Annotation of rpl/lapack/lapack/dgerqf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGERQF( 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: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 13: * ..
! 14: *
! 15: * Purpose
! 16: * =======
! 17: *
! 18: * DGERQF computes an RQ factorization of a real M-by-N matrix A:
! 19: * A = R * Q.
! 20: *
! 21: * Arguments
! 22: * =========
! 23: *
! 24: * M (input) INTEGER
! 25: * The number of rows of the matrix A. M >= 0.
! 26: *
! 27: * N (input) INTEGER
! 28: * The number of columns of the matrix A. N >= 0.
! 29: *
! 30: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
! 31: * On entry, the M-by-N matrix A.
! 32: * On exit,
! 33: * if m <= n, the upper triangle of the subarray
! 34: * A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
! 35: * if m >= n, the elements on and above the (m-n)-th subdiagonal
! 36: * contain the M-by-N upper trapezoidal matrix R;
! 37: * the remaining elements, with the array TAU, represent the
! 38: * orthogonal matrix Q as a product of min(m,n) elementary
! 39: * reflectors (see Further Details).
! 40: *
! 41: * LDA (input) INTEGER
! 42: * The leading dimension of the array A. LDA >= max(1,M).
! 43: *
! 44: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
! 45: * The scalar factors of the elementary reflectors (see Further
! 46: * Details).
! 47: *
! 48: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 49: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 50: *
! 51: * LWORK (input) INTEGER
! 52: * The dimension of the array WORK. LWORK >= max(1,M).
! 53: * For optimum performance LWORK >= M*NB, where NB is
! 54: * the optimal blocksize.
! 55: *
! 56: * If LWORK = -1, then a workspace query is assumed; the routine
! 57: * only calculates the optimal size of the WORK array, returns
! 58: * this value as the first entry of the WORK array, and no error
! 59: * message related to LWORK is issued by XERBLA.
! 60: *
! 61: * INFO (output) INTEGER
! 62: * = 0: successful exit
! 63: * < 0: if INFO = -i, the i-th argument had an illegal value
! 64: *
! 65: * Further Details
! 66: * ===============
! 67: *
! 68: * The matrix Q is represented as a product of elementary reflectors
! 69: *
! 70: * Q = H(1) H(2) . . . H(k), where k = min(m,n).
! 71: *
! 72: * Each H(i) has the form
! 73: *
! 74: * H(i) = I - tau * v * v'
! 75: *
! 76: * where tau is a real scalar, and v is a real vector with
! 77: * v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
! 78: * A(m-k+i,1:n-k+i-1), and tau in TAU(i).
! 79: *
! 80: * =====================================================================
! 81: *
! 82: * .. Local Scalars ..
! 83: LOGICAL LQUERY
! 84: INTEGER I, IB, IINFO, IWS, K, KI, KK, LDWORK, LWKOPT,
! 85: $ MU, NB, NBMIN, NU, NX
! 86: * ..
! 87: * .. External Subroutines ..
! 88: EXTERNAL DGERQ2, DLARFB, DLARFT, XERBLA
! 89: * ..
! 90: * .. Intrinsic Functions ..
! 91: INTRINSIC MAX, MIN
! 92: * ..
! 93: * .. External Functions ..
! 94: INTEGER ILAENV
! 95: EXTERNAL ILAENV
! 96: * ..
! 97: * .. Executable Statements ..
! 98: *
! 99: * Test the input arguments
! 100: *
! 101: INFO = 0
! 102: LQUERY = ( LWORK.EQ.-1 )
! 103: IF( M.LT.0 ) THEN
! 104: INFO = -1
! 105: ELSE IF( N.LT.0 ) THEN
! 106: INFO = -2
! 107: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 108: INFO = -4
! 109: END IF
! 110: *
! 111: IF( INFO.EQ.0 ) THEN
! 112: K = MIN( M, N )
! 113: IF( K.EQ.0 ) THEN
! 114: LWKOPT = 1
! 115: ELSE
! 116: NB = ILAENV( 1, 'DGERQF', ' ', M, N, -1, -1 )
! 117: LWKOPT = M*NB
! 118: END IF
! 119: WORK( 1 ) = LWKOPT
! 120: *
! 121: IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
! 122: INFO = -7
! 123: END IF
! 124: END IF
! 125: *
! 126: IF( INFO.NE.0 ) THEN
! 127: CALL XERBLA( 'DGERQF', -INFO )
! 128: RETURN
! 129: ELSE IF( LQUERY ) THEN
! 130: RETURN
! 131: END IF
! 132: *
! 133: * Quick return if possible
! 134: *
! 135: IF( K.EQ.0 ) THEN
! 136: RETURN
! 137: END IF
! 138: *
! 139: NBMIN = 2
! 140: NX = 1
! 141: IWS = M
! 142: IF( NB.GT.1 .AND. NB.LT.K ) THEN
! 143: *
! 144: * Determine when to cross over from blocked to unblocked code.
! 145: *
! 146: NX = MAX( 0, ILAENV( 3, 'DGERQF', ' ', M, N, -1, -1 ) )
! 147: IF( NX.LT.K ) THEN
! 148: *
! 149: * Determine if workspace is large enough for blocked code.
! 150: *
! 151: LDWORK = M
! 152: IWS = LDWORK*NB
! 153: IF( LWORK.LT.IWS ) THEN
! 154: *
! 155: * Not enough workspace to use optimal NB: reduce NB and
! 156: * determine the minimum value of NB.
! 157: *
! 158: NB = LWORK / LDWORK
! 159: NBMIN = MAX( 2, ILAENV( 2, 'DGERQF', ' ', M, N, -1,
! 160: $ -1 ) )
! 161: END IF
! 162: END IF
! 163: END IF
! 164: *
! 165: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
! 166: *
! 167: * Use blocked code initially.
! 168: * The last kk rows are handled by the block method.
! 169: *
! 170: KI = ( ( K-NX-1 ) / NB )*NB
! 171: KK = MIN( K, KI+NB )
! 172: *
! 173: DO 10 I = K - KK + KI + 1, K - KK + 1, -NB
! 174: IB = MIN( K-I+1, NB )
! 175: *
! 176: * Compute the RQ factorization of the current block
! 177: * A(m-k+i:m-k+i+ib-1,1:n-k+i+ib-1)
! 178: *
! 179: CALL DGERQ2( IB, N-K+I+IB-1, A( M-K+I, 1 ), LDA, TAU( I ),
! 180: $ WORK, IINFO )
! 181: IF( M-K+I.GT.1 ) THEN
! 182: *
! 183: * Form the triangular factor of the block reflector
! 184: * H = H(i+ib-1) . . . H(i+1) H(i)
! 185: *
! 186: CALL DLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB,
! 187: $ A( M-K+I, 1 ), LDA, TAU( I ), WORK, LDWORK )
! 188: *
! 189: * Apply H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
! 190: *
! 191: CALL DLARFB( 'Right', 'No transpose', 'Backward',
! 192: $ 'Rowwise', M-K+I-1, N-K+I+IB-1, IB,
! 193: $ A( M-K+I, 1 ), LDA, WORK, LDWORK, A, LDA,
! 194: $ WORK( IB+1 ), LDWORK )
! 195: END IF
! 196: 10 CONTINUE
! 197: MU = M - K + I + NB - 1
! 198: NU = N - K + I + NB - 1
! 199: ELSE
! 200: MU = M
! 201: NU = N
! 202: END IF
! 203: *
! 204: * Use unblocked code to factor the last or only block
! 205: *
! 206: IF( MU.GT.0 .AND. NU.GT.0 )
! 207: $ CALL DGERQ2( MU, NU, A, LDA, TAU, WORK, IINFO )
! 208: *
! 209: WORK( 1 ) = IWS
! 210: RETURN
! 211: *
! 212: * End of DGERQF
! 213: *
! 214: END
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