 |
LAPACK 3.3.1
Linear Algebra PACKage
|
|
LAPACK 3.3.1
Linear Algebra PACKage
|
00001 SUBROUTINE SGEQP3( 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 REAL A( LDA, * ), TAU( * ), WORK( * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * SGEQP3 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) REAL 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) REAL array, dimension (min(M,N)) 00050 * The scalar factors of the elementary reflectors. 00051 * 00052 * WORK (workspace/output) REAL 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 SGEQRF, SLAQP2, SLAQPS, SORMQR, SSWAP, XERBLA 00101 * .. 00102 * .. External Functions .. 00103 INTEGER ILAENV 00104 REAL SNRM2 00105 EXTERNAL ILAENV, SNRM2 00106 * .. 00107 * .. Intrinsic Functions .. 00108 INTRINSIC INT, MAX, MIN 00109 * .. 00110 * .. Executable Statements .. 00111 * 00112 INFO = 0 00113 LQUERY = ( LWORK.EQ.-1 ) 00114 IF( M.LT.0 ) THEN 00115 INFO = -1 00116 ELSE IF( N.LT.0 ) THEN 00117 INFO = -2 00118 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00119 INFO = -4 00120 END IF 00121 * 00122 IF( INFO.EQ.0 ) THEN 00123 MINMN = MIN( M, N ) 00124 IF( MINMN.EQ.0 ) THEN 00125 IWS = 1 00126 LWKOPT = 1 00127 ELSE 00128 IWS = 3*N + 1 00129 NB = ILAENV( INB, 'SGEQRF', ' ', M, N, -1, -1 ) 00130 LWKOPT = 2*N + ( N + 1 )*NB 00131 END IF 00132 WORK( 1 ) = LWKOPT 00133 * 00134 IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN 00135 INFO = -8 00136 END IF 00137 END IF 00138 * 00139 IF( INFO.NE.0 ) THEN 00140 CALL XERBLA( 'SGEQP3', -INFO ) 00141 RETURN 00142 ELSE IF( LQUERY ) THEN 00143 RETURN 00144 END IF 00145 * 00146 * Quick return if possible. 00147 * 00148 IF( MINMN.EQ.0 ) THEN 00149 RETURN 00150 END IF 00151 * 00152 * Move initial columns up front. 00153 * 00154 NFXD = 1 00155 DO 10 J = 1, N 00156 IF( JPVT( J ).NE.0 ) THEN 00157 IF( J.NE.NFXD ) THEN 00158 CALL SSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 ) 00159 JPVT( J ) = JPVT( NFXD ) 00160 JPVT( NFXD ) = J 00161 ELSE 00162 JPVT( J ) = J 00163 END IF 00164 NFXD = NFXD + 1 00165 ELSE 00166 JPVT( J ) = J 00167 END IF 00168 10 CONTINUE 00169 NFXD = NFXD - 1 00170 * 00171 * Factorize fixed columns 00172 * ======================= 00173 * 00174 * Compute the QR factorization of fixed columns and update 00175 * remaining columns. 00176 * 00177 IF( NFXD.GT.0 ) THEN 00178 NA = MIN( M, NFXD ) 00179 *CC CALL SGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) 00180 CALL SGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO ) 00181 IWS = MAX( IWS, INT( WORK( 1 ) ) ) 00182 IF( NA.LT.N ) THEN 00183 *CC CALL SORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA, 00184 *CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO ) 00185 CALL SORMQR( 'Left', 'Transpose', M, N-NA, NA, A, LDA, TAU, 00186 $ A( 1, NA+1 ), LDA, WORK, LWORK, INFO ) 00187 IWS = MAX( IWS, INT( WORK( 1 ) ) ) 00188 END IF 00189 END IF 00190 * 00191 * Factorize free columns 00192 * ====================== 00193 * 00194 IF( NFXD.LT.MINMN ) THEN 00195 * 00196 SM = M - NFXD 00197 SN = N - NFXD 00198 SMINMN = MINMN - NFXD 00199 * 00200 * Determine the block size. 00201 * 00202 NB = ILAENV( INB, 'SGEQRF', ' ', SM, SN, -1, -1 ) 00203 NBMIN = 2 00204 NX = 0 00205 * 00206 IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN 00207 * 00208 * Determine when to cross over from blocked to unblocked code. 00209 * 00210 NX = MAX( 0, ILAENV( IXOVER, 'SGEQRF', ' ', SM, SN, -1, 00211 $ -1 ) ) 00212 * 00213 * 00214 IF( NX.LT.SMINMN ) THEN 00215 * 00216 * Determine if workspace is large enough for blocked code. 00217 * 00218 MINWS = 2*SN + ( SN+1 )*NB 00219 IWS = MAX( IWS, MINWS ) 00220 IF( LWORK.LT.MINWS ) THEN 00221 * 00222 * Not enough workspace to use optimal NB: Reduce NB and 00223 * determine the minimum value of NB. 00224 * 00225 NB = ( LWORK-2*SN ) / ( SN+1 ) 00226 NBMIN = MAX( 2, ILAENV( INBMIN, 'SGEQRF', ' ', SM, SN, 00227 $ -1, -1 ) ) 00228 * 00229 * 00230 END IF 00231 END IF 00232 END IF 00233 * 00234 * Initialize partial column norms. The first N elements of work 00235 * store the exact column norms. 00236 * 00237 DO 20 J = NFXD + 1, N 00238 WORK( J ) = SNRM2( SM, A( NFXD+1, J ), 1 ) 00239 WORK( N+J ) = WORK( J ) 00240 20 CONTINUE 00241 * 00242 IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND. 00243 $ ( NX.LT.SMINMN ) ) THEN 00244 * 00245 * Use blocked code initially. 00246 * 00247 J = NFXD + 1 00248 * 00249 * Compute factorization: while loop. 00250 * 00251 * 00252 TOPBMN = MINMN - NX 00253 30 CONTINUE 00254 IF( J.LE.TOPBMN ) THEN 00255 JB = MIN( NB, TOPBMN-J+1 ) 00256 * 00257 * Factorize JB columns among columns J:N. 00258 * 00259 CALL SLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA, 00260 $ JPVT( J ), TAU( J ), WORK( J ), WORK( N+J ), 00261 $ WORK( 2*N+1 ), WORK( 2*N+JB+1 ), N-J+1 ) 00262 * 00263 J = J + FJB 00264 GO TO 30 00265 END IF 00266 ELSE 00267 J = NFXD + 1 00268 END IF 00269 * 00270 * Use unblocked code to factor the last or only block. 00271 * 00272 * 00273 IF( J.LE.MINMN ) 00274 $ CALL SLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ), 00275 $ TAU( J ), WORK( J ), WORK( N+J ), 00276 $ WORK( 2*N+1 ) ) 00277 * 00278 END IF 00279 * 00280 WORK( 1 ) = IWS 00281 RETURN 00282 * 00283 * End of SGEQP3 00284 * 00285 END
1.7.3 
