Annotation of rpl/lapack/lapack/dormbr.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
! 2: $ LDC, 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: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER SIDE, TRANS, VECT
! 11: INTEGER INFO, K, LDA, LDC, LWORK, M, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
! 21: * with
! 22: * SIDE = 'L' SIDE = 'R'
! 23: * TRANS = 'N': Q * C C * Q
! 24: * TRANS = 'T': Q**T * C C * Q**T
! 25: *
! 26: * If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
! 27: * with
! 28: * SIDE = 'L' SIDE = 'R'
! 29: * TRANS = 'N': P * C C * P
! 30: * TRANS = 'T': P**T * C C * P**T
! 31: *
! 32: * Here Q and P**T are the orthogonal matrices determined by DGEBRD when
! 33: * reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
! 34: * P**T are defined as products of elementary reflectors H(i) and G(i)
! 35: * respectively.
! 36: *
! 37: * Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
! 38: * order of the orthogonal matrix Q or P**T that is applied.
! 39: *
! 40: * If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
! 41: * if nq >= k, Q = H(1) H(2) . . . H(k);
! 42: * if nq < k, Q = H(1) H(2) . . . H(nq-1).
! 43: *
! 44: * If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
! 45: * if k < nq, P = G(1) G(2) . . . G(k);
! 46: * if k >= nq, P = G(1) G(2) . . . G(nq-1).
! 47: *
! 48: * Arguments
! 49: * =========
! 50: *
! 51: * VECT (input) CHARACTER*1
! 52: * = 'Q': apply Q or Q**T;
! 53: * = 'P': apply P or P**T.
! 54: *
! 55: * SIDE (input) CHARACTER*1
! 56: * = 'L': apply Q, Q**T, P or P**T from the Left;
! 57: * = 'R': apply Q, Q**T, P or P**T from the Right.
! 58: *
! 59: * TRANS (input) CHARACTER*1
! 60: * = 'N': No transpose, apply Q or P;
! 61: * = 'T': Transpose, apply Q**T or P**T.
! 62: *
! 63: * M (input) INTEGER
! 64: * The number of rows of the matrix C. M >= 0.
! 65: *
! 66: * N (input) INTEGER
! 67: * The number of columns of the matrix C. N >= 0.
! 68: *
! 69: * K (input) INTEGER
! 70: * If VECT = 'Q', the number of columns in the original
! 71: * matrix reduced by DGEBRD.
! 72: * If VECT = 'P', the number of rows in the original
! 73: * matrix reduced by DGEBRD.
! 74: * K >= 0.
! 75: *
! 76: * A (input) DOUBLE PRECISION array, dimension
! 77: * (LDA,min(nq,K)) if VECT = 'Q'
! 78: * (LDA,nq) if VECT = 'P'
! 79: * The vectors which define the elementary reflectors H(i) and
! 80: * G(i), whose products determine the matrices Q and P, as
! 81: * returned by DGEBRD.
! 82: *
! 83: * LDA (input) INTEGER
! 84: * The leading dimension of the array A.
! 85: * If VECT = 'Q', LDA >= max(1,nq);
! 86: * if VECT = 'P', LDA >= max(1,min(nq,K)).
! 87: *
! 88: * TAU (input) DOUBLE PRECISION array, dimension (min(nq,K))
! 89: * TAU(i) must contain the scalar factor of the elementary
! 90: * reflector H(i) or G(i) which determines Q or P, as returned
! 91: * by DGEBRD in the array argument TAUQ or TAUP.
! 92: *
! 93: * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
! 94: * On entry, the M-by-N matrix C.
! 95: * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
! 96: * or P*C or P**T*C or C*P or C*P**T.
! 97: *
! 98: * LDC (input) INTEGER
! 99: * The leading dimension of the array C. LDC >= max(1,M).
! 100: *
! 101: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 102: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 103: *
! 104: * LWORK (input) INTEGER
! 105: * The dimension of the array WORK.
! 106: * If SIDE = 'L', LWORK >= max(1,N);
! 107: * if SIDE = 'R', LWORK >= max(1,M).
! 108: * For optimum performance LWORK >= N*NB if SIDE = 'L', and
! 109: * LWORK >= M*NB if SIDE = 'R', where NB is the optimal
! 110: * blocksize.
! 111: *
! 112: * If LWORK = -1, then a workspace query is assumed; the routine
! 113: * only calculates the optimal size of the WORK array, returns
! 114: * this value as the first entry of the WORK array, and no error
! 115: * message related to LWORK is issued by XERBLA.
! 116: *
! 117: * INFO (output) INTEGER
! 118: * = 0: successful exit
! 119: * < 0: if INFO = -i, the i-th argument had an illegal value
! 120: *
! 121: * =====================================================================
! 122: *
! 123: * .. Local Scalars ..
! 124: LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
! 125: CHARACTER TRANST
! 126: INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
! 127: * ..
! 128: * .. External Functions ..
! 129: LOGICAL LSAME
! 130: INTEGER ILAENV
! 131: EXTERNAL LSAME, ILAENV
! 132: * ..
! 133: * .. External Subroutines ..
! 134: EXTERNAL DORMLQ, DORMQR, XERBLA
! 135: * ..
! 136: * .. Intrinsic Functions ..
! 137: INTRINSIC MAX, MIN
! 138: * ..
! 139: * .. Executable Statements ..
! 140: *
! 141: * Test the input arguments
! 142: *
! 143: INFO = 0
! 144: APPLYQ = LSAME( VECT, 'Q' )
! 145: LEFT = LSAME( SIDE, 'L' )
! 146: NOTRAN = LSAME( TRANS, 'N' )
! 147: LQUERY = ( LWORK.EQ.-1 )
! 148: *
! 149: * NQ is the order of Q or P and NW is the minimum dimension of WORK
! 150: *
! 151: IF( LEFT ) THEN
! 152: NQ = M
! 153: NW = N
! 154: ELSE
! 155: NQ = N
! 156: NW = M
! 157: END IF
! 158: IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
! 159: INFO = -1
! 160: ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
! 161: INFO = -2
! 162: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
! 163: INFO = -3
! 164: ELSE IF( M.LT.0 ) THEN
! 165: INFO = -4
! 166: ELSE IF( N.LT.0 ) THEN
! 167: INFO = -5
! 168: ELSE IF( K.LT.0 ) THEN
! 169: INFO = -6
! 170: ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
! 171: $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
! 172: $ THEN
! 173: INFO = -8
! 174: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
! 175: INFO = -11
! 176: ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
! 177: INFO = -13
! 178: END IF
! 179: *
! 180: IF( INFO.EQ.0 ) THEN
! 181: IF( APPLYQ ) THEN
! 182: IF( LEFT ) THEN
! 183: NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1,
! 184: $ -1 )
! 185: ELSE
! 186: NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1,
! 187: $ -1 )
! 188: END IF
! 189: ELSE
! 190: IF( LEFT ) THEN
! 191: NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1,
! 192: $ -1 )
! 193: ELSE
! 194: NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1,
! 195: $ -1 )
! 196: END IF
! 197: END IF
! 198: LWKOPT = MAX( 1, NW )*NB
! 199: WORK( 1 ) = LWKOPT
! 200: END IF
! 201: *
! 202: IF( INFO.NE.0 ) THEN
! 203: CALL XERBLA( 'DORMBR', -INFO )
! 204: RETURN
! 205: ELSE IF( LQUERY ) THEN
! 206: RETURN
! 207: END IF
! 208: *
! 209: * Quick return if possible
! 210: *
! 211: WORK( 1 ) = 1
! 212: IF( M.EQ.0 .OR. N.EQ.0 )
! 213: $ RETURN
! 214: *
! 215: IF( APPLYQ ) THEN
! 216: *
! 217: * Apply Q
! 218: *
! 219: IF( NQ.GE.K ) THEN
! 220: *
! 221: * Q was determined by a call to DGEBRD with nq >= k
! 222: *
! 223: CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
! 224: $ WORK, LWORK, IINFO )
! 225: ELSE IF( NQ.GT.1 ) THEN
! 226: *
! 227: * Q was determined by a call to DGEBRD with nq < k
! 228: *
! 229: IF( LEFT ) THEN
! 230: MI = M - 1
! 231: NI = N
! 232: I1 = 2
! 233: I2 = 1
! 234: ELSE
! 235: MI = M
! 236: NI = N - 1
! 237: I1 = 1
! 238: I2 = 2
! 239: END IF
! 240: CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
! 241: $ C( I1, I2 ), LDC, WORK, LWORK, IINFO )
! 242: END IF
! 243: ELSE
! 244: *
! 245: * Apply P
! 246: *
! 247: IF( NOTRAN ) THEN
! 248: TRANST = 'T'
! 249: ELSE
! 250: TRANST = 'N'
! 251: END IF
! 252: IF( NQ.GT.K ) THEN
! 253: *
! 254: * P was determined by a call to DGEBRD with nq > k
! 255: *
! 256: CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
! 257: $ WORK, LWORK, IINFO )
! 258: ELSE IF( NQ.GT.1 ) THEN
! 259: *
! 260: * P was determined by a call to DGEBRD with nq <= k
! 261: *
! 262: IF( LEFT ) THEN
! 263: MI = M - 1
! 264: NI = N
! 265: I1 = 2
! 266: I2 = 1
! 267: ELSE
! 268: MI = M
! 269: NI = N - 1
! 270: I1 = 1
! 271: I2 = 2
! 272: END IF
! 273: CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
! 274: $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
! 275: END IF
! 276: END IF
! 277: WORK( 1 ) = LWKOPT
! 278: RETURN
! 279: *
! 280: * End of DORMBR
! 281: *
! 282: END
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