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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE ZUNBDB( 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 COMPLEX*16 TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ), 00022 $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ), 00023 $ X21( LDX21, * ), X22( LDX22, * ) 00024 * .. 00025 * 00026 * Purpose 00027 * ======= 00028 * 00029 * ZUNBDB simultaneously bidiagonalizes the blocks of an M-by-M 00030 * partitioned unitary matrix X: 00031 * 00032 * [ B11 | B12 0 0 ] 00033 * [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**H 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 ZUNCSD 00041 * for details.) 00042 * 00043 * The unitary 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) COMPLEX*16 array, dimension (LDX11,Q) 00076 * On entry, the top-left block of the unitary 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) COMPLEX*16 array, dimension (LDX12,M-Q) 00090 * On entry, the top-right block of the unitary 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) COMPLEX*16 array, dimension (LDX21,Q) 00104 * On entry, the bottom-left block of the unitary 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) COMPLEX*16 array, dimension (LDX22,M-Q) 00116 * On entry, the bottom-right block of the unitary 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) COMPLEX*16 array, dimension (P) 00140 * The scalar factors of the elementary reflectors that define 00141 * P1. 00142 * 00143 * TAUP2 (output) COMPLEX*16 array, dimension (M-P) 00144 * The scalar factors of the elementary reflectors that define 00145 * P2. 00146 * 00147 * TAUQ1 (output) COMPLEX*16 array, dimension (Q) 00148 * The scalar factors of the elementary reflectors that define 00149 * Q1. 00150 * 00151 * TAUQ2 (output) COMPLEX*16 array, dimension (M-Q) 00152 * The scalar factors of the elementary reflectors that define 00153 * Q2. 00154 * 00155 * WORK (workspace) COMPLEX*16 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 ZUNCSD for details. 00178 * 00179 * P1, P2, Q1, and Q2 are represented as products of elementary 00180 * reflectors. See ZUNCSD for details on generating P1, P2, Q1, and Q2 00181 * using ZUNGQR and ZUNGLQ. 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 COMPLEX*16 NEGONE, ONE 00195 PARAMETER ( NEGONE = (-1.0D0,0.0D0), 00196 $ ONE = (1.0D0,0.0D0) ) 00197 * .. 00198 * .. Local Scalars .. 00199 LOGICAL COLMAJOR, LQUERY 00200 INTEGER I, LWORKMIN, LWORKOPT 00201 DOUBLE PRECISION Z1, Z2, Z3, Z4 00202 * .. 00203 * .. External Subroutines .. 00204 EXTERNAL ZAXPY, ZLARF, ZLARFGP, ZSCAL, XERBLA 00205 EXTERNAL ZLACGV 00206 * 00207 * .. 00208 * .. External Functions .. 00209 DOUBLE PRECISION DZNRM2 00210 LOGICAL LSAME 00211 EXTERNAL DZNRM2, LSAME 00212 * .. 00213 * .. Intrinsic Functions 00214 INTRINSIC ATAN2, COS, MAX, MIN, SIN 00215 INTRINSIC DCMPLX, DCONJG 00216 * .. 00217 * .. Executable Statements .. 00218 * 00219 * Test input arguments 00220 * 00221 INFO = 0 00222 COLMAJOR = .NOT. LSAME( TRANS, 'T' ) 00223 IF( .NOT. LSAME( SIGNS, 'O' ) ) THEN 00224 Z1 = REALONE 00225 Z2 = REALONE 00226 Z3 = REALONE 00227 Z4 = REALONE 00228 ELSE 00229 Z1 = REALONE 00230 Z2 = -REALONE 00231 Z3 = REALONE 00232 Z4 = -REALONE 00233 END IF 00234 LQUERY = LWORK .EQ. -1 00235 * 00236 IF( M .LT. 0 ) THEN 00237 INFO = -3 00238 ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN 00239 INFO = -4 00240 ELSE IF( Q .LT. 0 .OR. Q .GT. P .OR. Q .GT. M-P .OR. 00241 $ Q .GT. M-Q ) THEN 00242 INFO = -5 00243 ELSE IF( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN 00244 INFO = -7 00245 ELSE IF( .NOT.COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN 00246 INFO = -7 00247 ELSE IF( COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN 00248 INFO = -9 00249 ELSE IF( .NOT.COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN 00250 INFO = -9 00251 ELSE IF( COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN 00252 INFO = -11 00253 ELSE IF( .NOT.COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN 00254 INFO = -11 00255 ELSE IF( COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN 00256 INFO = -13 00257 ELSE IF( .NOT.COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN 00258 INFO = -13 00259 END IF 00260 * 00261 * Compute workspace 00262 * 00263 IF( INFO .EQ. 0 ) THEN 00264 LWORKOPT = M - Q 00265 LWORKMIN = M - Q 00266 WORK(1) = LWORKOPT 00267 IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN 00268 INFO = -21 00269 END IF 00270 END IF 00271 IF( INFO .NE. 0 ) THEN 00272 CALL XERBLA( 'xORBDB', -INFO ) 00273 RETURN 00274 ELSE IF( LQUERY ) THEN 00275 RETURN 00276 END IF 00277 * 00278 * Handle column-major and row-major separately 00279 * 00280 IF( COLMAJOR ) THEN 00281 * 00282 * Reduce columns 1, ..., Q of X11, X12, X21, and X22 00283 * 00284 DO I = 1, Q 00285 * 00286 IF( I .EQ. 1 ) THEN 00287 CALL ZSCAL( P-I+1, DCMPLX( Z1, 0.0D0 ), X11(I,I), 1 ) 00288 ELSE 00289 CALL ZSCAL( P-I+1, DCMPLX( Z1*COS(PHI(I-1)), 0.0D0 ), 00290 $ X11(I,I), 1 ) 00291 CALL ZAXPY( P-I+1, DCMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)), 00292 $ 0.0D0 ), X12(I,I-1), 1, X11(I,I), 1 ) 00293 END IF 00294 IF( I .EQ. 1 ) THEN 00295 CALL ZSCAL( M-P-I+1, DCMPLX( Z2, 0.0D0 ), X21(I,I), 1 ) 00296 ELSE 00297 CALL ZSCAL( M-P-I+1, DCMPLX( Z2*COS(PHI(I-1)), 0.0D0 ), 00298 $ X21(I,I), 1 ) 00299 CALL ZAXPY( M-P-I+1, DCMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)), 00300 $ 0.0D0 ), X22(I,I-1), 1, X21(I,I), 1 ) 00301 END IF 00302 * 00303 THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), 1 ), 00304 $ DZNRM2( P-I+1, X11(I,I), 1 ) ) 00305 * 00306 CALL ZLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) ) 00307 X11(I,I) = ONE 00308 CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) ) 00309 X21(I,I) = ONE 00310 * 00311 CALL ZLARF( 'L', P-I+1, Q-I, X11(I,I), 1, DCONJG(TAUP1(I)), 00312 $ X11(I,I+1), LDX11, WORK ) 00313 CALL ZLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1, 00314 $ DCONJG(TAUP1(I)), X12(I,I), LDX12, WORK ) 00315 CALL ZLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, 00316 $ DCONJG(TAUP2(I)), X21(I,I+1), LDX21, WORK ) 00317 CALL ZLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1, 00318 $ DCONJG(TAUP2(I)), X22(I,I), LDX22, WORK ) 00319 * 00320 IF( I .LT. Q ) THEN 00321 CALL ZSCAL( Q-I, DCMPLX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ), 00322 $ X11(I,I+1), LDX11 ) 00323 CALL ZAXPY( Q-I, DCMPLX( Z2*Z3*COS(THETA(I)), 0.0D0 ), 00324 $ X21(I,I+1), LDX21, X11(I,I+1), LDX11 ) 00325 END IF 00326 CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ), 00327 $ X12(I,I), LDX12 ) 00328 CALL ZAXPY( M-Q-I+1, DCMPLX( Z2*Z4*COS(THETA(I)), 0.0D0 ), 00329 $ X22(I,I), LDX22, X12(I,I), LDX12 ) 00330 * 00331 IF( I .LT. Q ) 00332 $ PHI(I) = ATAN2( DZNRM2( Q-I, X11(I,I+1), LDX11 ), 00333 $ DZNRM2( M-Q-I+1, X12(I,I), LDX12 ) ) 00334 * 00335 IF( I .LT. Q ) THEN 00336 CALL ZLACGV( Q-I, X11(I,I+1), LDX11 ) 00337 CALL ZLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11, 00338 $ TAUQ1(I) ) 00339 X11(I,I+1) = ONE 00340 END IF 00341 CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 ) 00342 CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12, 00343 $ TAUQ2(I) ) 00344 X12(I,I) = ONE 00345 * 00346 IF( I .LT. Q ) THEN 00347 CALL ZLARF( 'R', P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I), 00348 $ X11(I+1,I+1), LDX11, WORK ) 00349 CALL ZLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I), 00350 $ X21(I+1,I+1), LDX21, WORK ) 00351 END IF 00352 CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I), 00353 $ X12(I+1,I), LDX12, WORK ) 00354 CALL ZLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I), 00355 $ X22(I+1,I), LDX22, WORK ) 00356 * 00357 IF( I .LT. Q ) 00358 $ CALL ZLACGV( Q-I, X11(I,I+1), LDX11 ) 00359 CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 ) 00360 * 00361 END DO 00362 * 00363 * Reduce columns Q + 1, ..., P of X12, X22 00364 * 00365 DO I = Q + 1, P 00366 * 00367 CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4, 0.0D0 ), X12(I,I), 00368 $ LDX12 ) 00369 CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 ) 00370 CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12, 00371 $ TAUQ2(I) ) 00372 X12(I,I) = ONE 00373 * 00374 CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I), 00375 $ X12(I+1,I), LDX12, WORK ) 00376 IF( M-P-Q .GE. 1 ) 00377 $ CALL ZLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12, 00378 $ TAUQ2(I), X22(Q+1,I), LDX22, WORK ) 00379 * 00380 CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 ) 00381 * 00382 END DO 00383 * 00384 * Reduce columns P + 1, ..., M - Q of X12, X22 00385 * 00386 DO I = 1, M - P - Q 00387 * 00388 CALL ZSCAL( M-P-Q-I+1, DCMPLX( Z2*Z4, 0.0D0 ), 00389 $ X22(Q+I,P+I), LDX22 ) 00390 CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 ) 00391 CALL ZLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1), 00392 $ LDX22, TAUQ2(P+I) ) 00393 X22(Q+I,P+I) = ONE 00394 CALL ZLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22, 00395 $ TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK ) 00396 * 00397 CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 ) 00398 * 00399 END DO 00400 * 00401 ELSE 00402 * 00403 * Reduce columns 1, ..., Q of X11, X12, X21, X22 00404 * 00405 DO I = 1, Q 00406 * 00407 IF( I .EQ. 1 ) THEN 00408 CALL ZSCAL( P-I+1, DCMPLX( Z1, 0.0D0 ), X11(I,I), 00409 $ LDX11 ) 00410 ELSE 00411 CALL ZSCAL( P-I+1, DCMPLX( Z1*COS(PHI(I-1)), 0.0D0 ), 00412 $ X11(I,I), LDX11 ) 00413 CALL ZAXPY( P-I+1, DCMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)), 00414 $ 0.0D0 ), X12(I-1,I), LDX12, X11(I,I), LDX11 ) 00415 END IF 00416 IF( I .EQ. 1 ) THEN 00417 CALL ZSCAL( M-P-I+1, DCMPLX( Z2, 0.0D0 ), X21(I,I), 00418 $ LDX21 ) 00419 ELSE 00420 CALL ZSCAL( M-P-I+1, DCMPLX( Z2*COS(PHI(I-1)), 0.0D0 ), 00421 $ X21(I,I), LDX21 ) 00422 CALL ZAXPY( M-P-I+1, DCMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)), 00423 $ 0.0D0 ), X22(I-1,I), LDX22, X21(I,I), LDX21 ) 00424 END IF 00425 * 00426 THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), LDX21 ), 00427 $ DZNRM2( P-I+1, X11(I,I), LDX11 ) ) 00428 * 00429 CALL ZLACGV( P-I+1, X11(I,I), LDX11 ) 00430 CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 ) 00431 * 00432 CALL ZLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) ) 00433 X11(I,I) = ONE 00434 CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21, 00435 $ TAUP2(I) ) 00436 X21(I,I) = ONE 00437 * 00438 CALL ZLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I), 00439 $ X11(I+1,I), LDX11, WORK ) 00440 CALL ZLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11, TAUP1(I), 00441 $ X12(I,I), LDX12, WORK ) 00442 CALL ZLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I), 00443 $ X21(I+1,I), LDX21, WORK ) 00444 CALL ZLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21, 00445 $ TAUP2(I), X22(I,I), LDX22, WORK ) 00446 * 00447 CALL ZLACGV( P-I+1, X11(I,I), LDX11 ) 00448 CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 ) 00449 * 00450 IF( I .LT. Q ) THEN 00451 CALL ZSCAL( Q-I, DCMPLX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ), 00452 $ X11(I+1,I), 1 ) 00453 CALL ZAXPY( Q-I, DCMPLX( Z2*Z3*COS(THETA(I)), 0.0D0 ), 00454 $ X21(I+1,I), 1, X11(I+1,I), 1 ) 00455 END IF 00456 CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ), 00457 $ X12(I,I), 1 ) 00458 CALL ZAXPY( M-Q-I+1, DCMPLX( Z2*Z4*COS(THETA(I)), 0.0D0 ), 00459 $ X22(I,I), 1, X12(I,I), 1 ) 00460 * 00461 IF( I .LT. Q ) 00462 $ PHI(I) = ATAN2( DZNRM2( Q-I, X11(I+1,I), 1 ), 00463 $ DZNRM2( M-Q-I+1, X12(I,I), 1 ) ) 00464 * 00465 IF( I .LT. Q ) THEN 00466 CALL ZLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1, TAUQ1(I) ) 00467 X11(I+1,I) = ONE 00468 END IF 00469 CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) ) 00470 X12(I,I) = ONE 00471 * 00472 IF( I .LT. Q ) THEN 00473 CALL ZLARF( 'L', Q-I, P-I, X11(I+1,I), 1, 00474 $ DCONJG(TAUQ1(I)), X11(I+1,I+1), LDX11, WORK ) 00475 CALL ZLARF( 'L', Q-I, M-P-I, X11(I+1,I), 1, 00476 $ DCONJG(TAUQ1(I)), X21(I+1,I+1), LDX21, WORK ) 00477 END IF 00478 CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, 00479 $ DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK ) 00480 CALL ZLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1, 00481 $ DCONJG(TAUQ2(I)), X22(I,I+1), LDX22, WORK ) 00482 * 00483 END DO 00484 * 00485 * Reduce columns Q + 1, ..., P of X12, X22 00486 * 00487 DO I = Q + 1, P 00488 * 00489 CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4, 0.0D0 ), X12(I,I), 1 ) 00490 CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) ) 00491 X12(I,I) = ONE 00492 * 00493 CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, 00494 $ DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK ) 00495 IF( M-P-Q .GE. 1 ) 00496 $ CALL ZLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1, 00497 $ DCONJG(TAUQ2(I)), X22(I,Q+1), LDX22, WORK ) 00498 * 00499 END DO 00500 * 00501 * Reduce columns P + 1, ..., M - Q of X12, X22 00502 * 00503 DO I = 1, M - P - Q 00504 * 00505 CALL ZSCAL( M-P-Q-I+1, DCMPLX( Z2*Z4, 0.0D0 ), 00506 $ X22(P+I,Q+I), 1 ) 00507 CALL ZLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1, 00508 $ TAUQ2(P+I) ) 00509 X22(P+I,Q+I) = ONE 00510 * 00511 CALL ZLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1, 00512 $ DCONJG(TAUQ2(P+I)), X22(P+I,Q+I+1), LDX22, 00513 $ WORK ) 00514 * 00515 END DO 00516 * 00517 END IF 00518 * 00519 RETURN 00520 * 00521 * End of ZUNBDB 00522 * 00523 END 00524
1.7.3 
