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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 RECURSIVE SUBROUTINE DORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, 00002 $ SIGNS, M, P, Q, X11, LDX11, X12, 00003 $ LDX12, X21, LDX21, X22, LDX22, THETA, 00004 $ U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, 00005 $ LDV2T, WORK, LWORK, IWORK, INFO ) 00006 IMPLICIT NONE 00007 * 00008 * -- LAPACK routine (version 3.3.0) -- 00009 * 00010 * -- Contributed by Brian Sutton of the Randolph-Macon College -- 00011 * -- November 2010 00012 * 00013 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00014 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00015 * 00016 * .. Scalar Arguments .. 00017 CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS 00018 INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, 00019 $ LDX21, LDX22, LWORK, M, P, Q 00020 * .. 00021 * .. Array Arguments .. 00022 INTEGER IWORK( * ) 00023 DOUBLE PRECISION THETA( * ) 00024 DOUBLE PRECISION U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ), 00025 $ V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ), 00026 $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22, 00027 $ * ) 00028 * .. 00029 * 00030 * Purpose 00031 * ======= 00032 * 00033 * DORCSD computes the CS decomposition of an M-by-M partitioned 00034 * orthogonal matrix X: 00035 * 00036 * [ I 0 0 | 0 0 0 ] 00037 * [ 0 C 0 | 0 -S 0 ] 00038 * [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**T 00039 * X = [-----------] = [---------] [---------------------] [---------] . 00040 * [ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ] 00041 * [ 0 S 0 | 0 C 0 ] 00042 * [ 0 0 I | 0 0 0 ] 00043 * 00044 * X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P, 00045 * (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are 00046 * R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in 00047 * which R = MIN(P,M-P,Q,M-Q). 00048 * 00049 * Arguments 00050 * ========= 00051 * 00052 * JOBU1 (input) CHARACTER 00053 * = 'Y': U1 is computed; 00054 * otherwise: U1 is not computed. 00055 * 00056 * JOBU2 (input) CHARACTER 00057 * = 'Y': U2 is computed; 00058 * otherwise: U2 is not computed. 00059 * 00060 * JOBV1T (input) CHARACTER 00061 * = 'Y': V1T is computed; 00062 * otherwise: V1T is not computed. 00063 * 00064 * JOBV2T (input) CHARACTER 00065 * = 'Y': V2T is computed; 00066 * otherwise: V2T is not computed. 00067 * 00068 * TRANS (input) CHARACTER 00069 * = 'T': X, U1, U2, V1T, and V2T are stored in row-major 00070 * order; 00071 * otherwise: X, U1, U2, V1T, and V2T are stored in column- 00072 * major order. 00073 * 00074 * SIGNS (input) CHARACTER 00075 * = 'O': The lower-left block is made nonpositive (the 00076 * "other" convention); 00077 * otherwise: The upper-right block is made nonpositive (the 00078 * "default" convention). 00079 * 00080 * M (input) INTEGER 00081 * The number of rows and columns in X. 00082 * 00083 * P (input) INTEGER 00084 * The number of rows in X11 and X12. 0 <= P <= M. 00085 * 00086 * Q (input) INTEGER 00087 * The number of columns in X11 and X21. 0 <= Q <= M. 00088 * 00089 * X (input/workspace) DOUBLE PRECISION array, dimension (LDX,M) 00090 * On entry, the orthogonal matrix whose CSD is desired. 00091 * 00092 * LDX (input) INTEGER 00093 * The leading dimension of X. LDX >= MAX(1,M). 00094 * 00095 * THETA (output) DOUBLE PRECISION array, dimension (R), in which R = 00096 * MIN(P,M-P,Q,M-Q). 00097 * C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and 00098 * S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ). 00099 * 00100 * U1 (output) DOUBLE PRECISION array, dimension (P) 00101 * If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1. 00102 * 00103 * LDU1 (input) INTEGER 00104 * The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= 00105 * MAX(1,P). 00106 * 00107 * U2 (output) DOUBLE PRECISION array, dimension (M-P) 00108 * If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal 00109 * matrix U2. 00110 * 00111 * LDU2 (input) INTEGER 00112 * The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= 00113 * MAX(1,M-P). 00114 * 00115 * V1T (output) DOUBLE PRECISION array, dimension (Q) 00116 * If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal 00117 * matrix V1**T. 00118 * 00119 * LDV1T (input) INTEGER 00120 * The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= 00121 * MAX(1,Q). 00122 * 00123 * V2T (output) DOUBLE PRECISION array, dimension (M-Q) 00124 * If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal 00125 * matrix V2**T. 00126 * 00127 * LDV2T (input) INTEGER 00128 * The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >= 00129 * MAX(1,M-Q). 00130 * 00131 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00132 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00133 * If INFO > 0 on exit, WORK(2:R) contains the values PHI(1), 00134 * ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), 00135 * define the matrix in intermediate bidiagonal-block form 00136 * remaining after nonconvergence. INFO specifies the number 00137 * of nonzero PHI's. 00138 * 00139 * LWORK (input) INTEGER 00140 * The dimension of the array WORK. 00141 * 00142 * If LWORK = -1, then a workspace query is assumed; the routine 00143 * only calculates the optimal size of the WORK array, returns 00144 * this value as the first entry of the work array, and no error 00145 * message related to LWORK is issued by XERBLA. 00146 * 00147 * IWORK (workspace) INTEGER array, dimension (M-Q) 00148 * 00149 * INFO (output) INTEGER 00150 * = 0: successful exit. 00151 * < 0: if INFO = -i, the i-th argument had an illegal value. 00152 * > 0: DBBCSD did not converge. See the description of WORK 00153 * above for details. 00154 * 00155 * Reference 00156 * ========= 00157 * 00158 * [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. 00159 * Algorithms, 50(1):33-65, 2009. 00160 * 00161 * =================================================================== 00162 * 00163 * .. Parameters .. 00164 DOUBLE PRECISION REALONE 00165 PARAMETER ( REALONE = 1.0D0 ) 00166 DOUBLE PRECISION NEGONE, ONE, PIOVER2, ZERO 00167 PARAMETER ( NEGONE = -1.0D0, ONE = 1.0D0, 00168 $ PIOVER2 = 1.57079632679489662D0, 00169 $ ZERO = 0.0D0 ) 00170 * .. 00171 * .. Local Scalars .. 00172 CHARACTER TRANST, SIGNST 00173 INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E, 00174 $ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB, 00175 $ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1, 00176 $ ITAUQ2, J, LBBCSDWORK, LBBCSDWORKMIN, 00177 $ LBBCSDWORKOPT, LORBDBWORK, LORBDBWORKMIN, 00178 $ LORBDBWORKOPT, LORGLQWORK, LORGLQWORKMIN, 00179 $ LORGLQWORKOPT, LORGQRWORK, LORGQRWORKMIN, 00180 $ LORGQRWORKOPT, LWORKMIN, LWORKOPT 00181 LOGICAL COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2, 00182 $ WANTV1T, WANTV2T 00183 * .. 00184 * .. External Subroutines .. 00185 EXTERNAL DBBCSD, DLACPY, DLAPMR, DLAPMT, DLASCL, DLASET, 00186 $ DORBDB, DORGLQ, DORGQR, XERBLA 00187 * .. 00188 * .. External Functions .. 00189 LOGICAL LSAME 00190 EXTERNAL LSAME 00191 * .. 00192 * .. Intrinsic Functions 00193 INTRINSIC COS, INT, MAX, MIN, SIN 00194 * .. 00195 * .. Executable Statements .. 00196 * 00197 * Test input arguments 00198 * 00199 INFO = 0 00200 WANTU1 = LSAME( JOBU1, 'Y' ) 00201 WANTU2 = LSAME( JOBU2, 'Y' ) 00202 WANTV1T = LSAME( JOBV1T, 'Y' ) 00203 WANTV2T = LSAME( JOBV2T, 'Y' ) 00204 COLMAJOR = .NOT. LSAME( TRANS, 'T' ) 00205 DEFAULTSIGNS = .NOT. LSAME( SIGNS, 'O' ) 00206 LQUERY = LWORK .EQ. -1 00207 IF( M .LT. 0 ) THEN 00208 INFO = -7 00209 ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN 00210 INFO = -8 00211 ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN 00212 INFO = -9 00213 ELSE IF( ( COLMAJOR .AND. LDX11 .LT. MAX(1,P) ) .OR. 00214 $ ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN 00215 INFO = -11 00216 ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN 00217 INFO = -14 00218 ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN 00219 INFO = -16 00220 ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN 00221 INFO = -18 00222 ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN 00223 INFO = -20 00224 END IF 00225 * 00226 * Work with transpose if convenient 00227 * 00228 IF( INFO .EQ. 0 .AND. MIN( P, M-P ) .LT. MIN( Q, M-Q ) ) THEN 00229 IF( COLMAJOR ) THEN 00230 TRANST = 'T' 00231 ELSE 00232 TRANST = 'N' 00233 END IF 00234 IF( DEFAULTSIGNS ) THEN 00235 SIGNST = 'O' 00236 ELSE 00237 SIGNST = 'D' 00238 END IF 00239 CALL DORCSD( JOBV1T, JOBV2T, JOBU1, JOBU2, TRANST, SIGNST, M, 00240 $ Q, P, X11, LDX11, X21, LDX21, X12, LDX12, X22, 00241 $ LDX22, THETA, V1T, LDV1T, V2T, LDV2T, U1, LDU1, 00242 $ U2, LDU2, WORK, LWORK, IWORK, INFO ) 00243 RETURN 00244 END IF 00245 * 00246 * Work with permutation [ 0 I; I 0 ] * X * [ 0 I; I 0 ] if 00247 * convenient 00248 * 00249 IF( INFO .EQ. 0 .AND. M-Q .LT. Q ) THEN 00250 IF( DEFAULTSIGNS ) THEN 00251 SIGNST = 'O' 00252 ELSE 00253 SIGNST = 'D' 00254 END IF 00255 CALL DORCSD( JOBU2, JOBU1, JOBV2T, JOBV1T, TRANS, SIGNST, M, 00256 $ M-P, M-Q, X22, LDX22, X21, LDX21, X12, LDX12, X11, 00257 $ LDX11, THETA, U2, LDU2, U1, LDU1, V2T, LDV2T, V1T, 00258 $ LDV1T, WORK, LWORK, IWORK, INFO ) 00259 RETURN 00260 END IF 00261 * 00262 * Compute workspace 00263 * 00264 IF( INFO .EQ. 0 ) THEN 00265 * 00266 IPHI = 2 00267 ITAUP1 = IPHI + MAX( 1, Q - 1 ) 00268 ITAUP2 = ITAUP1 + MAX( 1, P ) 00269 ITAUQ1 = ITAUP2 + MAX( 1, M - P ) 00270 ITAUQ2 = ITAUQ1 + MAX( 1, Q ) 00271 IORGQR = ITAUQ2 + MAX( 1, M - Q ) 00272 CALL DORGQR( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1, 00273 $ CHILDINFO ) 00274 LORGQRWORKOPT = INT( WORK(1) ) 00275 LORGQRWORKMIN = MAX( 1, M - Q ) 00276 IORGLQ = ITAUQ2 + MAX( 1, M - Q ) 00277 CALL DORGLQ( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1, 00278 $ CHILDINFO ) 00279 LORGLQWORKOPT = INT( WORK(1) ) 00280 LORGLQWORKMIN = MAX( 1, M - Q ) 00281 IORBDB = ITAUQ2 + MAX( 1, M - Q ) 00282 CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, 00283 $ X21, LDX21, X22, LDX22, 0, 0, 0, 0, 0, 0, WORK, 00284 $ -1, CHILDINFO ) 00285 LORBDBWORKOPT = INT( WORK(1) ) 00286 LORBDBWORKMIN = LORBDBWORKOPT 00287 IB11D = ITAUQ2 + MAX( 1, M - Q ) 00288 IB11E = IB11D + MAX( 1, Q ) 00289 IB12D = IB11E + MAX( 1, Q - 1 ) 00290 IB12E = IB12D + MAX( 1, Q ) 00291 IB21D = IB12E + MAX( 1, Q - 1 ) 00292 IB21E = IB21D + MAX( 1, Q ) 00293 IB22D = IB21E + MAX( 1, Q - 1 ) 00294 IB22E = IB22D + MAX( 1, Q ) 00295 IBBCSD = IB22E + MAX( 1, Q - 1 ) 00296 CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 0, 00297 $ 0, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, 0, 00298 $ 0, 0, 0, 0, 0, 0, 0, WORK, -1, CHILDINFO ) 00299 LBBCSDWORKOPT = INT( WORK(1) ) 00300 LBBCSDWORKMIN = LBBCSDWORKOPT 00301 LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT, 00302 $ IORBDB + LORBDBWORKOPT, IBBCSD + LBBCSDWORKOPT ) - 1 00303 LWORKMIN = MAX( IORGQR + LORGQRWORKMIN, IORGLQ + LORGLQWORKMIN, 00304 $ IORBDB + LORBDBWORKOPT, IBBCSD + LBBCSDWORKMIN ) - 1 00305 WORK(1) = LWORKOPT 00306 * 00307 IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN 00308 INFO = -22 00309 ELSE 00310 LORGQRWORK = LWORK - IORGQR + 1 00311 LORGLQWORK = LWORK - IORGLQ + 1 00312 LORBDBWORK = LWORK - IORBDB + 1 00313 LBBCSDWORK = LWORK - IBBCSD + 1 00314 END IF 00315 END IF 00316 * 00317 * Abort if any illegal arguments 00318 * 00319 IF( INFO .NE. 0 ) THEN 00320 CALL XERBLA( 'DORCSD', -INFO ) 00321 RETURN 00322 ELSE IF( LQUERY ) THEN 00323 RETURN 00324 END IF 00325 * 00326 * Transform to bidiagonal block form 00327 * 00328 CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, 00329 $ LDX21, X22, LDX22, THETA, WORK(IPHI), WORK(ITAUP1), 00330 $ WORK(ITAUP2), WORK(ITAUQ1), WORK(ITAUQ2), 00331 $ WORK(IORBDB), LORBDBWORK, CHILDINFO ) 00332 * 00333 * Accumulate Householder reflectors 00334 * 00335 IF( COLMAJOR ) THEN 00336 IF( WANTU1 .AND. P .GT. 0 ) THEN 00337 CALL DLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 ) 00338 CALL DORGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR), 00339 $ LORGQRWORK, INFO) 00340 END IF 00341 IF( WANTU2 .AND. M-P .GT. 0 ) THEN 00342 CALL DLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 ) 00343 CALL DORGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2), 00344 $ WORK(IORGQR), LORGQRWORK, INFO ) 00345 END IF 00346 IF( WANTV1T .AND. Q .GT. 0 ) THEN 00347 CALL DLACPY( 'U', Q-1, Q-1, X11(1,2), LDX11, V1T(2,2), 00348 $ LDV1T ) 00349 V1T(1, 1) = ONE 00350 DO J = 2, Q 00351 V1T(1,J) = ZERO 00352 V1T(J,1) = ZERO 00353 END DO 00354 CALL DORGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1), 00355 $ WORK(IORGLQ), LORGLQWORK, INFO ) 00356 END IF 00357 IF( WANTV2T .AND. M-Q .GT. 0 ) THEN 00358 CALL DLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T ) 00359 CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22, 00360 $ V2T(P+1,P+1), LDV2T ) 00361 CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2), 00362 $ WORK(IORGLQ), LORGLQWORK, INFO ) 00363 END IF 00364 ELSE 00365 IF( WANTU1 .AND. P .GT. 0 ) THEN 00366 CALL DLACPY( 'U', Q, P, X11, LDX11, U1, LDU1 ) 00367 CALL DORGLQ( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGLQ), 00368 $ LORGLQWORK, INFO) 00369 END IF 00370 IF( WANTU2 .AND. M-P .GT. 0 ) THEN 00371 CALL DLACPY( 'U', Q, M-P, X21, LDX21, U2, LDU2 ) 00372 CALL DORGLQ( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2), 00373 $ WORK(IORGLQ), LORGLQWORK, INFO ) 00374 END IF 00375 IF( WANTV1T .AND. Q .GT. 0 ) THEN 00376 CALL DLACPY( 'L', Q-1, Q-1, X11(2,1), LDX11, V1T(2,2), 00377 $ LDV1T ) 00378 V1T(1, 1) = ONE 00379 DO J = 2, Q 00380 V1T(1,J) = ZERO 00381 V1T(J,1) = ZERO 00382 END DO 00383 CALL DORGQR( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1), 00384 $ WORK(IORGQR), LORGQRWORK, INFO ) 00385 END IF 00386 IF( WANTV2T .AND. M-Q .GT. 0 ) THEN 00387 CALL DLACPY( 'L', M-Q, P, X12, LDX12, V2T, LDV2T ) 00388 CALL DLACPY( 'L', M-P-Q, M-P-Q, X22(P+1,Q+1), LDX22, 00389 $ V2T(P+1,P+1), LDV2T ) 00390 CALL DORGQR( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2), 00391 $ WORK(IORGQR), LORGQRWORK, INFO ) 00392 END IF 00393 END IF 00394 * 00395 * Compute the CSD of the matrix in bidiagonal-block form 00396 * 00397 CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, 00398 $ WORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, 00399 $ LDV2T, WORK(IB11D), WORK(IB11E), WORK(IB12D), 00400 $ WORK(IB12E), WORK(IB21D), WORK(IB21E), WORK(IB22D), 00401 $ WORK(IB22E), WORK(IBBCSD), LBBCSDWORK, INFO ) 00402 * 00403 * Permute rows and columns to place identity submatrices in top- 00404 * left corner of (1,1)-block and/or bottom-right corner of (1,2)- 00405 * block and/or bottom-right corner of (2,1)-block and/or top-left 00406 * corner of (2,2)-block 00407 * 00408 IF( Q .GT. 0 .AND. WANTU2 ) THEN 00409 DO I = 1, Q 00410 IWORK(I) = M - P - Q + I 00411 END DO 00412 DO I = Q + 1, M - P 00413 IWORK(I) = I - Q 00414 END DO 00415 IF( COLMAJOR ) THEN 00416 CALL DLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK ) 00417 ELSE 00418 CALL DLAPMR( .FALSE., M-P, M-P, U2, LDU2, IWORK ) 00419 END IF 00420 END IF 00421 IF( M .GT. 0 .AND. WANTV2T ) THEN 00422 DO I = 1, P 00423 IWORK(I) = M - P - Q + I 00424 END DO 00425 DO I = P + 1, M - Q 00426 IWORK(I) = I - P 00427 END DO 00428 IF( .NOT. COLMAJOR ) THEN 00429 CALL DLAPMT( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK ) 00430 ELSE 00431 CALL DLAPMR( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK ) 00432 END IF 00433 END IF 00434 * 00435 RETURN 00436 * 00437 * End DORCSD 00438 * 00439 END 00440
1.7.3 
