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    1:       SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          VECT
   10:       INTEGER            INFO, K, LDA, LWORK, M, N
   11: *     ..
   12: *     .. Array Arguments ..
   13:       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  ZUNGBR generates one of the complex unitary matrices Q or P**H
   20: *  determined by ZGEBRD when reducing a complex matrix A to bidiagonal
   21: *  form: A = Q * B * P**H.  Q and P**H are defined as products of
   22: *  elementary reflectors H(i) or G(i) respectively.
   23: *
   24: *  If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
   25: *  is of order M:
   26: *  if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n
   27: *  columns of Q, where m >= n >= k;
   28: *  if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an
   29: *  M-by-M matrix.
   30: *
   31: *  If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
   32: *  is of order N:
   33: *  if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
   34: *  rows of P**H, where n >= m >= k;
   35: *  if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as
   36: *  an N-by-N matrix.
   37: *
   38: *  Arguments
   39: *  =========
   40: *
   41: *  VECT    (input) CHARACTER*1
   42: *          Specifies whether the matrix Q or the matrix P**H is
   43: *          required, as defined in the transformation applied by ZGEBRD:
   44: *          = 'Q':  generate Q;
   45: *          = 'P':  generate P**H.
   46: *
   47: *  M       (input) INTEGER
   48: *          The number of rows of the matrix Q or P**H to be returned.
   49: *          M >= 0.
   50: *
   51: *  N       (input) INTEGER
   52: *          The number of columns of the matrix Q or P**H to be returned.
   53: *          N >= 0.
   54: *          If VECT = 'Q', M >= N >= min(M,K);
   55: *          if VECT = 'P', N >= M >= min(N,K).
   56: *
   57: *  K       (input) INTEGER
   58: *          If VECT = 'Q', the number of columns in the original M-by-K
   59: *          matrix reduced by ZGEBRD.
   60: *          If VECT = 'P', the number of rows in the original K-by-N
   61: *          matrix reduced by ZGEBRD.
   62: *          K >= 0.
   63: *
   64: *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
   65: *          On entry, the vectors which define the elementary reflectors,
   66: *          as returned by ZGEBRD.
   67: *          On exit, the M-by-N matrix Q or P**H.
   68: *
   69: *  LDA     (input) INTEGER
   70: *          The leading dimension of the array A. LDA >= M.
   71: *
   72: *  TAU     (input) COMPLEX*16 array, dimension
   73: *                                (min(M,K)) if VECT = 'Q'
   74: *                                (min(N,K)) if VECT = 'P'
   75: *          TAU(i) must contain the scalar factor of the elementary
   76: *          reflector H(i) or G(i), which determines Q or P**H, as
   77: *          returned by ZGEBRD in its array argument TAUQ or TAUP.
   78: *
   79: *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
   80: *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   81: *
   82: *  LWORK   (input) INTEGER
   83: *          The dimension of the array WORK. LWORK >= max(1,min(M,N)).
   84: *          For optimum performance LWORK >= min(M,N)*NB, where NB
   85: *          is the optimal blocksize.
   86: *
   87: *          If LWORK = -1, then a workspace query is assumed; the routine
   88: *          only calculates the optimal size of the WORK array, returns
   89: *          this value as the first entry of the WORK array, and no error
   90: *          message related to LWORK is issued by XERBLA.
   91: *
   92: *  INFO    (output) INTEGER
   93: *          = 0:  successful exit
   94: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   95: *
   96: *  =====================================================================
   97: *
   98: *     .. Parameters ..
   99:       COMPLEX*16         ZERO, ONE
  100:       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
  101:      $                   ONE = ( 1.0D+0, 0.0D+0 ) )
  102: *     ..
  103: *     .. Local Scalars ..
  104:       LOGICAL            LQUERY, WANTQ
  105:       INTEGER            I, IINFO, J, LWKOPT, MN, NB
  106: *     ..
  107: *     .. External Functions ..
  108:       LOGICAL            LSAME
  109:       INTEGER            ILAENV
  110:       EXTERNAL           LSAME, ILAENV
  111: *     ..
  112: *     .. External Subroutines ..
  113:       EXTERNAL           XERBLA, ZUNGLQ, ZUNGQR
  114: *     ..
  115: *     .. Intrinsic Functions ..
  116:       INTRINSIC          MAX, MIN
  117: *     ..
  118: *     .. Executable Statements ..
  119: *
  120: *     Test the input arguments
  121: *
  122:       INFO = 0
  123:       WANTQ = LSAME( VECT, 'Q' )
  124:       MN = MIN( M, N )
  125:       LQUERY = ( LWORK.EQ.-1 )
  126:       IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
  127:          INFO = -1
  128:       ELSE IF( M.LT.0 ) THEN
  129:          INFO = -2
  130:       ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
  131:      $         K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
  132:      $         MIN( N, K ) ) ) ) THEN
  133:          INFO = -3
  134:       ELSE IF( K.LT.0 ) THEN
  135:          INFO = -4
  136:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
  137:          INFO = -6
  138:       ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
  139:          INFO = -9
  140:       END IF
  141: *
  142:       IF( INFO.EQ.0 ) THEN
  143:          IF( WANTQ ) THEN
  144:             NB = ILAENV( 1, 'ZUNGQR', ' ', M, N, K, -1 )
  145:          ELSE
  146:             NB = ILAENV( 1, 'ZUNGLQ', ' ', M, N, K, -1 )
  147:          END IF
  148:          LWKOPT = MAX( 1, MN )*NB
  149:          WORK( 1 ) = LWKOPT
  150:       END IF
  151: *
  152:       IF( INFO.NE.0 ) THEN
  153:          CALL XERBLA( 'ZUNGBR', -INFO )
  154:          RETURN
  155:       ELSE IF( LQUERY ) THEN
  156:          RETURN
  157:       END IF
  158: *
  159: *     Quick return if possible
  160: *
  161:       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
  162:          WORK( 1 ) = 1
  163:          RETURN
  164:       END IF
  165: *
  166:       IF( WANTQ ) THEN
  167: *
  168: *        Form Q, determined by a call to ZGEBRD to reduce an m-by-k
  169: *        matrix
  170: *
  171:          IF( M.GE.K ) THEN
  172: *
  173: *           If m >= k, assume m >= n >= k
  174: *
  175:             CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
  176: *
  177:          ELSE
  178: *
  179: *           If m < k, assume m = n
  180: *
  181: *           Shift the vectors which define the elementary reflectors one
  182: *           column to the right, and set the first row and column of Q
  183: *           to those of the unit matrix
  184: *
  185:             DO 20 J = M, 2, -1
  186:                A( 1, J ) = ZERO
  187:                DO 10 I = J + 1, M
  188:                   A( I, J ) = A( I, J-1 )
  189:    10          CONTINUE
  190:    20       CONTINUE
  191:             A( 1, 1 ) = ONE
  192:             DO 30 I = 2, M
  193:                A( I, 1 ) = ZERO
  194:    30       CONTINUE
  195:             IF( M.GT.1 ) THEN
  196: *
  197: *              Form Q(2:m,2:m)
  198: *
  199:                CALL ZUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
  200:      $                      LWORK, IINFO )
  201:             END IF
  202:          END IF
  203:       ELSE
  204: *
  205: *        Form P', determined by a call to ZGEBRD to reduce a k-by-n
  206: *        matrix
  207: *
  208:          IF( K.LT.N ) THEN
  209: *
  210: *           If k < n, assume k <= m <= n
  211: *
  212:             CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
  213: *
  214:          ELSE
  215: *
  216: *           If k >= n, assume m = n
  217: *
  218: *           Shift the vectors which define the elementary reflectors one
  219: *           row downward, and set the first row and column of P' to
  220: *           those of the unit matrix
  221: *
  222:             A( 1, 1 ) = ONE
  223:             DO 40 I = 2, N
  224:                A( I, 1 ) = ZERO
  225:    40       CONTINUE
  226:             DO 60 J = 2, N
  227:                DO 50 I = J - 1, 2, -1
  228:                   A( I, J ) = A( I-1, J )
  229:    50          CONTINUE
  230:                A( 1, J ) = ZERO
  231:    60       CONTINUE
  232:             IF( N.GT.1 ) THEN
  233: *
  234: *              Form P'(2:n,2:n)
  235: *
  236:                CALL ZUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
  237:      $                      LWORK, IINFO )
  238:             END IF
  239:          END IF
  240:       END IF
  241:       WORK( 1 ) = LWKOPT
  242:       RETURN
  243: *
  244: *     End of ZUNGBR
  245: *
  246:       END