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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 DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.3.1) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * -- April 2011 -- 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER INFO, LDA, LWORK, M, N 00010 * .. 00011 * .. Array Arguments .. 00012 INTEGER JPVT( * ) 00013 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * DGEQP3 computes a QR factorization with column pivoting of a 00020 * matrix A: A*P = Q*R using Level 3 BLAS. 00021 * 00022 * Arguments 00023 * ========= 00024 * 00025 * M (input) INTEGER 00026 * The number of rows of the matrix A. M >= 0. 00027 * 00028 * N (input) INTEGER 00029 * The number of columns of the matrix A. N >= 0. 00030 * 00031 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) 00032 * On entry, the M-by-N matrix A. 00033 * On exit, the upper triangle of the array contains the 00034 * min(M,N)-by-N upper trapezoidal matrix R; the elements below 00035 * the diagonal, together with the array TAU, represent the 00036 * orthogonal matrix Q as a product of min(M,N) elementary 00037 * reflectors. 00038 * 00039 * LDA (input) INTEGER 00040 * The leading dimension of the array A. LDA >= max(1,M). 00041 * 00042 * JPVT (input/output) INTEGER array, dimension (N) 00043 * On entry, if JPVT(J).ne.0, the J-th column of A is permuted 00044 * to the front of A*P (a leading column); if JPVT(J)=0, 00045 * the J-th column of A is a free column. 00046 * On exit, if JPVT(J)=K, then the J-th column of A*P was the 00047 * the K-th column of A. 00048 * 00049 * TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) 00050 * The scalar factors of the elementary reflectors. 00051 * 00052 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00053 * On exit, if INFO=0, WORK(1) returns the optimal LWORK. 00054 * 00055 * LWORK (input) INTEGER 00056 * The dimension of the array WORK. LWORK >= 3*N+1. 00057 * For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB 00058 * is the optimal blocksize. 00059 * 00060 * If LWORK = -1, then a workspace query is assumed; the routine 00061 * only calculates the optimal size of the WORK array, returns 00062 * this value as the first entry of the WORK array, and no error 00063 * message related to LWORK is issued by XERBLA. 00064 * 00065 * INFO (output) INTEGER 00066 * = 0: successful exit. 00067 * < 0: if INFO = -i, the i-th argument had an illegal value. 00068 * 00069 * Further Details 00070 * =============== 00071 * 00072 * The matrix Q is represented as a product of elementary reflectors 00073 * 00074 * Q = H(1) H(2) . . . H(k), where k = min(m,n). 00075 * 00076 * Each H(i) has the form 00077 * 00078 * H(i) = I - tau * v * v**T 00079 * 00080 * where tau is a real/complex scalar, and v is a real/complex vector 00081 * with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in 00082 * A(i+1:m,i), and tau in TAU(i). 00083 * 00084 * Based on contributions by 00085 * G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain 00086 * X. Sun, Computer Science Dept., Duke University, USA 00087 * 00088 * ===================================================================== 00089 * 00090 * .. Parameters .. 00091 INTEGER INB, INBMIN, IXOVER 00092 PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 ) 00093 * .. 00094 * .. Local Scalars .. 00095 LOGICAL LQUERY 00096 INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB, 00097 $ NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN 00098 * .. 00099 * .. External Subroutines .. 00100 EXTERNAL DGEQRF, DLAQP2, DLAQPS, DORMQR, DSWAP, XERBLA 00101 * .. 00102 * .. External Functions .. 00103 INTEGER ILAENV 00104 DOUBLE PRECISION DNRM2 00105 EXTERNAL ILAENV, DNRM2 00106 * .. 00107 * .. Intrinsic Functions .. 00108 INTRINSIC INT, MAX, MIN 00109 * .. 00110 * .. Executable Statements .. 00111 * 00112 * Test input arguments 00113 * ==================== 00114 * 00115 INFO = 0 00116 LQUERY = ( LWORK.EQ.-1 ) 00117 IF( M.LT.0 ) THEN 00118 INFO = -1 00119 ELSE IF( N.LT.0 ) THEN 00120 INFO = -2 00121 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00122 INFO = -4 00123 END IF 00124 * 00125 IF( INFO.EQ.0 ) THEN 00126 MINMN = MIN( M, N ) 00127 IF( MINMN.EQ.0 ) THEN 00128 IWS = 1 00129 LWKOPT = 1 00130 ELSE 00131 IWS = 3*N + 1 00132 NB = ILAENV( INB, 'DGEQRF', ' ', M, N, -1, -1 ) 00133 LWKOPT = 2*N + ( N + 1 )*NB 00134 END IF 00135 WORK( 1 ) = LWKOPT 00136 * 00137 IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN 00138 INFO = -8 00139 END IF 00140 END IF 00141 * 00142 IF( INFO.NE.0 ) THEN 00143 CALL XERBLA( 'DGEQP3', -INFO ) 00144 RETURN 00145 ELSE IF( LQUERY ) THEN 00146 RETURN 00147 END IF 00148 * 00149 * Quick return if possible. 00150 * 00151 IF( MINMN.EQ.0 ) THEN 00152 RETURN 00153 END IF 00154 * 00155 * Move initial columns up front. 00156 * 00157 NFXD = 1 00158 DO 10 J = 1, N 00159 IF( JPVT( J ).NE.0 ) THEN 00160 IF( J.NE.NFXD ) THEN 00161 CALL DSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 ) 00162 JPVT( J ) = JPVT( NFXD ) 00163 JPVT( NFXD ) = J 00164 ELSE 00165 JPVT( J ) = J 00166 END IF 00167 NFXD = NFXD + 1 00168 ELSE 00169 JPVT( J ) = J 00170 END IF 00171 10 CONTINUE 00172 NFXD = NFXD - 1 00173 * 00174 * Factorize fixed columns 00175 * ======================= 00176 * 00177 * Compute the QR factorization of fixed columns and update 00178 * remaining columns. 00179 * 00180 IF( NFXD.GT.0 ) THEN 00181 NA = MIN( M, NFXD ) 00182 *CC CALL DGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) 00183 CALL DGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO ) 00184 IWS = MAX( IWS, INT( WORK( 1 ) ) ) 00185 IF( NA.LT.N ) THEN 00186 *CC CALL DORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA, 00187 *CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO ) 00188 CALL DORMQR( 'Left', 'Transpose', M, N-NA, NA, A, LDA, TAU, 00189 $ A( 1, NA+1 ), LDA, WORK, LWORK, INFO ) 00190 IWS = MAX( IWS, INT( WORK( 1 ) ) ) 00191 END IF 00192 END IF 00193 * 00194 * Factorize free columns 00195 * ====================== 00196 * 00197 IF( NFXD.LT.MINMN ) THEN 00198 * 00199 SM = M - NFXD 00200 SN = N - NFXD 00201 SMINMN = MINMN - NFXD 00202 * 00203 * Determine the block size. 00204 * 00205 NB = ILAENV( INB, 'DGEQRF', ' ', SM, SN, -1, -1 ) 00206 NBMIN = 2 00207 NX = 0 00208 * 00209 IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN 00210 * 00211 * Determine when to cross over from blocked to unblocked code. 00212 * 00213 NX = MAX( 0, ILAENV( IXOVER, 'DGEQRF', ' ', SM, SN, -1, 00214 $ -1 ) ) 00215 * 00216 * 00217 IF( NX.LT.SMINMN ) THEN 00218 * 00219 * Determine if workspace is large enough for blocked code. 00220 * 00221 MINWS = 2*SN + ( SN+1 )*NB 00222 IWS = MAX( IWS, MINWS ) 00223 IF( LWORK.LT.MINWS ) THEN 00224 * 00225 * Not enough workspace to use optimal NB: Reduce NB and 00226 * determine the minimum value of NB. 00227 * 00228 NB = ( LWORK-2*SN ) / ( SN+1 ) 00229 NBMIN = MAX( 2, ILAENV( INBMIN, 'DGEQRF', ' ', SM, SN, 00230 $ -1, -1 ) ) 00231 * 00232 * 00233 END IF 00234 END IF 00235 END IF 00236 * 00237 * Initialize partial column norms. The first N elements of work 00238 * store the exact column norms. 00239 * 00240 DO 20 J = NFXD + 1, N 00241 WORK( J ) = DNRM2( SM, A( NFXD+1, J ), 1 ) 00242 WORK( N+J ) = WORK( J ) 00243 20 CONTINUE 00244 * 00245 IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND. 00246 $ ( NX.LT.SMINMN ) ) THEN 00247 * 00248 * Use blocked code initially. 00249 * 00250 J = NFXD + 1 00251 * 00252 * Compute factorization: while loop. 00253 * 00254 * 00255 TOPBMN = MINMN - NX 00256 30 CONTINUE 00257 IF( J.LE.TOPBMN ) THEN 00258 JB = MIN( NB, TOPBMN-J+1 ) 00259 * 00260 * Factorize JB columns among columns J:N. 00261 * 00262 CALL DLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA, 00263 $ JPVT( J ), TAU( J ), WORK( J ), WORK( N+J ), 00264 $ WORK( 2*N+1 ), WORK( 2*N+JB+1 ), N-J+1 ) 00265 * 00266 J = J + FJB 00267 GO TO 30 00268 END IF 00269 ELSE 00270 J = NFXD + 1 00271 END IF 00272 * 00273 * Use unblocked code to factor the last or only block. 00274 * 00275 * 00276 IF( J.LE.MINMN ) 00277 $ CALL DLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ), 00278 $ TAU( J ), WORK( J ), WORK( N+J ), 00279 $ WORK( 2*N+1 ) ) 00280 * 00281 END IF 00282 * 00283 WORK( 1 ) = IWS 00284 RETURN 00285 * 00286 * End of DGEQP3 00287 * 00288 END
1.7.3 
