Annotation of rpl/lapack/lapack/zunbdb.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
! 2: $ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
! 3: $ TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
! 4: IMPLICIT NONE
! 5: *
! 6: * -- LAPACK routine ((version 3.3.0)) --
! 7: *
! 8: * -- Contributed by Brian Sutton of the Randolph-Macon College --
! 9: * -- November 2010
! 10: *
! 11: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 12: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 13: *
! 14: * .. Scalar Arguments ..
! 15: CHARACTER SIGNS, TRANS
! 16: INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
! 17: $ Q
! 18: * ..
! 19: * .. Array Arguments ..
! 20: DOUBLE PRECISION PHI( * ), THETA( * )
! 21: COMPLEX*16 TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
! 22: $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
! 23: $ X21( LDX21, * ), X22( LDX22, * )
! 24: * ..
! 25: *
! 26: * Purpose
! 27: * =======
! 28: *
! 29: * ZUNBDB simultaneously bidiagonalizes the blocks of an M-by-M
! 30: * partitioned unitary matrix X:
! 31: *
! 32: * [ B11 | B12 0 0 ]
! 33: * [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**H
! 34: * X = [-----------] = [---------] [----------------] [---------] .
! 35: * [ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ]
! 36: * [ 0 | 0 0 I ]
! 37: *
! 38: * X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is
! 39: * not the case, then X must be transposed and/or permuted. This can be
! 40: * done in constant time using the TRANS and SIGNS options. See ZUNCSD
! 41: * for details.)
! 42: *
! 43: * The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by-
! 44: * (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are
! 45: * represented implicitly by Householder vectors.
! 46: *
! 47: * B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
! 48: * implicitly by angles THETA, PHI.
! 49: *
! 50: * Arguments
! 51: * =========
! 52: *
! 53: * TRANS (input) CHARACTER
! 54: * = 'T': X, U1, U2, V1T, and V2T are stored in row-major
! 55: * order;
! 56: * otherwise: X, U1, U2, V1T, and V2T are stored in column-
! 57: * major order.
! 58: *
! 59: * SIGNS (input) CHARACTER
! 60: * = 'O': The lower-left block is made nonpositive (the
! 61: * "other" convention);
! 62: * otherwise: The upper-right block is made nonpositive (the
! 63: * "default" convention).
! 64: *
! 65: * M (input) INTEGER
! 66: * The number of rows and columns in X.
! 67: *
! 68: * P (input) INTEGER
! 69: * The number of rows in X11 and X12. 0 <= P <= M.
! 70: *
! 71: * Q (input) INTEGER
! 72: * The number of columns in X11 and X21. 0 <= Q <=
! 73: * MIN(P,M-P,M-Q).
! 74: *
! 75: * X11 (input/output) COMPLEX*16 array, dimension (LDX11,Q)
! 76: * On entry, the top-left block of the unitary matrix to be
! 77: * reduced. On exit, the form depends on TRANS:
! 78: * If TRANS = 'N', then
! 79: * the columns of tril(X11) specify reflectors for P1,
! 80: * the rows of triu(X11,1) specify reflectors for Q1;
! 81: * else TRANS = 'T', and
! 82: * the rows of triu(X11) specify reflectors for P1,
! 83: * the columns of tril(X11,-1) specify reflectors for Q1.
! 84: *
! 85: * LDX11 (input) INTEGER
! 86: * The leading dimension of X11. If TRANS = 'N', then LDX11 >=
! 87: * P; else LDX11 >= Q.
! 88: *
! 89: * X12 (input/output) COMPLEX*16 array, dimension (LDX12,M-Q)
! 90: * On entry, the top-right block of the unitary matrix to
! 91: * be reduced. On exit, the form depends on TRANS:
! 92: * If TRANS = 'N', then
! 93: * the rows of triu(X12) specify the first P reflectors for
! 94: * Q2;
! 95: * else TRANS = 'T', and
! 96: * the columns of tril(X12) specify the first P reflectors
! 97: * for Q2.
! 98: *
! 99: * LDX12 (input) INTEGER
! 100: * The leading dimension of X12. If TRANS = 'N', then LDX12 >=
! 101: * P; else LDX11 >= M-Q.
! 102: *
! 103: * X21 (input/output) COMPLEX*16 array, dimension (LDX21,Q)
! 104: * On entry, the bottom-left block of the unitary matrix to
! 105: * be reduced. On exit, the form depends on TRANS:
! 106: * If TRANS = 'N', then
! 107: * the columns of tril(X21) specify reflectors for P2;
! 108: * else TRANS = 'T', and
! 109: * the rows of triu(X21) specify reflectors for P2.
! 110: *
! 111: * LDX21 (input) INTEGER
! 112: * The leading dimension of X21. If TRANS = 'N', then LDX21 >=
! 113: * M-P; else LDX21 >= Q.
! 114: *
! 115: * X22 (input/output) COMPLEX*16 array, dimension (LDX22,M-Q)
! 116: * On entry, the bottom-right block of the unitary matrix to
! 117: * be reduced. On exit, the form depends on TRANS:
! 118: * If TRANS = 'N', then
! 119: * the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last
! 120: * M-P-Q reflectors for Q2,
! 121: * else TRANS = 'T', and
! 122: * the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last
! 123: * M-P-Q reflectors for P2.
! 124: *
! 125: * LDX22 (input) INTEGER
! 126: * The leading dimension of X22. If TRANS = 'N', then LDX22 >=
! 127: * M-P; else LDX22 >= M-Q.
! 128: *
! 129: * THETA (output) DOUBLE PRECISION array, dimension (Q)
! 130: * The entries of the bidiagonal blocks B11, B12, B21, B22 can
! 131: * be computed from the angles THETA and PHI. See Further
! 132: * Details.
! 133: *
! 134: * PHI (output) DOUBLE PRECISION array, dimension (Q-1)
! 135: * The entries of the bidiagonal blocks B11, B12, B21, B22 can
! 136: * be computed from the angles THETA and PHI. See Further
! 137: * Details.
! 138: *
! 139: * TAUP1 (output) COMPLEX*16 array, dimension (P)
! 140: * The scalar factors of the elementary reflectors that define
! 141: * P1.
! 142: *
! 143: * TAUP2 (output) COMPLEX*16 array, dimension (M-P)
! 144: * The scalar factors of the elementary reflectors that define
! 145: * P2.
! 146: *
! 147: * TAUQ1 (output) COMPLEX*16 array, dimension (Q)
! 148: * The scalar factors of the elementary reflectors that define
! 149: * Q1.
! 150: *
! 151: * TAUQ2 (output) COMPLEX*16 array, dimension (M-Q)
! 152: * The scalar factors of the elementary reflectors that define
! 153: * Q2.
! 154: *
! 155: * WORK (workspace) COMPLEX*16 array, dimension (LWORK)
! 156: *
! 157: * LWORK (input) INTEGER
! 158: * The dimension of the array WORK. LWORK >= M-Q.
! 159: *
! 160: * If LWORK = -1, then a workspace query is assumed; the routine
! 161: * only calculates the optimal size of the WORK array, returns
! 162: * this value as the first entry of the WORK array, and no error
! 163: * message related to LWORK is issued by XERBLA.
! 164: *
! 165: * INFO (output) INTEGER
! 166: * = 0: successful exit.
! 167: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 168: *
! 169: * Further Details
! 170: * ===============
! 171: *
! 172: * The bidiagonal blocks B11, B12, B21, and B22 are represented
! 173: * implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,
! 174: * PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are
! 175: * lower bidiagonal. Every entry in each bidiagonal band is a product
! 176: * of a sine or cosine of a THETA with a sine or cosine of a PHI. See
! 177: * [1] or ZUNCSD for details.
! 178: *
! 179: * P1, P2, Q1, and Q2 are represented as products of elementary
! 180: * reflectors. See ZUNCSD for details on generating P1, P2, Q1, and Q2
! 181: * using ZUNGQR and ZUNGLQ.
! 182: *
! 183: * Reference
! 184: * =========
! 185: *
! 186: * [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
! 187: * Algorithms, 50(1):33-65, 2009.
! 188: *
! 189: * ====================================================================
! 190: *
! 191: * .. Parameters ..
! 192: DOUBLE PRECISION REALONE
! 193: PARAMETER ( REALONE = 1.0D0 )
! 194: COMPLEX*16 NEGONE, ONE
! 195: PARAMETER ( NEGONE = (-1.0D0,0.0D0),
! 196: $ ONE = (1.0D0,0.0D0) )
! 197: * ..
! 198: * .. Local Scalars ..
! 199: LOGICAL COLMAJOR, LQUERY
! 200: INTEGER I, LWORKMIN, LWORKOPT
! 201: DOUBLE PRECISION Z1, Z2, Z3, Z4
! 202: * ..
! 203: * .. External Subroutines ..
! 204: EXTERNAL ZAXPY, ZLARF, ZLARFGP, ZSCAL, XERBLA
! 205: EXTERNAL ZLACGV
! 206: *
! 207: * ..
! 208: * .. External Functions ..
! 209: DOUBLE PRECISION DZNRM2
! 210: LOGICAL LSAME
! 211: EXTERNAL DZNRM2, LSAME
! 212: * ..
! 213: * .. Intrinsic Functions
! 214: INTRINSIC ATAN2, COS, MAX, MIN, SIN
! 215: INTRINSIC DCMPLX, DCONJG
! 216: * ..
! 217: * .. Executable Statements ..
! 218: *
! 219: * Test input arguments
! 220: *
! 221: INFO = 0
! 222: COLMAJOR = .NOT. LSAME( TRANS, 'T' )
! 223: IF( .NOT. LSAME( SIGNS, 'O' ) ) THEN
! 224: Z1 = REALONE
! 225: Z2 = REALONE
! 226: Z3 = REALONE
! 227: Z4 = REALONE
! 228: ELSE
! 229: Z1 = REALONE
! 230: Z2 = -REALONE
! 231: Z3 = REALONE
! 232: Z4 = -REALONE
! 233: END IF
! 234: LQUERY = LWORK .EQ. -1
! 235: *
! 236: IF( M .LT. 0 ) THEN
! 237: INFO = -3
! 238: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
! 239: INFO = -4
! 240: ELSE IF( Q .LT. 0 .OR. Q .GT. P .OR. Q .GT. M-P .OR.
! 241: $ Q .GT. M-Q ) THEN
! 242: INFO = -5
! 243: ELSE IF( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN
! 244: INFO = -7
! 245: ELSE IF( .NOT.COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
! 246: INFO = -7
! 247: ELSE IF( COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
! 248: INFO = -9
! 249: ELSE IF( .NOT.COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
! 250: INFO = -9
! 251: ELSE IF( COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
! 252: INFO = -11
! 253: ELSE IF( .NOT.COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
! 254: INFO = -11
! 255: ELSE IF( COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
! 256: INFO = -13
! 257: ELSE IF( .NOT.COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
! 258: INFO = -13
! 259: END IF
! 260: *
! 261: * Compute workspace
! 262: *
! 263: IF( INFO .EQ. 0 ) THEN
! 264: LWORKOPT = M - Q
! 265: LWORKMIN = M - Q
! 266: WORK(1) = LWORKOPT
! 267: IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN
! 268: INFO = -21
! 269: END IF
! 270: END IF
! 271: IF( INFO .NE. 0 ) THEN
! 272: CALL XERBLA( 'xORBDB', -INFO )
! 273: RETURN
! 274: ELSE IF( LQUERY ) THEN
! 275: RETURN
! 276: END IF
! 277: *
! 278: * Handle column-major and row-major separately
! 279: *
! 280: IF( COLMAJOR ) THEN
! 281: *
! 282: * Reduce columns 1, ..., Q of X11, X12, X21, and X22
! 283: *
! 284: DO I = 1, Q
! 285: *
! 286: IF( I .EQ. 1 ) THEN
! 287: CALL ZSCAL( P-I+1, DCMPLX( Z1, 0.0D0 ), X11(I,I), 1 )
! 288: ELSE
! 289: CALL ZSCAL( P-I+1, DCMPLX( Z1*COS(PHI(I-1)), 0.0D0 ),
! 290: $ X11(I,I), 1 )
! 291: CALL ZAXPY( P-I+1, DCMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)),
! 292: $ 0.0D0 ), X12(I,I-1), 1, X11(I,I), 1 )
! 293: END IF
! 294: IF( I .EQ. 1 ) THEN
! 295: CALL ZSCAL( M-P-I+1, DCMPLX( Z2, 0.0D0 ), X21(I,I), 1 )
! 296: ELSE
! 297: CALL ZSCAL( M-P-I+1, DCMPLX( Z2*COS(PHI(I-1)), 0.0D0 ),
! 298: $ X21(I,I), 1 )
! 299: CALL ZAXPY( M-P-I+1, DCMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)),
! 300: $ 0.0D0 ), X22(I,I-1), 1, X21(I,I), 1 )
! 301: END IF
! 302: *
! 303: THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), 1 ),
! 304: $ DZNRM2( P-I+1, X11(I,I), 1 ) )
! 305: *
! 306: CALL ZLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
! 307: X11(I,I) = ONE
! 308: CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) )
! 309: X21(I,I) = ONE
! 310: *
! 311: CALL ZLARF( 'L', P-I+1, Q-I, X11(I,I), 1, DCONJG(TAUP1(I)),
! 312: $ X11(I,I+1), LDX11, WORK )
! 313: CALL ZLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1,
! 314: $ DCONJG(TAUP1(I)), X12(I,I), LDX12, WORK )
! 315: CALL ZLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1,
! 316: $ DCONJG(TAUP2(I)), X21(I,I+1), LDX21, WORK )
! 317: CALL ZLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1,
! 318: $ DCONJG(TAUP2(I)), X22(I,I), LDX22, WORK )
! 319: *
! 320: IF( I .LT. Q ) THEN
! 321: CALL ZSCAL( Q-I, DCMPLX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ),
! 322: $ X11(I,I+1), LDX11 )
! 323: CALL ZAXPY( Q-I, DCMPLX( Z2*Z3*COS(THETA(I)), 0.0D0 ),
! 324: $ X21(I,I+1), LDX21, X11(I,I+1), LDX11 )
! 325: END IF
! 326: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ),
! 327: $ X12(I,I), LDX12 )
! 328: CALL ZAXPY( M-Q-I+1, DCMPLX( Z2*Z4*COS(THETA(I)), 0.0D0 ),
! 329: $ X22(I,I), LDX22, X12(I,I), LDX12 )
! 330: *
! 331: IF( I .LT. Q )
! 332: $ PHI(I) = ATAN2( DZNRM2( Q-I, X11(I,I+1), LDX11 ),
! 333: $ DZNRM2( M-Q-I+1, X12(I,I), LDX12 ) )
! 334: *
! 335: IF( I .LT. Q ) THEN
! 336: CALL ZLACGV( Q-I, X11(I,I+1), LDX11 )
! 337: CALL ZLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11,
! 338: $ TAUQ1(I) )
! 339: X11(I,I+1) = ONE
! 340: END IF
! 341: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
! 342: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
! 343: $ TAUQ2(I) )
! 344: X12(I,I) = ONE
! 345: *
! 346: IF( I .LT. Q ) THEN
! 347: CALL ZLARF( 'R', P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
! 348: $ X11(I+1,I+1), LDX11, WORK )
! 349: CALL ZLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
! 350: $ X21(I+1,I+1), LDX21, WORK )
! 351: END IF
! 352: CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
! 353: $ X12(I+1,I), LDX12, WORK )
! 354: CALL ZLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
! 355: $ X22(I+1,I), LDX22, WORK )
! 356: *
! 357: IF( I .LT. Q )
! 358: $ CALL ZLACGV( Q-I, X11(I,I+1), LDX11 )
! 359: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
! 360: *
! 361: END DO
! 362: *
! 363: * Reduce columns Q + 1, ..., P of X12, X22
! 364: *
! 365: DO I = Q + 1, P
! 366: *
! 367: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4, 0.0D0 ), X12(I,I),
! 368: $ LDX12 )
! 369: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
! 370: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
! 371: $ TAUQ2(I) )
! 372: X12(I,I) = ONE
! 373: *
! 374: CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
! 375: $ X12(I+1,I), LDX12, WORK )
! 376: IF( M-P-Q .GE. 1 )
! 377: $ CALL ZLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12,
! 378: $ TAUQ2(I), X22(Q+1,I), LDX22, WORK )
! 379: *
! 380: CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 )
! 381: *
! 382: END DO
! 383: *
! 384: * Reduce columns P + 1, ..., M - Q of X12, X22
! 385: *
! 386: DO I = 1, M - P - Q
! 387: *
! 388: CALL ZSCAL( M-P-Q-I+1, DCMPLX( Z2*Z4, 0.0D0 ),
! 389: $ X22(Q+I,P+I), LDX22 )
! 390: CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 )
! 391: CALL ZLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1),
! 392: $ LDX22, TAUQ2(P+I) )
! 393: X22(Q+I,P+I) = ONE
! 394: CALL ZLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22,
! 395: $ TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK )
! 396: *
! 397: CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 )
! 398: *
! 399: END DO
! 400: *
! 401: ELSE
! 402: *
! 403: * Reduce columns 1, ..., Q of X11, X12, X21, X22
! 404: *
! 405: DO I = 1, Q
! 406: *
! 407: IF( I .EQ. 1 ) THEN
! 408: CALL ZSCAL( P-I+1, DCMPLX( Z1, 0.0D0 ), X11(I,I),
! 409: $ LDX11 )
! 410: ELSE
! 411: CALL ZSCAL( P-I+1, DCMPLX( Z1*COS(PHI(I-1)), 0.0D0 ),
! 412: $ X11(I,I), LDX11 )
! 413: CALL ZAXPY( P-I+1, DCMPLX( -Z1*Z3*Z4*SIN(PHI(I-1)),
! 414: $ 0.0D0 ), X12(I-1,I), LDX12, X11(I,I), LDX11 )
! 415: END IF
! 416: IF( I .EQ. 1 ) THEN
! 417: CALL ZSCAL( M-P-I+1, DCMPLX( Z2, 0.0D0 ), X21(I,I),
! 418: $ LDX21 )
! 419: ELSE
! 420: CALL ZSCAL( M-P-I+1, DCMPLX( Z2*COS(PHI(I-1)), 0.0D0 ),
! 421: $ X21(I,I), LDX21 )
! 422: CALL ZAXPY( M-P-I+1, DCMPLX( -Z2*Z3*Z4*SIN(PHI(I-1)),
! 423: $ 0.0D0 ), X22(I-1,I), LDX22, X21(I,I), LDX21 )
! 424: END IF
! 425: *
! 426: THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), LDX21 ),
! 427: $ DZNRM2( P-I+1, X11(I,I), LDX11 ) )
! 428: *
! 429: CALL ZLACGV( P-I+1, X11(I,I), LDX11 )
! 430: CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 )
! 431: *
! 432: CALL ZLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) )
! 433: X11(I,I) = ONE
! 434: CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21,
! 435: $ TAUP2(I) )
! 436: X21(I,I) = ONE
! 437: *
! 438: CALL ZLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I),
! 439: $ X11(I+1,I), LDX11, WORK )
! 440: CALL ZLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11, TAUP1(I),
! 441: $ X12(I,I), LDX12, WORK )
! 442: CALL ZLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I),
! 443: $ X21(I+1,I), LDX21, WORK )
! 444: CALL ZLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21,
! 445: $ TAUP2(I), X22(I,I), LDX22, WORK )
! 446: *
! 447: CALL ZLACGV( P-I+1, X11(I,I), LDX11 )
! 448: CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 )
! 449: *
! 450: IF( I .LT. Q ) THEN
! 451: CALL ZSCAL( Q-I, DCMPLX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ),
! 452: $ X11(I+1,I), 1 )
! 453: CALL ZAXPY( Q-I, DCMPLX( Z2*Z3*COS(THETA(I)), 0.0D0 ),
! 454: $ X21(I+1,I), 1, X11(I+1,I), 1 )
! 455: END IF
! 456: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ),
! 457: $ X12(I,I), 1 )
! 458: CALL ZAXPY( M-Q-I+1, DCMPLX( Z2*Z4*COS(THETA(I)), 0.0D0 ),
! 459: $ X22(I,I), 1, X12(I,I), 1 )
! 460: *
! 461: IF( I .LT. Q )
! 462: $ PHI(I) = ATAN2( DZNRM2( Q-I, X11(I+1,I), 1 ),
! 463: $ DZNRM2( M-Q-I+1, X12(I,I), 1 ) )
! 464: *
! 465: IF( I .LT. Q ) THEN
! 466: CALL ZLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1, TAUQ1(I) )
! 467: X11(I+1,I) = ONE
! 468: END IF
! 469: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
! 470: X12(I,I) = ONE
! 471: *
! 472: IF( I .LT. Q ) THEN
! 473: CALL ZLARF( 'L', Q-I, P-I, X11(I+1,I), 1,
! 474: $ DCONJG(TAUQ1(I)), X11(I+1,I+1), LDX11, WORK )
! 475: CALL ZLARF( 'L', Q-I, M-P-I, X11(I+1,I), 1,
! 476: $ DCONJG(TAUQ1(I)), X21(I+1,I+1), LDX21, WORK )
! 477: END IF
! 478: CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1,
! 479: $ DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK )
! 480: CALL ZLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1,
! 481: $ DCONJG(TAUQ2(I)), X22(I,I+1), LDX22, WORK )
! 482: *
! 483: END DO
! 484: *
! 485: * Reduce columns Q + 1, ..., P of X12, X22
! 486: *
! 487: DO I = Q + 1, P
! 488: *
! 489: CALL ZSCAL( M-Q-I+1, DCMPLX( -Z1*Z4, 0.0D0 ), X12(I,I), 1 )
! 490: CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
! 491: X12(I,I) = ONE
! 492: *
! 493: CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1,
! 494: $ DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK )
! 495: IF( M-P-Q .GE. 1 )
! 496: $ CALL ZLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1,
! 497: $ DCONJG(TAUQ2(I)), X22(I,Q+1), LDX22, WORK )
! 498: *
! 499: END DO
! 500: *
! 501: * Reduce columns P + 1, ..., M - Q of X12, X22
! 502: *
! 503: DO I = 1, M - P - Q
! 504: *
! 505: CALL ZSCAL( M-P-Q-I+1, DCMPLX( Z2*Z4, 0.0D0 ),
! 506: $ X22(P+I,Q+I), 1 )
! 507: CALL ZLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1,
! 508: $ TAUQ2(P+I) )
! 509: X22(P+I,Q+I) = ONE
! 510: *
! 511: CALL ZLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1,
! 512: $ DCONJG(TAUQ2(P+I)), X22(P+I,Q+I+1), LDX22,
! 513: $ WORK )
! 514: *
! 515: END DO
! 516: *
! 517: END IF
! 518: *
! 519: RETURN
! 520: *
! 521: * End of ZUNBDB
! 522: *
! 523: END
! 524:
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