Annotation of rpl/lapack/lapack/dgeqrfp.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * June 2010
! 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: * DGEQRFP computes a QR factorization of a real M-by-N matrix A:
! 19: * A = Q * R.
! 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, the elements on and above the diagonal of the array
! 33: * contain the min(M,N)-by-N upper trapezoidal matrix R (R is
! 34: * upper triangular if m >= n); the elements below the diagonal,
! 35: * with the array TAU, represent the orthogonal matrix Q as a
! 36: * product of min(m,n) elementary reflectors (see Further
! 37: * Details).
! 38: *
! 39: * LDA (input) INTEGER
! 40: * The leading dimension of the array A. LDA >= max(1,M).
! 41: *
! 42: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
! 43: * The scalar factors of the elementary reflectors (see Further
! 44: * Details).
! 45: *
! 46: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 47: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 48: *
! 49: * LWORK (input) INTEGER
! 50: * The dimension of the array WORK. LWORK >= max(1,N).
! 51: * For optimum performance LWORK >= N*NB, where NB is
! 52: * the optimal blocksize.
! 53: *
! 54: * If LWORK = -1, then a workspace query is assumed; the routine
! 55: * only calculates the optimal size of the WORK array, returns
! 56: * this value as the first entry of the WORK array, and no error
! 57: * message related to LWORK is issued by XERBLA.
! 58: *
! 59: * INFO (output) INTEGER
! 60: * = 0: successful exit
! 61: * < 0: if INFO = -i, the i-th argument had an illegal value
! 62: *
! 63: * Further Details
! 64: * ===============
! 65: *
! 66: * The matrix Q is represented as a product of elementary reflectors
! 67: *
! 68: * Q = H(1) H(2) . . . H(k), where k = min(m,n).
! 69: *
! 70: * Each H(i) has the form
! 71: *
! 72: * H(i) = I - tau * v * v'
! 73: *
! 74: * where tau is a real scalar, and v is a real vector with
! 75: * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
! 76: * and tau in TAU(i).
! 77: *
! 78: * =====================================================================
! 79: *
! 80: * .. Local Scalars ..
! 81: LOGICAL LQUERY
! 82: INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB,
! 83: $ NBMIN, NX
! 84: * ..
! 85: * .. External Subroutines ..
! 86: EXTERNAL DGEQR2P, DLARFB, DLARFT, XERBLA
! 87: * ..
! 88: * .. Intrinsic Functions ..
! 89: INTRINSIC MAX, MIN
! 90: * ..
! 91: * .. External Functions ..
! 92: INTEGER ILAENV
! 93: EXTERNAL ILAENV
! 94: * ..
! 95: * .. Executable Statements ..
! 96: *
! 97: * Test the input arguments
! 98: *
! 99: INFO = 0
! 100: NB = ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
! 101: LWKOPT = N*NB
! 102: WORK( 1 ) = LWKOPT
! 103: LQUERY = ( LWORK.EQ.-1 )
! 104: IF( M.LT.0 ) THEN
! 105: INFO = -1
! 106: ELSE IF( N.LT.0 ) THEN
! 107: INFO = -2
! 108: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 109: INFO = -4
! 110: ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
! 111: INFO = -7
! 112: END IF
! 113: IF( INFO.NE.0 ) THEN
! 114: CALL XERBLA( 'DGEQRFP', -INFO )
! 115: RETURN
! 116: ELSE IF( LQUERY ) THEN
! 117: RETURN
! 118: END IF
! 119: *
! 120: * Quick return if possible
! 121: *
! 122: K = MIN( M, N )
! 123: IF( K.EQ.0 ) THEN
! 124: WORK( 1 ) = 1
! 125: RETURN
! 126: END IF
! 127: *
! 128: NBMIN = 2
! 129: NX = 0
! 130: IWS = N
! 131: IF( NB.GT.1 .AND. NB.LT.K ) THEN
! 132: *
! 133: * Determine when to cross over from blocked to unblocked code.
! 134: *
! 135: NX = MAX( 0, ILAENV( 3, 'DGEQRF', ' ', M, N, -1, -1 ) )
! 136: IF( NX.LT.K ) THEN
! 137: *
! 138: * Determine if workspace is large enough for blocked code.
! 139: *
! 140: LDWORK = N
! 141: IWS = LDWORK*NB
! 142: IF( LWORK.LT.IWS ) THEN
! 143: *
! 144: * Not enough workspace to use optimal NB: reduce NB and
! 145: * determine the minimum value of NB.
! 146: *
! 147: NB = LWORK / LDWORK
! 148: NBMIN = MAX( 2, ILAENV( 2, 'DGEQRF', ' ', M, N, -1,
! 149: $ -1 ) )
! 150: END IF
! 151: END IF
! 152: END IF
! 153: *
! 154: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
! 155: *
! 156: * Use blocked code initially
! 157: *
! 158: DO 10 I = 1, K - NX, NB
! 159: IB = MIN( K-I+1, NB )
! 160: *
! 161: * Compute the QR factorization of the current block
! 162: * A(i:m,i:i+ib-1)
! 163: *
! 164: CALL DGEQR2P( M-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
! 165: $ IINFO )
! 166: IF( I+IB.LE.N ) THEN
! 167: *
! 168: * Form the triangular factor of the block reflector
! 169: * H = H(i) H(i+1) . . . H(i+ib-1)
! 170: *
! 171: CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
! 172: $ A( I, I ), LDA, TAU( I ), WORK, LDWORK )
! 173: *
! 174: * Apply H' to A(i:m,i+ib:n) from the left
! 175: *
! 176: CALL DLARFB( 'Left', 'Transpose', 'Forward',
! 177: $ 'Columnwise', M-I+1, N-I-IB+1, IB,
! 178: $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
! 179: $ LDA, WORK( IB+1 ), LDWORK )
! 180: END IF
! 181: 10 CONTINUE
! 182: ELSE
! 183: I = 1
! 184: END IF
! 185: *
! 186: * Use unblocked code to factor the last or only block.
! 187: *
! 188: IF( I.LE.K )
! 189: $ CALL DGEQR2P( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
! 190: $ IINFO )
! 191: *
! 192: WORK( 1 ) = IWS
! 193: RETURN
! 194: *
! 195: * End of DGEQRFP
! 196: *
! 197: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dgeqrfp.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack