00001 SUBROUTINE SGELQF( M, N, 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, LDA, LWORK, M, N 00010 * .. 00011 * .. Array Arguments .. 00012 REAL A( LDA, * ), TAU( * ), WORK( * ) 00013 * .. 00014 * 00015 * Purpose 00016 * ======= 00017 * 00018 * SGELQF computes an LQ factorization of a real M-by-N matrix A: 00019 * A = L * Q. 00020 * 00021 * Arguments 00022 * ========= 00023 * 00024 * M (input) INTEGER 00025 * The number of rows of the matrix A. M >= 0. 00026 * 00027 * N (input) INTEGER 00028 * The number of columns of the matrix A. N >= 0. 00029 * 00030 * A (input/output) REAL array, dimension (LDA,N) 00031 * On entry, the M-by-N matrix A. 00032 * On exit, the elements on and below the diagonal of the array 00033 * contain the m-by-min(m,n) lower trapezoidal matrix L (L is 00034 * lower triangular if m <= n); the elements above the diagonal, 00035 * with the array TAU, represent the orthogonal matrix Q as a 00036 * product of elementary reflectors (see Further Details). 00037 * 00038 * LDA (input) INTEGER 00039 * The leading dimension of the array A. LDA >= max(1,M). 00040 * 00041 * TAU (output) REAL array, dimension (min(M,N)) 00042 * The scalar factors of the elementary reflectors (see Further 00043 * Details). 00044 * 00045 * WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) 00046 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00047 * 00048 * LWORK (input) INTEGER 00049 * The dimension of the array WORK. LWORK >= max(1,M). 00050 * For optimum performance LWORK >= M*NB, where NB is the 00051 * optimal blocksize. 00052 * 00053 * If LWORK = -1, then a workspace query is assumed; the routine 00054 * only calculates the optimal size of the WORK array, returns 00055 * this value as the first entry of the WORK array, and no error 00056 * message related to LWORK is issued by XERBLA. 00057 * 00058 * INFO (output) INTEGER 00059 * = 0: successful exit 00060 * < 0: if INFO = -i, the i-th argument had an illegal value 00061 * 00062 * Further Details 00063 * =============== 00064 * 00065 * The matrix Q is represented as a product of elementary reflectors 00066 * 00067 * Q = H(k) . . . H(2) H(1), where k = min(m,n). 00068 * 00069 * Each H(i) has the form 00070 * 00071 * H(i) = I - tau * v * v' 00072 * 00073 * where tau is a real scalar, and v is a real vector with 00074 * v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), 00075 * and tau in TAU(i). 00076 * 00077 * ===================================================================== 00078 * 00079 * .. Local Scalars .. 00080 LOGICAL LQUERY 00081 INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, 00082 $ NBMIN, NX 00083 * .. 00084 * .. External Subroutines .. 00085 EXTERNAL SGELQ2, SLARFB, SLARFT, XERBLA 00086 * .. 00087 * .. Intrinsic Functions .. 00088 INTRINSIC MAX, MIN 00089 * .. 00090 * .. External Functions .. 00091 INTEGER ILAENV 00092 EXTERNAL ILAENV 00093 * .. 00094 * .. Executable Statements .. 00095 * 00096 * Test the input arguments 00097 * 00098 INFO = 0 00099 NB = ILAENV( 1, 'SGELQF', ' ', M, N, -1, -1 ) 00100 LWKOPT = M*NB 00101 WORK( 1 ) = LWKOPT 00102 LQUERY = ( LWORK.EQ.-1 ) 00103 IF( M.LT.0 ) THEN 00104 INFO = -1 00105 ELSE IF( N.LT.0 ) THEN 00106 INFO = -2 00107 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00108 INFO = -4 00109 ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN 00110 INFO = -7 00111 END IF 00112 IF( INFO.NE.0 ) THEN 00113 CALL XERBLA( 'SGELQF', -INFO ) 00114 RETURN 00115 ELSE IF( LQUERY ) THEN 00116 RETURN 00117 END IF 00118 * 00119 * Quick return if possible 00120 * 00121 K = MIN( M, N ) 00122 IF( K.EQ.0 ) THEN 00123 WORK( 1 ) = 1 00124 RETURN 00125 END IF 00126 * 00127 NBMIN = 2 00128 NX = 0 00129 IWS = M 00130 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00131 * 00132 * Determine when to cross over from blocked to unblocked code. 00133 * 00134 NX = MAX( 0, ILAENV( 3, 'SGELQF', ' ', M, N, -1, -1 ) ) 00135 IF( NX.LT.K ) THEN 00136 * 00137 * Determine if workspace is large enough for blocked code. 00138 * 00139 LDWORK = M 00140 IWS = LDWORK*NB 00141 IF( LWORK.LT.IWS ) THEN 00142 * 00143 * Not enough workspace to use optimal NB: reduce NB and 00144 * determine the minimum value of NB. 00145 * 00146 NB = LWORK / LDWORK 00147 NBMIN = MAX( 2, ILAENV( 2, 'SGELQF', ' ', M, N, -1, 00148 $ -1 ) ) 00149 END IF 00150 END IF 00151 END IF 00152 * 00153 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN 00154 * 00155 * Use blocked code initially 00156 * 00157 DO 10 I = 1, K - NX, NB 00158 IB = MIN( K-I+1, NB ) 00159 * 00160 * Compute the LQ factorization of the current block 00161 * A(i:i+ib-1,i:n) 00162 * 00163 CALL SGELQ2( IB, N-I+1, A( I, I ), LDA, TAU( I ), WORK, 00164 $ IINFO ) 00165 IF( I+IB.LE.M ) THEN 00166 * 00167 * Form the triangular factor of the block reflector 00168 * H = H(i) H(i+1) . . . H(i+ib-1) 00169 * 00170 CALL SLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ), 00171 $ LDA, TAU( I ), WORK, LDWORK ) 00172 * 00173 * Apply H to A(i+ib:m,i:n) from the right 00174 * 00175 CALL SLARFB( 'Right', 'No transpose', 'Forward', 00176 $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ), 00177 $ LDA, WORK, LDWORK, A( I+IB, I ), LDA, 00178 $ WORK( IB+1 ), LDWORK ) 00179 END IF 00180 10 CONTINUE 00181 ELSE 00182 I = 1 00183 END IF 00184 * 00185 * Use unblocked code to factor the last or only block. 00186 * 00187 IF( I.LE.K ) 00188 $ CALL SGELQ2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK, 00189 $ IINFO ) 00190 * 00191 WORK( 1 ) = IWS 00192 RETURN 00193 * 00194 * End of SGELQF 00195 * 00196 END
1.7.2