 00110 INTRINSIC MAX 00111 * .. 00112 * .. Executable Statements .. 00113 * 00114 * Test the input arguments 00115 * 00116 INFO = 0 00117 LEFT = LSAME( SIDE, 'L' ) 00118 NOTRAN = LSAME( TRANS, 'N' ) 00119 * 00120 * NQ is the order of Q 00121 * 00122 IF( LEFT ) THEN 00123 NQ = M 00124 ELSE 00125 NQ = N 00126 END IF 00127 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00128 INFO = -1 00129 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 00130 INFO = -2 00131 ELSE IF( M.LT.0 ) THEN 00132 INFO = -3 00133 ELSE IF( N.LT.0 ) THEN 00134 INFO = -4 00135 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN 00136 INFO = -5 00137 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN 00138 INFO = -7 00139 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00140 INFO = -10 00141 END IF 00142 IF( INFO.NE.0 ) THEN 00143 CALL XERBLA( 'DORM2L', -INFO ) 00144 RETURN 00145 END IF 00146 * 00147 * Quick return if possible 00148 * 00149 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) 00150 $ RETURN 00151 * 00152 IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) 00153 $ THEN 00154 I1 = 1 00155 I2 = K 00156 I3 = 1 00157 ELSE 00158 I1 = K 00159 I2 = 1 00160 I3 = -1 00161 END IF 00162 * 00163 IF( LEFT ) THEN 00164 NI = N 00165 ELSE 00166 MI = M 00167 END IF 00168 * 00169 DO 10 I = I1, I2, I3 00170 IF( LEFT ) THEN 00171 * 00172 * H(i) is applied to C(1:m-k+i,1:n) 00173 * 00174 MI = M - K + I 00175 ELSE 00176 * 00177 * H(i) is applied to C(1:m,1:n-k+i) 00178 * 00179 NI = N - K + I 00180 END IF 00181 * 00182 * Apply H(i) 00183 * 00184 AII = A( NQ-K+I, I ) 00185 A( NQ-K+I, I ) = ONE 00186 CALL DLARF( SIDE, MI, NI, A( 1, I ), 1, TAU( I ), C, LDC, 00187 $ WORK ) 00188 A( NQ-K+I, I ) = AII 00189 10 CONTINUE 00190 RETURN 00191 * 00192 * End of DORM2L 00193 * 00194 END
1.7.2