Annotation of rpl/lapack/lapack/zunbdb1.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZUNBDB1
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZUNBDB1 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunbdb1.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunbdb1.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunbdb1.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZUNBDB1( 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: * COMPLEX*16 TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
! 30: * $ X11(LDX11,*), X21(LDX21,*)
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: *> =============
! 36: *>
! 37: *>\verbatim
! 38: *>
! 39: *> ZUNBDB1 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 ZUNBDB2, ZUNBDB3, and ZUNBDB4 handle cases in
! 50: *> which Q is not the minimum dimension.
! 51: *>
! 52: *> The unitary 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 complex16OTHERcomputational
! 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 ZUNCSD for details.
! 190: *>
! 191: *> P1, P2, and Q1 are represented as products of elementary reflectors.
! 192: *> See ZUNCSD2BY1 for details on generating P1, P2, and Q1 using ZUNGQR
! 193: *> and ZUNGLQ.
! 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 ZUNBDB1( 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: COMPLEX*16 TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*),
! 217: $ X11(LDX11,*), X21(LDX21,*)
! 218: * ..
! 219: *
! 220: * ====================================================================
! 221: *
! 222: * .. Parameters ..
! 223: COMPLEX*16 ONE
! 224: PARAMETER ( ONE = (1.0D0,0.0D0) )
! 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 ZLARF, ZLARFGP, ZUNBDB5, ZDROT, XERBLA
! 234: EXTERNAL ZLACGV
! 235: * ..
! 236: * .. External Functions ..
! 237: DOUBLE PRECISION DZNRM2
! 238: EXTERNAL DZNRM2
! 239: * ..
! 240: * .. Intrinsic Function ..
! 241: INTRINSIC ATAN2, COS, MAX, SIN, SQRT
! 242: * ..
! 243: * .. Executable Statements ..
! 244: *
! 245: * Test input arguments
! 246: *
! 247: INFO = 0
! 248: LQUERY = LWORK .EQ. -1
! 249: *
! 250: IF( M .LT. 0 ) THEN
! 251: INFO = -1
! 252: ELSE IF( P .LT. Q .OR. M-P .LT. Q ) THEN
! 253: INFO = -2
! 254: ELSE IF( Q .LT. 0 .OR. M-Q .LT. Q ) THEN
! 255: INFO = -3
! 256: ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
! 257: INFO = -5
! 258: ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
! 259: INFO = -7
! 260: END IF
! 261: *
! 262: * Compute workspace
! 263: *
! 264: IF( INFO .EQ. 0 ) THEN
! 265: ILARF = 2
! 266: LLARF = MAX( P-1, M-P-1, Q-1 )
! 267: IORBDB5 = 2
! 268: LORBDB5 = Q-2
! 269: LWORKOPT = MAX( ILARF+LLARF-1, IORBDB5+LORBDB5-1 )
! 270: LWORKMIN = LWORKOPT
! 271: WORK(1) = LWORKOPT
! 272: IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
! 273: INFO = -14
! 274: END IF
! 275: END IF
! 276: IF( INFO .NE. 0 ) THEN
! 277: CALL XERBLA( 'ZUNBDB1', -INFO )
! 278: RETURN
! 279: ELSE IF( LQUERY ) THEN
! 280: RETURN
! 281: END IF
! 282: *
! 283: * Reduce columns 1, ..., Q of X11 and X21
! 284: *
! 285: DO I = 1, Q
! 286: *
! 287: CALL ZLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
! 288: CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
! 289: THETA(I) = ATAN2( DBLE( X21(I,I) ), DBLE( X11(I,I) ) )
! 290: C = COS( THETA(I) )
! 291: S = SIN( THETA(I) )
! 292: X11(I,I) = ONE
! 293: X21(I,I) = ONE
! 294: CALL ZLARF( 'L', P-I+1, Q-I, X11(I,I), 1, DCONJG(TAUP1(I)),
! 295: $ X11(I,I+1), LDX11, WORK(ILARF) )
! 296: CALL ZLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, DCONJG(TAUP2(I)),
! 297: $ X21(I,I+1), LDX21, WORK(ILARF) )
! 298: *
! 299: IF( I .LT. Q ) THEN
! 300: CALL ZDROT( Q-I, X11(I,I+1), LDX11, X21(I,I+1), LDX21, C,
! 301: $ S )
! 302: CALL ZLACGV( Q-I, X21(I,I+1), LDX21 )
! 303: CALL ZLARFGP( Q-I, X21(I,I+1), X21(I,I+2), LDX21, TAUQ1(I) )
! 304: S = DBLE( X21(I,I+1) )
! 305: X21(I,I+1) = ONE
! 306: CALL ZLARF( 'R', P-I, Q-I, X21(I,I+1), LDX21, TAUQ1(I),
! 307: $ X11(I+1,I+1), LDX11, WORK(ILARF) )
! 308: CALL ZLARF( 'R', M-P-I, Q-I, X21(I,I+1), LDX21, TAUQ1(I),
! 309: $ X21(I+1,I+1), LDX21, WORK(ILARF) )
! 310: CALL ZLACGV( Q-I, X21(I,I+1), LDX21 )
! 311: C = SQRT( DZNRM2( P-I, X11(I+1,I+1), 1, X11(I+1,I+1),
! 312: $ 1 )**2 + DZNRM2( M-P-I, X21(I+1,I+1), 1, X21(I+1,I+1),
! 313: $ 1 )**2 )
! 314: PHI(I) = ATAN2( S, C )
! 315: CALL ZUNBDB5( P-I, M-P-I, Q-I-1, X11(I+1,I+1), 1,
! 316: $ X21(I+1,I+1), 1, X11(I+1,I+2), LDX11,
! 317: $ X21(I+1,I+2), LDX21, WORK(IORBDB5), LORBDB5,
! 318: $ CHILDINFO )
! 319: END IF
! 320: *
! 321: END DO
! 322: *
! 323: RETURN
! 324: *
! 325: * End of ZUNBDB1
! 326: *
! 327: END
! 328:
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zunbdb1.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack