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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 SORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER INFO, K, LDA, LWORK, M, N 00010 * .. 00011 * .. Array Arguments .. 00012 REAL A( LDA, * ), TAU( * ), WORK( * ) 00013 * .. 00014 * 00015 * Purpose 00016 * ======= 00017 * 00018 * SORGQR generates an M-by-N real matrix Q with orthonormal columns, 00019 * which is defined as the first N columns of a product of K elementary 00020 * reflectors of order M 00021 * 00022 * Q = H(1) H(2) . . . H(k) 00023 * 00024 * as returned by SGEQRF. 00025 * 00026 * Arguments 00027 * ========= 00028 * 00029 * M (input) INTEGER 00030 * The number of rows of the matrix Q. M >= 0. 00031 * 00032 * N (input) INTEGER 00033 * The number of columns of the matrix Q. M >= N >= 0. 00034 * 00035 * K (input) INTEGER 00036 * The number of elementary reflectors whose product defines the 00037 * matrix Q. N >= K >= 0. 00038 * 00039 * A (input/output) REAL array, dimension (LDA,N) 00040 * On entry, the i-th column must contain the vector which 00041 * defines the elementary reflector H(i), for i = 1,2,...,k, as 00042 * returned by SGEQRF in the first k columns of its array 00043 * argument A. 00044 * On exit, the M-by-N matrix Q. 00045 * 00046 * LDA (input) INTEGER 00047 * The first dimension of the array A. LDA >= max(1,M). 00048 * 00049 * TAU (input) REAL array, dimension (K) 00050 * TAU(i) must contain the scalar factor of the elementary 00051 * reflector H(i), as returned by SGEQRF. 00052 * 00053 * WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) 00054 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00055 * 00056 * LWORK (input) INTEGER 00057 * The dimension of the array WORK. LWORK >= max(1,N). 00058 * For optimum performance LWORK >= N*NB, where NB is the 00059 * optimal blocksize. 00060 * 00061 * If LWORK = -1, then a workspace query is assumed; the routine 00062 * only calculates the optimal size of the WORK array, returns 00063 * this value as the first entry of the WORK array, and no error 00064 * message related to LWORK is issued by XERBLA. 00065 * 00066 * INFO (output) INTEGER 00067 * = 0: successful exit 00068 * < 0: if INFO = -i, the i-th argument has an illegal value 00069 * 00070 * ===================================================================== 00071 * 00072 * .. Parameters .. 00073 REAL ZERO 00074 PARAMETER ( ZERO = 0.0E+0 ) 00075 * .. 00076 * .. Local Scalars .. 00077 LOGICAL LQUERY 00078 INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, 00079 $ LWKOPT, NB, NBMIN, NX 00080 * .. 00081 * .. External Subroutines .. 00082 EXTERNAL SLARFB, SLARFT, SORG2R, XERBLA 00083 * .. 00084 * .. Intrinsic Functions .. 00085 INTRINSIC MAX, MIN 00086 * .. 00087 * .. External Functions .. 00088 INTEGER ILAENV 00089 EXTERNAL ILAENV 00090 * .. 00091 * .. Executable Statements .. 00092 * 00093 * Test the input arguments 00094 * 00095 INFO = 0 00096 NB = ILAENV( 1, 'SORGQR', ' ', M, N, K, -1 ) 00097 LWKOPT = MAX( 1, N )*NB 00098 WORK( 1 ) = LWKOPT 00099 LQUERY = ( LWORK.EQ.-1 ) 00100 IF( M.LT.0 ) THEN 00101 INFO = -1 00102 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN 00103 INFO = -2 00104 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN 00105 INFO = -3 00106 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00107 INFO = -5 00108 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN 00109 INFO = -8 00110 END IF 00111 IF( INFO.NE.0 ) THEN 00112 CALL XERBLA( 'SORGQR', -INFO ) 00113 RETURN 00114 ELSE IF( LQUERY ) THEN 00115 RETURN 00116 END IF 00117 * 00118 * Quick return if possible 00119 * 00120 IF( N.LE.0 ) THEN 00121 WORK( 1 ) = 1 00122 RETURN 00123 END IF 00124 * 00125 NBMIN = 2 00126 NX = 0 00127 IWS = N 00128 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00129 * 00130 * Determine when to cross over from blocked to unblocked code. 00131 * 00132 NX = MAX( 0, ILAENV( 3, 'SORGQR', ' ', M, N, K, -1 ) ) 00133 IF( NX.LT.K ) THEN 00134 * 00135 * Determine if workspace is large enough for blocked code. 00136 * 00137 LDWORK = N 00138 IWS = LDWORK*NB 00139 IF( LWORK.LT.IWS ) THEN 00140 * 00141 * Not enough workspace to use optimal NB: reduce NB and 00142 * determine the minimum value of NB. 00143 * 00144 NB = LWORK / LDWORK 00145 NBMIN = MAX( 2, ILAENV( 2, 'SORGQR', ' ', M, N, K, -1 ) ) 00146 END IF 00147 END IF 00148 END IF 00149 * 00150 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN 00151 * 00152 * Use blocked code after the last block. 00153 * The first kk columns are handled by the block method. 00154 * 00155 KI = ( ( K-NX-1 ) / NB )*NB 00156 KK = MIN( K, KI+NB ) 00157 * 00158 * Set A(1:kk,kk+1:n) to zero. 00159 * 00160 DO 20 J = KK + 1, N 00161 DO 10 I = 1, KK 00162 A( I, J ) = ZERO 00163 10 CONTINUE 00164 20 CONTINUE 00165 ELSE 00166 KK = 0 00167 END IF 00168 * 00169 * Use unblocked code for the last or only block. 00170 * 00171 IF( KK.LT.N ) 00172 $ CALL SORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA, 00173 $ TAU( KK+1 ), WORK, IINFO ) 00174 * 00175 IF( KK.GT.0 ) THEN 00176 * 00177 * Use blocked code 00178 * 00179 DO 50 I = KI + 1, 1, -NB 00180 IB = MIN( NB, K-I+1 ) 00181 IF( I+IB.LE.N ) THEN 00182 * 00183 * Form the triangular factor of the block reflector 00184 * H = H(i) H(i+1) . . . H(i+ib-1) 00185 * 00186 CALL SLARFT( 'Forward', 'Columnwise', M-I+1, IB, 00187 $ A( I, I ), LDA, TAU( I ), WORK, LDWORK ) 00188 * 00189 * Apply H to A(i:m,i+ib:n) from the left 00190 * 00191 CALL SLARFB( 'Left', 'No transpose', 'Forward', 00192 $ 'Columnwise', M-I+1, N-I-IB+1, IB, 00193 $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ), 00194 $ LDA, WORK( IB+1 ), LDWORK ) 00195 END IF 00196 * 00197 * Apply H to rows i:m of current block 00198 * 00199 CALL SORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK, 00200 $ IINFO ) 00201 * 00202 * Set rows 1:i-1 of current block to zero 00203 * 00204 DO 40 J = I, I + IB - 1 00205 DO 30 L = 1, I - 1 00206 A( L, J ) = ZERO 00207 30 CONTINUE 00208 40 CONTINUE 00209 50 CONTINUE 00210 END IF 00211 * 00212 WORK( 1 ) = IWS 00213 RETURN 00214 * 00215 * End of SORGQR 00216 * 00217 END
1.7.3 
