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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, 00002 $ LDC, WORK, LWORK, 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 IHI, ILO, INFO, LDA, LDC, LWORK, M, N 00012 * .. 00013 * .. Array Arguments .. 00014 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * DORMHR overwrites the general real M-by-N matrix C with 00021 * 00022 * SIDE = 'L' SIDE = 'R' 00023 * TRANS = 'N': Q * C C * Q 00024 * TRANS = 'T': Q**T * C C * Q**T 00025 * 00026 * where Q is a real orthogonal matrix of order nq, with nq = m if 00027 * SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of 00028 * IHI-ILO elementary reflectors, as returned by DGEHRD: 00029 * 00030 * Q = H(ilo) H(ilo+1) . . . H(ihi-1). 00031 * 00032 * Arguments 00033 * ========= 00034 * 00035 * SIDE (input) CHARACTER*1 00036 * = 'L': apply Q or Q**T from the Left; 00037 * = 'R': apply Q or Q**T from the Right. 00038 * 00039 * TRANS (input) CHARACTER*1 00040 * = 'N': No transpose, apply Q; 00041 * = 'T': Transpose, apply Q**T. 00042 * 00043 * M (input) INTEGER 00044 * The number of rows of the matrix C. M >= 0. 00045 * 00046 * N (input) INTEGER 00047 * The number of columns of the matrix C. N >= 0. 00048 * 00049 * ILO (input) INTEGER 00050 * IHI (input) INTEGER 00051 * ILO and IHI must have the same values as in the previous call 00052 * of DGEHRD. Q is equal to the unit matrix except in the 00053 * submatrix Q(ilo+1:ihi,ilo+1:ihi). 00054 * If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and 00055 * ILO = 1 and IHI = 0, if M = 0; 00056 * if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and 00057 * ILO = 1 and IHI = 0, if N = 0. 00058 * 00059 * A (input) DOUBLE PRECISION array, dimension 00060 * (LDA,M) if SIDE = 'L' 00061 * (LDA,N) if SIDE = 'R' 00062 * The vectors which define the elementary reflectors, as 00063 * returned by DGEHRD. 00064 * 00065 * LDA (input) INTEGER 00066 * The leading dimension of the array A. 00067 * LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. 00068 * 00069 * TAU (input) DOUBLE PRECISION array, dimension 00070 * (M-1) if SIDE = 'L' 00071 * (N-1) if SIDE = 'R' 00072 * TAU(i) must contain the scalar factor of the elementary 00073 * reflector H(i), as returned by DGEHRD. 00074 * 00075 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) 00076 * On entry, the M-by-N matrix C. 00077 * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. 00078 * 00079 * LDC (input) INTEGER 00080 * The leading dimension of the array C. LDC >= max(1,M). 00081 * 00082 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00083 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00084 * 00085 * LWORK (input) INTEGER 00086 * The dimension of the array WORK. 00087 * If SIDE = 'L', LWORK >= max(1,N); 00088 * if SIDE = 'R', LWORK >= max(1,M). 00089 * For optimum performance LWORK >= N*NB if SIDE = 'L', and 00090 * LWORK >= M*NB if SIDE = 'R', where NB is the optimal 00091 * blocksize. 00092 * 00093 * If LWORK = -1, then a workspace query is assumed; the routine 00094 * only calculates the optimal size of the WORK array, returns 00095 * this value as the first entry of the WORK array, and no error 00096 * message related to LWORK is issued by XERBLA. 00097 * 00098 * INFO (output) INTEGER 00099 * = 0: successful exit 00100 * < 0: if INFO = -i, the i-th argument had an illegal value 00101 * 00102 * ===================================================================== 00103 * 00104 * .. Local Scalars .. 00105 LOGICAL LEFT, LQUERY 00106 INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW 00107 * .. 00108 * .. External Functions .. 00109 LOGICAL LSAME 00110 INTEGER ILAENV 00111 EXTERNAL LSAME, ILAENV 00112 * .. 00113 * .. External Subroutines .. 00114 EXTERNAL DORMQR, XERBLA 00115 * .. 00116 * .. Intrinsic Functions .. 00117 INTRINSIC MAX, MIN 00118 * .. 00119 * .. Executable Statements .. 00120 * 00121 * Test the input arguments 00122 * 00123 INFO = 0 00124 NH = IHI - ILO 00125 LEFT = LSAME( SIDE, 'L' ) 00126 LQUERY = ( LWORK.EQ.-1 ) 00127 * 00128 * NQ is the order of Q and NW is the minimum dimension of WORK 00129 * 00130 IF( LEFT ) THEN 00131 NQ = M 00132 NW = N 00133 ELSE 00134 NQ = N 00135 NW = M 00136 END IF 00137 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00138 INFO = -1 00139 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) ) 00140 $ THEN 00141 INFO = -2 00142 ELSE IF( M.LT.0 ) THEN 00143 INFO = -3 00144 ELSE IF( N.LT.0 ) THEN 00145 INFO = -4 00146 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, NQ ) ) THEN 00147 INFO = -5 00148 ELSE IF( IHI.LT.MIN( ILO, NQ ) .OR. IHI.GT.NQ ) THEN 00149 INFO = -6 00150 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN 00151 INFO = -8 00152 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00153 INFO = -11 00154 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00155 INFO = -13 00156 END IF 00157 * 00158 IF( INFO.EQ.0 ) THEN 00159 IF( LEFT ) THEN 00160 NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, NH, N, NH, -1 ) 00161 ELSE 00162 NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, NH, NH, -1 ) 00163 END IF 00164 LWKOPT = MAX( 1, NW )*NB 00165 WORK( 1 ) = LWKOPT 00166 END IF 00167 * 00168 IF( INFO.NE.0 ) THEN 00169 CALL XERBLA( 'DORMHR', -INFO ) 00170 RETURN 00171 ELSE IF( LQUERY ) THEN 00172 RETURN 00173 END IF 00174 * 00175 * Quick return if possible 00176 * 00177 IF( M.EQ.0 .OR. N.EQ.0 .OR. NH.EQ.0 ) THEN 00178 WORK( 1 ) = 1 00179 RETURN 00180 END IF 00181 * 00182 IF( LEFT ) THEN 00183 MI = NH 00184 NI = N 00185 I1 = ILO + 1 00186 I2 = 1 00187 ELSE 00188 MI = M 00189 NI = NH 00190 I1 = 1 00191 I2 = ILO + 1 00192 END IF 00193 * 00194 CALL DORMQR( SIDE, TRANS, MI, NI, NH, A( ILO+1, ILO ), LDA, 00195 $ TAU( ILO ), C( I1, I2 ), LDC, WORK, LWORK, IINFO ) 00196 * 00197 WORK( 1 ) = LWKOPT 00198 RETURN 00199 * 00200 * End of DORMHR 00201 * 00202 END
1.7.3 
