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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 DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, 00002 $ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, 00003 $ TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO ) 00004 IMPLICIT NONE 00005 * 00006 * -- LAPACK routine (version 3.3.0) -- 00007 * 00008 * -- Contributed by Brian Sutton of the Randolph-Macon College -- 00009 * -- November 2010 00010 * 00011 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00012 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00013 * 00014 * .. Scalar Arguments .. 00015 CHARACTER SIGNS, TRANS 00016 INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P, 00017 $ Q 00018 * .. 00019 * .. Array Arguments .. 00020 DOUBLE PRECISION PHI( * ), THETA( * ) 00021 DOUBLE PRECISION TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ), 00022 $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ), 00023 $ X21( LDX21, * ), X22( LDX22, * ) 00024 * .. 00025 * 00026 * Purpose 00027 * ======= 00028 * 00029 * DORBDB simultaneously bidiagonalizes the blocks of an M-by-M 00030 * partitioned orthogonal matrix X: 00031 * 00032 * [ B11 | B12 0 0 ] 00033 * [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**T 00034 * X = [-----------] = [---------] [----------------] [---------] . 00035 * [ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ] 00036 * [ 0 | 0 0 I ] 00037 * 00038 * X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is 00039 * not the case, then X must be transposed and/or permuted. This can be 00040 * done in constant time using the TRANS and SIGNS options. See DORCSD 00041 * for details.) 00042 * 00043 * The orthogonal matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by- 00044 * (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are 00045 * represented implicitly by Householder vectors. 00046 * 00047 * B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented 00048 * implicitly by angles THETA, PHI. 00049 * 00050 * Arguments 00051 * ========= 00052 * 00053 * TRANS (input) CHARACTER 00054 * = 'T': X, U1, U2, V1T, and V2T are stored in row-major 00055 * order; 00056 * otherwise: X, U1, U2, V1T, and V2T are stored in column- 00057 * major order. 00058 * 00059 * SIGNS (input) CHARACTER 00060 * = 'O': The lower-left block is made nonpositive (the 00061 * "other" convention); 00062 * otherwise: The upper-right block is made nonpositive (the 00063 * "default" convention). 00064 * 00065 * M (input) INTEGER 00066 * The number of rows and columns in X. 00067 * 00068 * P (input) INTEGER 00069 * The number of rows in X11 and X12. 0 <= P <= M. 00070 * 00071 * Q (input) INTEGER 00072 * The number of columns in X11 and X21. 0 <= Q <= 00073 * MIN(P,M-P,M-Q). 00074 * 00075 * X11 (input/output) DOUBLE PRECISION array, dimension (LDX11,Q) 00076 * On entry, the top-left block of the orthogonal matrix to be 00077 * reduced. On exit, the form depends on TRANS: 00078 * If TRANS = 'N', then 00079 * the columns of tril(X11) specify reflectors for P1, 00080 * the rows of triu(X11,1) specify reflectors for Q1; 00081 * else TRANS = 'T', and 00082 * the rows of triu(X11) specify reflectors for P1, 00083 * the columns of tril(X11,-1) specify reflectors for Q1. 00084 * 00085 * LDX11 (input) INTEGER 00086 * The leading dimension of X11. If TRANS = 'N', then LDX11 >= 00087 * P; else LDX11 >= Q. 00088 * 00089 * X12 (input/output) DOUBLE PRECISION array, dimension (LDX12,M-Q) 00090 * On entry, the top-right block of the orthogonal matrix to 00091 * be reduced. On exit, the form depends on TRANS: 00092 * If TRANS = 'N', then 00093 * the rows of triu(X12) specify the first P reflectors for 00094 * Q2; 00095 * else TRANS = 'T', and 00096 * the columns of tril(X12) specify the first P reflectors 00097 * for Q2. 00098 * 00099 * LDX12 (input) INTEGER 00100 * The leading dimension of X12. If TRANS = 'N', then LDX12 >= 00101 * P; else LDX11 >= M-Q. 00102 * 00103 * X21 (input/output) DOUBLE PRECISION array, dimension (LDX21,Q) 00104 * On entry, the bottom-left block of the orthogonal matrix to 00105 * be reduced. On exit, the form depends on TRANS: 00106 * If TRANS = 'N', then 00107 * the columns of tril(X21) specify reflectors for P2; 00108 * else TRANS = 'T', and 00109 * the rows of triu(X21) specify reflectors for P2. 00110 * 00111 * LDX21 (input) INTEGER 00112 * The leading dimension of X21. If TRANS = 'N', then LDX21 >= 00113 * M-P; else LDX21 >= Q. 00114 * 00115 * X22 (input/output) DOUBLE PRECISION array, dimension (LDX22,M-Q) 00116 * On entry, the bottom-right block of the orthogonal matrix to 00117 * be reduced. On exit, the form depends on TRANS: 00118 * If TRANS = 'N', then 00119 * the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last 00120 * M-P-Q reflectors for Q2, 00121 * else TRANS = 'T', and 00122 * the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last 00123 * M-P-Q reflectors for P2. 00124 * 00125 * LDX22 (input) INTEGER 00126 * The leading dimension of X22. If TRANS = 'N', then LDX22 >= 00127 * M-P; else LDX22 >= M-Q. 00128 * 00129 * THETA (output) DOUBLE PRECISION array, dimension (Q) 00130 * The entries of the bidiagonal blocks B11, B12, B21, B22 can 00131 * be computed from the angles THETA and PHI. See Further 00132 * Details. 00133 * 00134 * PHI (output) DOUBLE PRECISION array, dimension (Q-1) 00135 * The entries of the bidiagonal blocks B11, B12, B21, B22 can 00136 * be computed from the angles THETA and PHI. See Further 00137 * Details. 00138 * 00139 * TAUP1 (output) DOUBLE PRECISION array, dimension (P) 00140 * The scalar factors of the elementary reflectors that define 00141 * P1. 00142 * 00143 * TAUP2 (output) DOUBLE PRECISION array, dimension (M-P) 00144 * The scalar factors of the elementary reflectors that define 00145 * P2. 00146 * 00147 * TAUQ1 (output) DOUBLE PRECISION array, dimension (Q) 00148 * The scalar factors of the elementary reflectors that define 00149 * Q1. 00150 * 00151 * TAUQ2 (output) DOUBLE PRECISION array, dimension (M-Q) 00152 * The scalar factors of the elementary reflectors that define 00153 * Q2. 00154 * 00155 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) 00156 * 00157 * LWORK (input) INTEGER 00158 * The dimension of the array WORK. LWORK >= M-Q. 00159 * 00160 * If LWORK = -1, then a workspace query is assumed; the routine 00161 * only calculates the optimal size of the WORK array, returns 00162 * this value as the first entry of the WORK array, and no error 00163 * message related to LWORK is issued by XERBLA. 00164 * 00165 * INFO (output) INTEGER 00166 * = 0: successful exit. 00167 * < 0: if INFO = -i, the i-th argument had an illegal value. 00168 * 00169 * Further Details 00170 * =============== 00171 * 00172 * The bidiagonal blocks B11, B12, B21, and B22 are represented 00173 * implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ..., 00174 * PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are 00175 * lower bidiagonal. Every entry in each bidiagonal band is a product 00176 * of a sine or cosine of a THETA with a sine or cosine of a PHI. See 00177 * [1] or DORCSD for details. 00178 * 00179 * P1, P2, Q1, and Q2 are represented as products of elementary 00180 * reflectors. See DORCSD for details on generating P1, P2, Q1, and Q2 00181 * using DORGQR and DORGLQ. 00182 * 00183 * Reference 00184 * ========= 00185 * 00186 * [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. 00187 * Algorithms, 50(1):33-65, 2009. 00188 * 00189 * ==================================================================== 00190 * 00191 * .. Parameters .. 00192 DOUBLE PRECISION REALONE 00193 PARAMETER ( REALONE = 1.0D0 ) 00194 DOUBLE PRECISION NEGONE, ONE 00195 PARAMETER ( NEGONE = -1.0D0, ONE = 1.0D0 ) 00196 * .. 00197 * .. Local Scalars .. 00198 LOGICAL COLMAJOR, LQUERY 00199 INTEGER I, LWORKMIN, LWORKOPT 00200 DOUBLE PRECISION Z1, Z2, Z3, Z4 00201 * .. 00202 * .. External Subroutines .. 00203 EXTERNAL DAXPY, DLARF, DLARFGP, DSCAL, XERBLA 00204 * .. 00205 * .. External Functions .. 00206 DOUBLE PRECISION DNRM2 00207 LOGICAL LSAME 00208 EXTERNAL DNRM2, LSAME 00209 * .. 00210 * .. Intrinsic Functions 00211 INTRINSIC ATAN2, COS, MAX, MIN, SIN 00212 * .. 00213 * .. Executable Statements .. 00214 * 00215 * Test input arguments 00216 * 00217 INFO = 0 00218 COLMAJOR = .NOT. LSAME( TRANS, 'T' ) 00219 IF( .NOT. LSAME( SIGNS, 'O' ) ) THEN 00220 Z1 = REALONE 00221 Z2 = REALONE 00222 Z3 = REALONE 00223 Z4 = REALONE 00224 ELSE 00225 Z1 = REALONE 00226 Z2 = -REALONE 00227 Z3 = REALONE 00228 Z4 = -REALONE 00229 END IF 00230 LQUERY = LWORK .EQ. -1 00231 * 00232 IF( M .LT. 0 ) THEN 00233 INFO = -3 00234 ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN 00235 INFO = -4 00236 ELSE IF( Q .LT. 0 .OR. Q .GT. P .OR. Q .GT. M-P .OR. 00237 $ Q .GT. M-Q ) THEN 00238 INFO = -5 00239 ELSE IF( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN 00240 INFO = -7 00241 ELSE IF( .NOT.COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN 00242 INFO = -7 00243 ELSE IF( COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN 00244 INFO = -9 00245 ELSE IF( .NOT.COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN 00246 INFO = -9 00247 ELSE IF( COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN 00248 INFO = -11 00249 ELSE IF( .NOT.COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN 00250 INFO = -11 00251 ELSE IF( COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN 00252 INFO = -13 00253 ELSE IF( .NOT.COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN 00254 INFO = -13 00255 END IF 00256 * 00257 * Compute workspace 00258 * 00259 IF( INFO .EQ. 0 ) THEN 00260 LWORKOPT = M - Q 00261 LWORKMIN = M - Q 00262 WORK(1) = LWORKOPT 00263 IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN 00264 INFO = -21 00265 END IF 00266 END IF 00267 IF( INFO .NE. 0 ) THEN 00268 CALL XERBLA( 'xORBDB', -INFO ) 00269 RETURN 00270 ELSE IF( LQUERY ) THEN 00271 RETURN 00272 END IF 00273 * 00274 * Handle column-major and row-major separately 00275 * 00276 IF( COLMAJOR ) THEN 00277 * 00278 * Reduce columns 1, ..., Q of X11, X12, X21, and X22 00279 * 00280 DO I = 1, Q 00281 * 00282 IF( I .EQ. 1 ) THEN 00283 CALL DSCAL( P-I+1, Z1, X11(I,I), 1 ) 00284 ELSE 00285 CALL DSCAL( P-I+1, Z1*COS(PHI(I-1)), X11(I,I), 1 ) 00286 CALL DAXPY( P-I+1, -Z1*Z3*Z4*SIN(PHI(I-1)), X12(I,I-1), 00287 $ 1, X11(I,I), 1 ) 00288 END IF 00289 IF( I .EQ. 1 ) THEN 00290 CALL DSCAL( M-P-I+1, Z2, X21(I,I), 1 ) 00291 ELSE 00292 CALL DSCAL( M-P-I+1, Z2*COS(PHI(I-1)), X21(I,I), 1 ) 00293 CALL DAXPY( M-P-I+1, -Z2*Z3*Z4*SIN(PHI(I-1)), X22(I,I-1), 00294 $ 1, X21(I,I), 1 ) 00295 END IF 00296 * 00297 THETA(I) = ATAN2( DNRM2( M-P-I+1, X21(I,I), 1 ), 00298 $ DNRM2( P-I+1, X11(I,I), 1 ) ) 00299 * 00300 CALL DLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) ) 00301 X11(I,I) = ONE 00302 CALL DLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) ) 00303 X21(I,I) = ONE 00304 * 00305 CALL DLARF( 'L', P-I+1, Q-I, X11(I,I), 1, TAUP1(I), 00306 $ X11(I,I+1), LDX11, WORK ) 00307 CALL DLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1, TAUP1(I), 00308 $ X12(I,I), LDX12, WORK ) 00309 CALL DLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, TAUP2(I), 00310 $ X21(I,I+1), LDX21, WORK ) 00311 CALL DLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1, TAUP2(I), 00312 $ X22(I,I), LDX22, WORK ) 00313 * 00314 IF( I .LT. Q ) THEN 00315 CALL DSCAL( Q-I, -Z1*Z3*SIN(THETA(I)), X11(I,I+1), 00316 $ LDX11 ) 00317 CALL DAXPY( Q-I, Z2*Z3*COS(THETA(I)), X21(I,I+1), LDX21, 00318 $ X11(I,I+1), LDX11 ) 00319 END IF 00320 CALL DSCAL( M-Q-I+1, -Z1*Z4*SIN(THETA(I)), X12(I,I), LDX12 ) 00321 CALL DAXPY( M-Q-I+1, Z2*Z4*COS(THETA(I)), X22(I,I), LDX22, 00322 $ X12(I,I), LDX12 ) 00323 * 00324 IF( I .LT. Q ) 00325 $ PHI(I) = ATAN2( DNRM2( Q-I, X11(I,I+1), LDX11 ), 00326 $ DNRM2( M-Q-I+1, X12(I,I), LDX12 ) ) 00327 * 00328 IF( I .LT. Q ) THEN 00329 CALL DLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11, 00330 $ TAUQ1(I) ) 00331 X11(I,I+1) = ONE 00332 END IF 00333 CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12, 00334 $ TAUQ2(I) ) 00335 X12(I,I) = ONE 00336 * 00337 IF( I .LT. Q ) THEN 00338 CALL DLARF( 'R', P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I), 00339 $ X11(I+1,I+1), LDX11, WORK ) 00340 CALL DLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I), 00341 $ X21(I+1,I+1), LDX21, WORK ) 00342 END IF 00343 CALL DLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I), 00344 $ X12(I+1,I), LDX12, WORK ) 00345 CALL DLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I), 00346 $ X22(I+1,I), LDX22, WORK ) 00347 * 00348 END DO 00349 * 00350 * Reduce columns Q + 1, ..., P of X12, X22 00351 * 00352 DO I = Q + 1, P 00353 * 00354 CALL DSCAL( M-Q-I+1, -Z1*Z4, X12(I,I), LDX12 ) 00355 CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12, 00356 $ TAUQ2(I) ) 00357 X12(I,I) = ONE 00358 * 00359 CALL DLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I), 00360 $ X12(I+1,I), LDX12, WORK ) 00361 IF( M-P-Q .GE. 1 ) 00362 $ CALL DLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12, 00363 $ TAUQ2(I), X22(Q+1,I), LDX22, WORK ) 00364 * 00365 END DO 00366 * 00367 * Reduce columns P + 1, ..., M - Q of X12, X22 00368 * 00369 DO I = 1, M - P - Q 00370 * 00371 CALL DSCAL( M-P-Q-I+1, Z2*Z4, X22(Q+I,P+I), LDX22 ) 00372 CALL DLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1), 00373 $ LDX22, TAUQ2(P+I) ) 00374 X22(Q+I,P+I) = ONE 00375 CALL DLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22, 00376 $ TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK ) 00377 * 00378 END DO 00379 * 00380 ELSE 00381 * 00382 * Reduce columns 1, ..., Q of X11, X12, X21, X22 00383 * 00384 DO I = 1, Q 00385 * 00386 IF( I .EQ. 1 ) THEN 00387 CALL DSCAL( P-I+1, Z1, X11(I,I), LDX11 ) 00388 ELSE 00389 CALL DSCAL( P-I+1, Z1*COS(PHI(I-1)), X11(I,I), LDX11 ) 00390 CALL DAXPY( P-I+1, -Z1*Z3*Z4*SIN(PHI(I-1)), X12(I-1,I), 00391 $ LDX12, X11(I,I), LDX11 ) 00392 END IF 00393 IF( I .EQ. 1 ) THEN 00394 CALL DSCAL( M-P-I+1, Z2, X21(I,I), LDX21 ) 00395 ELSE 00396 CALL DSCAL( M-P-I+1, Z2*COS(PHI(I-1)), X21(I,I), LDX21 ) 00397 CALL DAXPY( M-P-I+1, -Z2*Z3*Z4*SIN(PHI(I-1)), X22(I-1,I), 00398 $ LDX22, X21(I,I), LDX21 ) 00399 END IF 00400 * 00401 THETA(I) = ATAN2( DNRM2( M-P-I+1, X21(I,I), LDX21 ), 00402 $ DNRM2( P-I+1, X11(I,I), LDX11 ) ) 00403 * 00404 CALL DLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) ) 00405 X11(I,I) = ONE 00406 CALL DLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21, 00407 $ TAUP2(I) ) 00408 X21(I,I) = ONE 00409 * 00410 CALL DLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I), 00411 $ X11(I+1,I), LDX11, WORK ) 00412 CALL DLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11, TAUP1(I), 00413 $ X12(I,I), LDX12, WORK ) 00414 CALL DLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I), 00415 $ X21(I+1,I), LDX21, WORK ) 00416 CALL DLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21, 00417 $ TAUP2(I), X22(I,I), LDX22, WORK ) 00418 * 00419 IF( I .LT. Q ) THEN 00420 CALL DSCAL( Q-I, -Z1*Z3*SIN(THETA(I)), X11(I+1,I), 1 ) 00421 CALL DAXPY( Q-I, Z2*Z3*COS(THETA(I)), X21(I+1,I), 1, 00422 $ X11(I+1,I), 1 ) 00423 END IF 00424 CALL DSCAL( M-Q-I+1, -Z1*Z4*SIN(THETA(I)), X12(I,I), 1 ) 00425 CALL DAXPY( M-Q-I+1, Z2*Z4*COS(THETA(I)), X22(I,I), 1, 00426 $ X12(I,I), 1 ) 00427 * 00428 IF( I .LT. Q ) 00429 $ PHI(I) = ATAN2( DNRM2( Q-I, X11(I+1,I), 1 ), 00430 $ DNRM2( M-Q-I+1, X12(I,I), 1 ) ) 00431 * 00432 IF( I .LT. Q ) THEN 00433 CALL DLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1, TAUQ1(I) ) 00434 X11(I+1,I) = ONE 00435 END IF 00436 CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) ) 00437 X12(I,I) = ONE 00438 * 00439 IF( I .LT. Q ) THEN 00440 CALL DLARF( 'L', Q-I, P-I, X11(I+1,I), 1, TAUQ1(I), 00441 $ X11(I+1,I+1), LDX11, WORK ) 00442 CALL DLARF( 'L', Q-I, M-P-I, X11(I+1,I), 1, TAUQ1(I), 00443 $ X21(I+1,I+1), LDX21, WORK ) 00444 END IF 00445 CALL DLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, TAUQ2(I), 00446 $ X12(I,I+1), LDX12, WORK ) 00447 CALL DLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1, TAUQ2(I), 00448 $ X22(I,I+1), LDX22, WORK ) 00449 * 00450 END DO 00451 * 00452 * Reduce columns Q + 1, ..., P of X12, X22 00453 * 00454 DO I = Q + 1, P 00455 * 00456 CALL DSCAL( M-Q-I+1, -Z1*Z4, X12(I,I), 1 ) 00457 CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) ) 00458 X12(I,I) = ONE 00459 * 00460 CALL DLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, TAUQ2(I), 00461 $ X12(I,I+1), LDX12, WORK ) 00462 IF( M-P-Q .GE. 1 ) 00463 $ CALL DLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1, TAUQ2(I), 00464 $ X22(I,Q+1), LDX22, WORK ) 00465 * 00466 END DO 00467 * 00468 * Reduce columns P + 1, ..., M - Q of X12, X22 00469 * 00470 DO I = 1, M - P - Q 00471 * 00472 CALL DSCAL( M-P-Q-I+1, Z2*Z4, X22(P+I,Q+I), 1 ) 00473 CALL DLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1, 00474 $ TAUQ2(P+I) ) 00475 X22(P+I,Q+I) = ONE 00476 * 00477 CALL DLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1, 00478 $ TAUQ2(P+I), X22(P+I,Q+I+1), LDX22, WORK ) 00479 * 00480 END DO 00481 * 00482 END IF 00483 * 00484 RETURN 00485 * 00486 * End of DORBDB 00487 * 00488 END 00489
1.7.3 
