Annotation of rpl/lapack/lapack/dgeqpf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
! 2: *
! 3: * -- LAPACK deprecated driver 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, M, N
! 10: * ..
! 11: * .. Array Arguments ..
! 12: INTEGER JPVT( * )
! 13: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * This routine is deprecated and has been replaced by routine DGEQP3.
! 20: *
! 21: * DGEQPF computes a QR factorization with column pivoting of a
! 22: * real M-by-N matrix A: A*P = Q*R.
! 23: *
! 24: * Arguments
! 25: * =========
! 26: *
! 27: * M (input) INTEGER
! 28: * The number of rows of the matrix A. M >= 0.
! 29: *
! 30: * N (input) INTEGER
! 31: * The number of columns of the matrix A. N >= 0
! 32: *
! 33: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
! 34: * On entry, the M-by-N matrix A.
! 35: * On exit, the upper triangle of the array contains the
! 36: * min(M,N)-by-N upper triangular matrix R; the elements
! 37: * below the diagonal, together with the array TAU,
! 38: * represent the orthogonal matrix Q as a product of
! 39: * min(m,n) elementary reflectors.
! 40: *
! 41: * LDA (input) INTEGER
! 42: * The leading dimension of the array A. LDA >= max(1,M).
! 43: *
! 44: * JPVT (input/output) INTEGER array, dimension (N)
! 45: * On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
! 46: * to the front of A*P (a leading column); if JPVT(i) = 0,
! 47: * the i-th column of A is a free column.
! 48: * On exit, if JPVT(i) = k, then the i-th column of A*P
! 49: * was the k-th column of A.
! 50: *
! 51: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
! 52: * The scalar factors of the elementary reflectors.
! 53: *
! 54: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
! 55: *
! 56: * INFO (output) INTEGER
! 57: * = 0: successful exit
! 58: * < 0: if INFO = -i, the i-th argument had an illegal value
! 59: *
! 60: * Further Details
! 61: * ===============
! 62: *
! 63: * The matrix Q is represented as a product of elementary reflectors
! 64: *
! 65: * Q = H(1) H(2) . . . H(n)
! 66: *
! 67: * Each H(i) has the form
! 68: *
! 69: * H = I - tau * v * v'
! 70: *
! 71: * where tau is a real scalar, and v is a real vector with
! 72: * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
! 73: *
! 74: * The matrix P is represented in jpvt as follows: If
! 75: * jpvt(j) = i
! 76: * then the jth column of P is the ith canonical unit vector.
! 77: *
! 78: * Partial column norm updating strategy modified by
! 79: * Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
! 80: * University of Zagreb, Croatia.
! 81: * June 2006.
! 82: * For more details see LAPACK Working Note 176.
! 83: *
! 84: * =====================================================================
! 85: *
! 86: * .. Parameters ..
! 87: DOUBLE PRECISION ZERO, ONE
! 88: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 89: * ..
! 90: * .. Local Scalars ..
! 91: INTEGER I, ITEMP, J, MA, MN, PVT
! 92: DOUBLE PRECISION AII, TEMP, TEMP2, TOL3Z
! 93: * ..
! 94: * .. External Subroutines ..
! 95: EXTERNAL DGEQR2, DLARF, DLARFP, DORM2R, DSWAP, XERBLA
! 96: * ..
! 97: * .. Intrinsic Functions ..
! 98: INTRINSIC ABS, MAX, MIN, SQRT
! 99: * ..
! 100: * .. External Functions ..
! 101: INTEGER IDAMAX
! 102: DOUBLE PRECISION DLAMCH, DNRM2
! 103: EXTERNAL IDAMAX, DLAMCH, DNRM2
! 104: * ..
! 105: * .. Executable Statements ..
! 106: *
! 107: * Test the input arguments
! 108: *
! 109: INFO = 0
! 110: IF( M.LT.0 ) THEN
! 111: INFO = -1
! 112: ELSE IF( N.LT.0 ) THEN
! 113: INFO = -2
! 114: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 115: INFO = -4
! 116: END IF
! 117: IF( INFO.NE.0 ) THEN
! 118: CALL XERBLA( 'DGEQPF', -INFO )
! 119: RETURN
! 120: END IF
! 121: *
! 122: MN = MIN( M, N )
! 123: TOL3Z = SQRT(DLAMCH('Epsilon'))
! 124: *
! 125: * Move initial columns up front
! 126: *
! 127: ITEMP = 1
! 128: DO 10 I = 1, N
! 129: IF( JPVT( I ).NE.0 ) THEN
! 130: IF( I.NE.ITEMP ) THEN
! 131: CALL DSWAP( M, A( 1, I ), 1, A( 1, ITEMP ), 1 )
! 132: JPVT( I ) = JPVT( ITEMP )
! 133: JPVT( ITEMP ) = I
! 134: ELSE
! 135: JPVT( I ) = I
! 136: END IF
! 137: ITEMP = ITEMP + 1
! 138: ELSE
! 139: JPVT( I ) = I
! 140: END IF
! 141: 10 CONTINUE
! 142: ITEMP = ITEMP - 1
! 143: *
! 144: * Compute the QR factorization and update remaining columns
! 145: *
! 146: IF( ITEMP.GT.0 ) THEN
! 147: MA = MIN( ITEMP, M )
! 148: CALL DGEQR2( M, MA, A, LDA, TAU, WORK, INFO )
! 149: IF( MA.LT.N ) THEN
! 150: CALL DORM2R( 'Left', 'Transpose', M, N-MA, MA, A, LDA, TAU,
! 151: $ A( 1, MA+1 ), LDA, WORK, INFO )
! 152: END IF
! 153: END IF
! 154: *
! 155: IF( ITEMP.LT.MN ) THEN
! 156: *
! 157: * Initialize partial column norms. The first n elements of
! 158: * work store the exact column norms.
! 159: *
! 160: DO 20 I = ITEMP + 1, N
! 161: WORK( I ) = DNRM2( M-ITEMP, A( ITEMP+1, I ), 1 )
! 162: WORK( N+I ) = WORK( I )
! 163: 20 CONTINUE
! 164: *
! 165: * Compute factorization
! 166: *
! 167: DO 40 I = ITEMP + 1, MN
! 168: *
! 169: * Determine ith pivot column and swap if necessary
! 170: *
! 171: PVT = ( I-1 ) + IDAMAX( N-I+1, WORK( I ), 1 )
! 172: *
! 173: IF( PVT.NE.I ) THEN
! 174: CALL DSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 )
! 175: ITEMP = JPVT( PVT )
! 176: JPVT( PVT ) = JPVT( I )
! 177: JPVT( I ) = ITEMP
! 178: WORK( PVT ) = WORK( I )
! 179: WORK( N+PVT ) = WORK( N+I )
! 180: END IF
! 181: *
! 182: * Generate elementary reflector H(i)
! 183: *
! 184: IF( I.LT.M ) THEN
! 185: CALL DLARFP( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) )
! 186: ELSE
! 187: CALL DLARFP( 1, A( M, M ), A( M, M ), 1, TAU( M ) )
! 188: END IF
! 189: *
! 190: IF( I.LT.N ) THEN
! 191: *
! 192: * Apply H(i) to A(i:m,i+1:n) from the left
! 193: *
! 194: AII = A( I, I )
! 195: A( I, I ) = ONE
! 196: CALL DLARF( 'LEFT', M-I+1, N-I, A( I, I ), 1, TAU( I ),
! 197: $ A( I, I+1 ), LDA, WORK( 2*N+1 ) )
! 198: A( I, I ) = AII
! 199: END IF
! 200: *
! 201: * Update partial column norms
! 202: *
! 203: DO 30 J = I + 1, N
! 204: IF( WORK( J ).NE.ZERO ) THEN
! 205: *
! 206: * NOTE: The following 4 lines follow from the analysis in
! 207: * Lapack Working Note 176.
! 208: *
! 209: TEMP = ABS( A( I, J ) ) / WORK( J )
! 210: TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) )
! 211: TEMP2 = TEMP*( WORK( J ) / WORK( N+J ) )**2
! 212: IF( TEMP2 .LE. TOL3Z ) THEN
! 213: IF( M-I.GT.0 ) THEN
! 214: WORK( J ) = DNRM2( M-I, A( I+1, J ), 1 )
! 215: WORK( N+J ) = WORK( J )
! 216: ELSE
! 217: WORK( J ) = ZERO
! 218: WORK( N+J ) = ZERO
! 219: END IF
! 220: ELSE
! 221: WORK( J ) = WORK( J )*SQRT( TEMP )
! 222: END IF
! 223: END IF
! 224: 30 CONTINUE
! 225: *
! 226: 40 CONTINUE
! 227: END IF
! 228: RETURN
! 229: *
! 230: * End of DGEQPF
! 231: *
! 232: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dgeqpf.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack