Annotation of rpl/lapack/lapack/zunmrz.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
! 2: $ WORK, LWORK, INFO )
! 3: *
! 4: * -- LAPACK routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * January 2007
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER SIDE, TRANS
! 11: INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZUNMRZ overwrites the general complex M-by-N matrix C with
! 21: *
! 22: * SIDE = 'L' SIDE = 'R'
! 23: * TRANS = 'N': Q * C C * Q
! 24: * TRANS = 'C': Q**H * C C * Q**H
! 25: *
! 26: * where Q is a complex unitary matrix defined as the product of k
! 27: * elementary reflectors
! 28: *
! 29: * Q = H(1) H(2) . . . H(k)
! 30: *
! 31: * as returned by ZTZRZF. Q is of order M if SIDE = 'L' and of order N
! 32: * if SIDE = 'R'.
! 33: *
! 34: * Arguments
! 35: * =========
! 36: *
! 37: * SIDE (input) CHARACTER*1
! 38: * = 'L': apply Q or Q**H from the Left;
! 39: * = 'R': apply Q or Q**H from the Right.
! 40: *
! 41: * TRANS (input) CHARACTER*1
! 42: * = 'N': No transpose, apply Q;
! 43: * = 'C': Conjugate transpose, apply Q**H.
! 44: *
! 45: * M (input) INTEGER
! 46: * The number of rows of the matrix C. M >= 0.
! 47: *
! 48: * N (input) INTEGER
! 49: * The number of columns of the matrix C. N >= 0.
! 50: *
! 51: * K (input) INTEGER
! 52: * The number of elementary reflectors whose product defines
! 53: * the matrix Q.
! 54: * If SIDE = 'L', M >= K >= 0;
! 55: * if SIDE = 'R', N >= K >= 0.
! 56: *
! 57: * L (input) INTEGER
! 58: * The number of columns of the matrix A containing
! 59: * the meaningful part of the Householder reflectors.
! 60: * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
! 61: *
! 62: * A (input) COMPLEX*16 array, dimension
! 63: * (LDA,M) if SIDE = 'L',
! 64: * (LDA,N) if SIDE = 'R'
! 65: * The i-th row must contain the vector which defines the
! 66: * elementary reflector H(i), for i = 1,2,...,k, as returned by
! 67: * ZTZRZF in the last k rows of its array argument A.
! 68: * A is modified by the routine but restored on exit.
! 69: *
! 70: * LDA (input) INTEGER
! 71: * The leading dimension of the array A. LDA >= max(1,K).
! 72: *
! 73: * TAU (input) COMPLEX*16 array, dimension (K)
! 74: * TAU(i) must contain the scalar factor of the elementary
! 75: * reflector H(i), as returned by ZTZRZF.
! 76: *
! 77: * C (input/output) COMPLEX*16 array, dimension (LDC,N)
! 78: * On entry, the M-by-N matrix C.
! 79: * On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
! 80: *
! 81: * LDC (input) INTEGER
! 82: * The leading dimension of the array C. LDC >= max(1,M).
! 83: *
! 84: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 85: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 86: *
! 87: * LWORK (input) INTEGER
! 88: * The dimension of the array WORK.
! 89: * If SIDE = 'L', LWORK >= max(1,N);
! 90: * if SIDE = 'R', LWORK >= max(1,M).
! 91: * For optimum performance LWORK >= N*NB if SIDE = 'L', and
! 92: * LWORK >= M*NB if SIDE = 'R', where NB is the optimal
! 93: * blocksize.
! 94: *
! 95: * If LWORK = -1, then a workspace query is assumed; the routine
! 96: * only calculates the optimal size of the WORK array, returns
! 97: * this value as the first entry of the WORK array, and no error
! 98: * message related to LWORK is issued by XERBLA.
! 99: *
! 100: * INFO (output) INTEGER
! 101: * = 0: successful exit
! 102: * < 0: if INFO = -i, the i-th argument had an illegal value
! 103: *
! 104: * Further Details
! 105: * ===============
! 106: *
! 107: * Based on contributions by
! 108: * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
! 109: *
! 110: * =====================================================================
! 111: *
! 112: * .. Parameters ..
! 113: INTEGER NBMAX, LDT
! 114: PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
! 115: * ..
! 116: * .. Local Scalars ..
! 117: LOGICAL LEFT, LQUERY, NOTRAN
! 118: CHARACTER TRANST
! 119: INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JA, JC,
! 120: $ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW
! 121: * ..
! 122: * .. Local Arrays ..
! 123: COMPLEX*16 T( LDT, NBMAX )
! 124: * ..
! 125: * .. External Functions ..
! 126: LOGICAL LSAME
! 127: INTEGER ILAENV
! 128: EXTERNAL LSAME, ILAENV
! 129: * ..
! 130: * .. External Subroutines ..
! 131: EXTERNAL XERBLA, ZLARZB, ZLARZT, ZUNMR3
! 132: * ..
! 133: * .. Intrinsic Functions ..
! 134: INTRINSIC MAX, MIN
! 135: * ..
! 136: * .. Executable Statements ..
! 137: *
! 138: * Test the input arguments
! 139: *
! 140: INFO = 0
! 141: LEFT = LSAME( SIDE, 'L' )
! 142: NOTRAN = LSAME( TRANS, 'N' )
! 143: LQUERY = ( LWORK.EQ.-1 )
! 144: *
! 145: * NQ is the order of Q and NW is the minimum dimension of WORK
! 146: *
! 147: IF( LEFT ) THEN
! 148: NQ = M
! 149: NW = MAX( 1, N )
! 150: ELSE
! 151: NQ = N
! 152: NW = MAX( 1, M )
! 153: END IF
! 154: IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
! 155: INFO = -1
! 156: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
! 157: INFO = -2
! 158: ELSE IF( M.LT.0 ) THEN
! 159: INFO = -3
! 160: ELSE IF( N.LT.0 ) THEN
! 161: INFO = -4
! 162: ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
! 163: INFO = -5
! 164: ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
! 165: $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
! 166: INFO = -6
! 167: ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
! 168: INFO = -8
! 169: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
! 170: INFO = -11
! 171: END IF
! 172: *
! 173: IF( INFO.EQ.0 ) THEN
! 174: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
! 175: LWKOPT = 1
! 176: ELSE
! 177: *
! 178: * Determine the block size. NB may be at most NBMAX, where
! 179: * NBMAX is used to define the local array T.
! 180: *
! 181: NB = MIN( NBMAX, ILAENV( 1, 'ZUNMRQ', SIDE // TRANS, M, N,
! 182: $ K, -1 ) )
! 183: LWKOPT = NW*NB
! 184: END IF
! 185: WORK( 1 ) = LWKOPT
! 186: *
! 187: IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
! 188: INFO = -13
! 189: END IF
! 190: END IF
! 191: *
! 192: IF( INFO.NE.0 ) THEN
! 193: CALL XERBLA( 'ZUNMRZ', -INFO )
! 194: RETURN
! 195: ELSE IF( LQUERY ) THEN
! 196: RETURN
! 197: END IF
! 198: *
! 199: * Quick return if possible
! 200: *
! 201: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
! 202: RETURN
! 203: END IF
! 204: *
! 205: * Determine the block size. NB may be at most NBMAX, where NBMAX
! 206: * is used to define the local array T.
! 207: *
! 208: NB = MIN( NBMAX, ILAENV( 1, 'ZUNMRQ', SIDE // TRANS, M, N, K,
! 209: $ -1 ) )
! 210: NBMIN = 2
! 211: LDWORK = NW
! 212: IF( NB.GT.1 .AND. NB.LT.K ) THEN
! 213: IWS = NW*NB
! 214: IF( LWORK.LT.IWS ) THEN
! 215: NB = LWORK / LDWORK
! 216: NBMIN = MAX( 2, ILAENV( 2, 'ZUNMRQ', SIDE // TRANS, M, N, K,
! 217: $ -1 ) )
! 218: END IF
! 219: ELSE
! 220: IWS = NW
! 221: END IF
! 222: *
! 223: IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
! 224: *
! 225: * Use unblocked code
! 226: *
! 227: CALL ZUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
! 228: $ WORK, IINFO )
! 229: ELSE
! 230: *
! 231: * Use blocked code
! 232: *
! 233: IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
! 234: $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
! 235: I1 = 1
! 236: I2 = K
! 237: I3 = NB
! 238: ELSE
! 239: I1 = ( ( K-1 ) / NB )*NB + 1
! 240: I2 = 1
! 241: I3 = -NB
! 242: END IF
! 243: *
! 244: IF( LEFT ) THEN
! 245: NI = N
! 246: JC = 1
! 247: JA = M - L + 1
! 248: ELSE
! 249: MI = M
! 250: IC = 1
! 251: JA = N - L + 1
! 252: END IF
! 253: *
! 254: IF( NOTRAN ) THEN
! 255: TRANST = 'C'
! 256: ELSE
! 257: TRANST = 'N'
! 258: END IF
! 259: *
! 260: DO 10 I = I1, I2, I3
! 261: IB = MIN( NB, K-I+1 )
! 262: *
! 263: * Form the triangular factor of the block reflector
! 264: * H = H(i+ib-1) . . . H(i+1) H(i)
! 265: *
! 266: CALL ZLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA,
! 267: $ TAU( I ), T, LDT )
! 268: *
! 269: IF( LEFT ) THEN
! 270: *
! 271: * H or H' is applied to C(i:m,1:n)
! 272: *
! 273: MI = M - I + 1
! 274: IC = I
! 275: ELSE
! 276: *
! 277: * H or H' is applied to C(1:m,i:n)
! 278: *
! 279: NI = N - I + 1
! 280: JC = I
! 281: END IF
! 282: *
! 283: * Apply H or H'
! 284: *
! 285: CALL ZLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
! 286: $ IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ),
! 287: $ LDC, WORK, LDWORK )
! 288: 10 CONTINUE
! 289: *
! 290: END IF
! 291: *
! 292: WORK( 1 ) = LWKOPT
! 293: *
! 294: RETURN
! 295: *
! 296: * End of ZUNMRZ
! 297: *
! 298: END
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