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Mise à jour de lapack vers la version 3.5.0.
1: *> \brief \b DORBDB1 2: * 3: * =========== DOCUMENTATION =========== 4: * 5: * Online html documentation available at 6: * http://www.netlib.org/lapack/explore-html/ 7: * 8: *> \htmlonly 9: *> Download DORBDB1 + dependencies 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorbdb1.f"> 11: *> [TGZ]</a> 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorbdb1.f"> 13: *> [ZIP]</a> 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorbdb1.f"> 15: *> [TXT]</a> 16: *> \endhtmlonly 17: * 18: * Definition: 19: * =========== 20: * 21: * SUBROUTINE DORBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, 22: * TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO ) 23: * 24: * .. Scalar Arguments .. 25: * INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21 26: * .. 27: * .. Array Arguments .. 28: * DOUBLE PRECISION PHI(*), THETA(*) 29: * DOUBLE PRECISION TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), 30: * $ X11(LDX11,*), X21(LDX21,*) 31: * .. 32: * 33: * 34: *> \par Purpose: 35: *> ============= 36: *> 37: *>\verbatim 38: *> 39: *> DORBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny 40: *> matrix X with orthonomal columns: 41: *> 42: *> [ B11 ] 43: *> [ X11 ] [ P1 | ] [ 0 ] 44: *> [-----] = [---------] [-----] Q1**T . 45: *> [ X21 ] [ | P2 ] [ B21 ] 46: *> [ 0 ] 47: *> 48: *> X11 is P-by-Q, and X21 is (M-P)-by-Q. Q must be no larger than P, 49: *> M-P, or M-Q. Routines DORBDB2, DORBDB3, and DORBDB4 handle cases in 50: *> which Q is not the minimum dimension. 51: *> 52: *> The orthogonal matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P), 53: *> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by 54: *> Householder vectors. 55: *> 56: *> B11 and B12 are Q-by-Q bidiagonal matrices represented implicitly by 57: *> angles THETA, PHI. 58: *> 59: *>\endverbatim 60: * 61: * Arguments: 62: * ========== 63: * 64: *> \param[in] M 65: *> \verbatim 66: *> M is INTEGER 67: *> The number of rows X11 plus the number of rows in X21. 68: *> \endverbatim 69: *> 70: *> \param[in] P 71: *> \verbatim 72: *> P is INTEGER 73: *> The number of rows in X11. 0 <= P <= M. 74: *> \endverbatim 75: *> 76: *> \param[in] Q 77: *> \verbatim 78: *> Q is INTEGER 79: *> The number of columns in X11 and X21. 0 <= Q <= 80: *> MIN(P,M-P,M-Q). 81: *> \endverbatim 82: *> 83: *> \param[in,out] X11 84: *> \verbatim 85: *> X11 is DOUBLE PRECISION array, dimension (LDX11,Q) 86: *> On entry, the top block of the matrix X to be reduced. On 87: *> exit, the columns of tril(X11) specify reflectors for P1 and 88: *> the rows of triu(X11,1) specify reflectors for Q1. 89: *> \endverbatim 90: *> 91: *> \param[in] LDX11 92: *> \verbatim 93: *> LDX11 is INTEGER 94: *> The leading dimension of X11. LDX11 >= P. 95: *> \endverbatim 96: *> 97: *> \param[in,out] X21 98: *> \verbatim 99: *> X21 is DOUBLE PRECISION array, dimension (LDX21,Q) 100: *> On entry, the bottom block of the matrix X to be reduced. On 101: *> exit, the columns of tril(X21) specify reflectors for P2. 102: *> \endverbatim 103: *> 104: *> \param[in] LDX21 105: *> \verbatim 106: *> LDX21 is INTEGER 107: *> The leading dimension of X21. LDX21 >= M-P. 108: *> \endverbatim 109: *> 110: *> \param[out] THETA 111: *> \verbatim 112: *> THETA is DOUBLE PRECISION array, dimension (Q) 113: *> The entries of the bidiagonal blocks B11, B21 are defined by 114: *> THETA and PHI. See Further Details. 115: *> \endverbatim 116: *> 117: *> \param[out] PHI 118: *> \verbatim 119: *> PHI is DOUBLE PRECISION array, dimension (Q-1) 120: *> The entries of the bidiagonal blocks B11, B21 are defined by 121: *> THETA and PHI. See Further Details. 122: *> \endverbatim 123: *> 124: *> \param[out] TAUP1 125: *> \verbatim 126: *> TAUP1 is DOUBLE PRECISION array, dimension (P) 127: *> The scalar factors of the elementary reflectors that define 128: *> P1. 129: *> \endverbatim 130: *> 131: *> \param[out] TAUP2 132: *> \verbatim 133: *> TAUP2 is DOUBLE PRECISION array, dimension (M-P) 134: *> The scalar factors of the elementary reflectors that define 135: *> P2. 136: *> \endverbatim 137: *> 138: *> \param[out] TAUQ1 139: *> \verbatim 140: *> TAUQ1 is DOUBLE PRECISION array, dimension (Q) 141: *> The scalar factors of the elementary reflectors that define 142: *> Q1. 143: *> \endverbatim 144: *> 145: *> \param[out] WORK 146: *> \verbatim 147: *> WORK is DOUBLE PRECISION array, dimension (LWORK) 148: *> \endverbatim 149: *> 150: *> \param[in] LWORK 151: *> \verbatim 152: *> LWORK is INTEGER 153: *> The dimension of the array WORK. LWORK >= M-Q. 154: *> 155: *> If LWORK = -1, then a workspace query is assumed; the routine 156: *> only calculates the optimal size of the WORK array, returns 157: *> this value as the first entry of the WORK array, and no error 158: *> message related to LWORK is issued by XERBLA. 159: *> \endverbatim 160: *> 161: *> \param[out] INFO 162: *> \verbatim 163: *> INFO is INTEGER 164: *> = 0: successful exit. 165: *> < 0: if INFO = -i, the i-th argument had an illegal value. 166: *> \endverbatim 167: *> 168: * 169: * Authors: 170: * ======== 171: * 172: *> \author Univ. of Tennessee 173: *> \author Univ. of California Berkeley 174: *> \author Univ. of Colorado Denver 175: *> \author NAG Ltd. 176: * 177: *> \date July 2012 178: * 179: *> \ingroup doubleOTHERcomputational 180: * 181: *> \par Further Details: 182: * ===================== 183: *> 184: *> \verbatim 185: *> 186: *> The upper-bidiagonal blocks B11, B21 are represented implicitly by 187: *> angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry 188: *> in each bidiagonal band is a product of a sine or cosine of a THETA 189: *> with a sine or cosine of a PHI. See [1] or DORCSD for details. 190: *> 191: *> P1, P2, and Q1 are represented as products of elementary reflectors. 192: *> See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR 193: *> and DORGLQ. 194: *> \endverbatim 195: * 196: *> \par References: 197: * ================ 198: *> 199: *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. 200: *> Algorithms, 50(1):33-65, 2009. 201: *> 202: * ===================================================================== 203: SUBROUTINE DORBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, 204: $ TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO ) 205: * 206: * -- LAPACK computational routine (version 3.5.0) -- 207: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 208: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 209: * July 2012 210: * 211: * .. Scalar Arguments .. 212: INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21 213: * .. 214: * .. Array Arguments .. 215: DOUBLE PRECISION PHI(*), THETA(*) 216: DOUBLE PRECISION TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), 217: $ X11(LDX11,*), X21(LDX21,*) 218: * .. 219: * 220: * ==================================================================== 221: * 222: * .. Parameters .. 223: DOUBLE PRECISION ONE 224: PARAMETER ( ONE = 1.0D0 ) 225: * .. 226: * .. Local Scalars .. 227: DOUBLE PRECISION C, S 228: INTEGER CHILDINFO, I, ILARF, IORBDB5, LLARF, LORBDB5, 229: $ LWORKMIN, LWORKOPT 230: LOGICAL LQUERY 231: * .. 232: * .. External Subroutines .. 233: EXTERNAL DLARF, DLARFGP, DORBDB5, DROT, XERBLA 234: * .. 235: * .. External Functions .. 236: DOUBLE PRECISION DNRM2 237: EXTERNAL DNRM2 238: * .. 239: * .. Intrinsic Function .. 240: INTRINSIC ATAN2, COS, MAX, SIN, SQRT 241: * .. 242: * .. Executable Statements .. 243: * 244: * Test input arguments 245: * 246: INFO = 0 247: LQUERY = LWORK .EQ. -1 248: * 249: IF( M .LT. 0 ) THEN 250: INFO = -1 251: ELSE IF( P .LT. Q .OR. M-P .LT. Q ) THEN 252: INFO = -2 253: ELSE IF( Q .LT. 0 .OR. M-Q .LT. Q ) THEN 254: INFO = -3 255: ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN 256: INFO = -5 257: ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN 258: INFO = -7 259: END IF 260: * 261: * Compute workspace 262: * 263: IF( INFO .EQ. 0 ) THEN 264: ILARF = 2 265: LLARF = MAX( P-1, M-P-1, Q-1 ) 266: IORBDB5 = 2 267: LORBDB5 = Q-2 268: LWORKOPT = MAX( ILARF+LLARF-1, IORBDB5+LORBDB5-1 ) 269: LWORKMIN = LWORKOPT 270: WORK(1) = LWORKOPT 271: IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN 272: INFO = -14 273: END IF 274: END IF 275: IF( INFO .NE. 0 ) THEN 276: CALL XERBLA( 'DORBDB1', -INFO ) 277: RETURN 278: ELSE IF( LQUERY ) THEN 279: RETURN 280: END IF 281: * 282: * Reduce columns 1, ..., Q of X11 and X21 283: * 284: DO I = 1, Q 285: * 286: CALL DLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) ) 287: CALL DLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) ) 288: THETA(I) = ATAN2( X21(I,I), X11(I,I) ) 289: C = COS( THETA(I) ) 290: S = SIN( THETA(I) ) 291: X11(I,I) = ONE 292: X21(I,I) = ONE 293: CALL DLARF( 'L', P-I+1, Q-I, X11(I,I), 1, TAUP1(I), X11(I,I+1), 294: $ LDX11, WORK(ILARF) ) 295: CALL DLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, TAUP2(I), 296: $ X21(I,I+1), LDX21, WORK(ILARF) ) 297: * 298: IF( I .LT. Q ) THEN 299: CALL DROT( Q-I, X11(I,I+1), LDX11, X21(I,I+1), LDX21, C, S ) 300: CALL DLARFGP( Q-I, X21(I,I+1), X21(I,I+2), LDX21, TAUQ1(I) ) 301: S = X21(I,I+1) 302: X21(I,I+1) = ONE 303: CALL DLARF( 'R', P-I, Q-I, X21(I,I+1), LDX21, TAUQ1(I), 304: $ X11(I+1,I+1), LDX11, WORK(ILARF) ) 305: CALL DLARF( 'R', M-P-I, Q-I, X21(I,I+1), LDX21, TAUQ1(I), 306: $ X21(I+1,I+1), LDX21, WORK(ILARF) ) 307: C = SQRT( DNRM2( P-I, X11(I+1,I+1), 1, X11(I+1,I+1), 308: $ 1 )**2 + DNRM2( M-P-I, X21(I+1,I+1), 1, X21(I+1,I+1), 309: $ 1 )**2 ) 310: PHI(I) = ATAN2( S, C ) 311: CALL DORBDB5( P-I, M-P-I, Q-I-1, X11(I+1,I+1), 1, 312: $ X21(I+1,I+1), 1, X11(I+1,I+2), LDX11, 313: $ X21(I+1,I+2), LDX21, WORK(IORBDB5), LORBDB5, 314: $ CHILDINFO ) 315: END IF 316: * 317: END DO 318: * 319: RETURN 320: * 321: * End of DORBDB1 322: * 323: END 324: