Annotation of rpl/lapack/lapack/ztzrzf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTZRZF( M, N, 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: INTEGER INFO, LDA, LWORK, M, N
! 10: * ..
! 11: * .. Array Arguments ..
! 12: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 13: * ..
! 14: *
! 15: * Purpose
! 16: * =======
! 17: *
! 18: * ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
! 19: * to upper triangular form by means of unitary transformations.
! 20: *
! 21: * The upper trapezoidal matrix A is factored as
! 22: *
! 23: * A = ( R 0 ) * Z,
! 24: *
! 25: * where Z is an N-by-N unitary matrix and R is an M-by-M upper
! 26: * triangular matrix.
! 27: *
! 28: * Arguments
! 29: * =========
! 30: *
! 31: * M (input) INTEGER
! 32: * The number of rows of the matrix A. M >= 0.
! 33: *
! 34: * N (input) INTEGER
! 35: * The number of columns of the matrix A. N >= M.
! 36: *
! 37: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 38: * On entry, the leading M-by-N upper trapezoidal part of the
! 39: * array A must contain the matrix to be factorized.
! 40: * On exit, the leading M-by-M upper triangular part of A
! 41: * contains the upper triangular matrix R, and elements M+1 to
! 42: * N of the first M rows of A, with the array TAU, represent the
! 43: * unitary matrix Z as a product of M elementary reflectors.
! 44: *
! 45: * LDA (input) INTEGER
! 46: * The leading dimension of the array A. LDA >= max(1,M).
! 47: *
! 48: * TAU (output) COMPLEX*16 array, dimension (M)
! 49: * The scalar factors of the elementary reflectors.
! 50: *
! 51: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 52: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 53: *
! 54: * LWORK (input) INTEGER
! 55: * The dimension of the array WORK. LWORK >= max(1,M).
! 56: * For optimum performance LWORK >= M*NB, where NB is
! 57: * the optimal blocksize.
! 58: *
! 59: * If LWORK = -1, then a workspace query is assumed; the routine
! 60: * only calculates the optimal size of the WORK array, returns
! 61: * this value as the first entry of the WORK array, and no error
! 62: * message related to LWORK is issued by XERBLA.
! 63: *
! 64: * INFO (output) INTEGER
! 65: * = 0: successful exit
! 66: * < 0: if INFO = -i, the i-th argument had an illegal value
! 67: *
! 68: * Further Details
! 69: * ===============
! 70: *
! 71: * Based on contributions by
! 72: * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
! 73: *
! 74: * The factorization is obtained by Householder's method. The kth
! 75: * transformation matrix, Z( k ), which is used to introduce zeros into
! 76: * the ( m - k + 1 )th row of A, is given in the form
! 77: *
! 78: * Z( k ) = ( I 0 ),
! 79: * ( 0 T( k ) )
! 80: *
! 81: * where
! 82: *
! 83: * T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),
! 84: * ( 0 )
! 85: * ( z( k ) )
! 86: *
! 87: * tau is a scalar and z( k ) is an ( n - m ) element vector.
! 88: * tau and z( k ) are chosen to annihilate the elements of the kth row
! 89: * of X.
! 90: *
! 91: * The scalar tau is returned in the kth element of TAU and the vector
! 92: * u( k ) in the kth row of A, such that the elements of z( k ) are
! 93: * in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
! 94: * the upper triangular part of A.
! 95: *
! 96: * Z is given by
! 97: *
! 98: * Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
! 99: *
! 100: * =====================================================================
! 101: *
! 102: * .. Parameters ..
! 103: COMPLEX*16 ZERO
! 104: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
! 105: * ..
! 106: * .. Local Scalars ..
! 107: LOGICAL LQUERY
! 108: INTEGER I, IB, IWS, KI, KK, LDWORK, LWKOPT, M1, MU, NB,
! 109: $ NBMIN, NX
! 110: * ..
! 111: * .. External Subroutines ..
! 112: EXTERNAL XERBLA, ZLARZB, ZLARZT, ZLATRZ
! 113: * ..
! 114: * .. Intrinsic Functions ..
! 115: INTRINSIC MAX, MIN
! 116: * ..
! 117: * .. External Functions ..
! 118: INTEGER ILAENV
! 119: EXTERNAL ILAENV
! 120: * ..
! 121: * .. Executable Statements ..
! 122: *
! 123: * Test the input arguments
! 124: *
! 125: INFO = 0
! 126: LQUERY = ( LWORK.EQ.-1 )
! 127: IF( M.LT.0 ) THEN
! 128: INFO = -1
! 129: ELSE IF( N.LT.M ) THEN
! 130: INFO = -2
! 131: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 132: INFO = -4
! 133: END IF
! 134: *
! 135: IF( INFO.EQ.0 ) THEN
! 136: IF( M.EQ.0 .OR. M.EQ.N ) THEN
! 137: LWKOPT = 1
! 138: ELSE
! 139: *
! 140: * Determine the block size.
! 141: *
! 142: NB = ILAENV( 1, 'ZGERQF', ' ', M, N, -1, -1 )
! 143: LWKOPT = M*NB
! 144: END IF
! 145: WORK( 1 ) = LWKOPT
! 146: *
! 147: IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
! 148: INFO = -7
! 149: END IF
! 150: END IF
! 151: *
! 152: IF( INFO.NE.0 ) THEN
! 153: CALL XERBLA( 'ZTZRZF', -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 ) THEN
! 162: RETURN
! 163: ELSE IF( M.EQ.N ) THEN
! 164: DO 10 I = 1, N
! 165: TAU( I ) = ZERO
! 166: 10 CONTINUE
! 167: RETURN
! 168: END IF
! 169: *
! 170: NBMIN = 2
! 171: NX = 1
! 172: IWS = M
! 173: IF( NB.GT.1 .AND. NB.LT.M ) THEN
! 174: *
! 175: * Determine when to cross over from blocked to unblocked code.
! 176: *
! 177: NX = MAX( 0, ILAENV( 3, 'ZGERQF', ' ', M, N, -1, -1 ) )
! 178: IF( NX.LT.M ) THEN
! 179: *
! 180: * Determine if workspace is large enough for blocked code.
! 181: *
! 182: LDWORK = M
! 183: IWS = LDWORK*NB
! 184: IF( LWORK.LT.IWS ) THEN
! 185: *
! 186: * Not enough workspace to use optimal NB: reduce NB and
! 187: * determine the minimum value of NB.
! 188: *
! 189: NB = LWORK / LDWORK
! 190: NBMIN = MAX( 2, ILAENV( 2, 'ZGERQF', ' ', M, N, -1,
! 191: $ -1 ) )
! 192: END IF
! 193: END IF
! 194: END IF
! 195: *
! 196: IF( NB.GE.NBMIN .AND. NB.LT.M .AND. NX.LT.M ) THEN
! 197: *
! 198: * Use blocked code initially.
! 199: * The last kk rows are handled by the block method.
! 200: *
! 201: M1 = MIN( M+1, N )
! 202: KI = ( ( M-NX-1 ) / NB )*NB
! 203: KK = MIN( M, KI+NB )
! 204: *
! 205: DO 20 I = M - KK + KI + 1, M - KK + 1, -NB
! 206: IB = MIN( M-I+1, NB )
! 207: *
! 208: * Compute the TZ factorization of the current block
! 209: * A(i:i+ib-1,i:n)
! 210: *
! 211: CALL ZLATRZ( IB, N-I+1, N-M, A( I, I ), LDA, TAU( I ),
! 212: $ WORK )
! 213: IF( I.GT.1 ) THEN
! 214: *
! 215: * Form the triangular factor of the block reflector
! 216: * H = H(i+ib-1) . . . H(i+1) H(i)
! 217: *
! 218: CALL ZLARZT( 'Backward', 'Rowwise', N-M, IB, A( I, M1 ),
! 219: $ LDA, TAU( I ), WORK, LDWORK )
! 220: *
! 221: * Apply H to A(1:i-1,i:n) from the right
! 222: *
! 223: CALL ZLARZB( 'Right', 'No transpose', 'Backward',
! 224: $ 'Rowwise', I-1, N-I+1, IB, N-M, A( I, M1 ),
! 225: $ LDA, WORK, LDWORK, A( 1, I ), LDA,
! 226: $ WORK( IB+1 ), LDWORK )
! 227: END IF
! 228: 20 CONTINUE
! 229: MU = I + NB - 1
! 230: ELSE
! 231: MU = M
! 232: END IF
! 233: *
! 234: * Use unblocked code to factor the last or only block
! 235: *
! 236: IF( MU.GT.0 )
! 237: $ CALL ZLATRZ( MU, N, N-M, A, LDA, TAU, WORK )
! 238: *
! 239: WORK( 1 ) = LWKOPT
! 240: *
! 241: RETURN
! 242: *
! 243: * End of ZTZRZF
! 244: *
! 245: END
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