Annotation of rpl/lapack/lapack/zgeqpf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, 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 RWORK( * )
! 14: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * This routine is deprecated and has been replaced by routine ZGEQP3.
! 21: *
! 22: * ZGEQPF computes a QR factorization with column pivoting of a
! 23: * complex M-by-N matrix A: A*P = Q*R.
! 24: *
! 25: * Arguments
! 26: * =========
! 27: *
! 28: * M (input) INTEGER
! 29: * The number of rows of the matrix A. M >= 0.
! 30: *
! 31: * N (input) INTEGER
! 32: * The number of columns of the matrix A. N >= 0
! 33: *
! 34: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 35: * On entry, the M-by-N matrix A.
! 36: * On exit, the upper triangle of the array contains the
! 37: * min(M,N)-by-N upper triangular matrix R; the elements
! 38: * below the diagonal, together with the array TAU,
! 39: * represent the unitary matrix Q as a product of
! 40: * min(m,n) elementary reflectors.
! 41: *
! 42: * LDA (input) INTEGER
! 43: * The leading dimension of the array A. LDA >= max(1,M).
! 44: *
! 45: * JPVT (input/output) INTEGER array, dimension (N)
! 46: * On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
! 47: * to the front of A*P (a leading column); if JPVT(i) = 0,
! 48: * the i-th column of A is a free column.
! 49: * On exit, if JPVT(i) = k, then the i-th column of A*P
! 50: * was the k-th column of A.
! 51: *
! 52: * TAU (output) COMPLEX*16 array, dimension (min(M,N))
! 53: * The scalar factors of the elementary reflectors.
! 54: *
! 55: * WORK (workspace) COMPLEX*16 array, dimension (N)
! 56: *
! 57: * RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
! 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(n)
! 69: *
! 70: * Each H(i) has the form
! 71: *
! 72: * H = I - tau * v * v'
! 73: *
! 74: * where tau is a complex scalar, and v is a complex 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: *
! 77: * The matrix P is represented in jpvt as follows: If
! 78: * jpvt(j) = i
! 79: * then the jth column of P is the ith canonical unit vector.
! 80: *
! 81: * Partial column norm updating strategy modified by
! 82: * Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
! 83: * University of Zagreb, Croatia.
! 84: * June 2006.
! 85: * For more details see LAPACK Working Note 176.
! 86: *
! 87: * =====================================================================
! 88: *
! 89: * .. Parameters ..
! 90: DOUBLE PRECISION ZERO, ONE
! 91: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 92: * ..
! 93: * .. Local Scalars ..
! 94: INTEGER I, ITEMP, J, MA, MN, PVT
! 95: DOUBLE PRECISION TEMP, TEMP2, TOL3Z
! 96: COMPLEX*16 AII
! 97: * ..
! 98: * .. External Subroutines ..
! 99: EXTERNAL XERBLA, ZGEQR2, ZLARF, ZLARFP, ZSWAP, ZUNM2R
! 100: * ..
! 101: * .. Intrinsic Functions ..
! 102: INTRINSIC ABS, DCMPLX, DCONJG, MAX, MIN, SQRT
! 103: * ..
! 104: * .. External Functions ..
! 105: INTEGER IDAMAX
! 106: DOUBLE PRECISION DLAMCH, DZNRM2
! 107: EXTERNAL IDAMAX, DLAMCH, DZNRM2
! 108: * ..
! 109: * .. Executable Statements ..
! 110: *
! 111: * Test the input arguments
! 112: *
! 113: INFO = 0
! 114: IF( M.LT.0 ) THEN
! 115: INFO = -1
! 116: ELSE IF( N.LT.0 ) THEN
! 117: INFO = -2
! 118: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 119: INFO = -4
! 120: END IF
! 121: IF( INFO.NE.0 ) THEN
! 122: CALL XERBLA( 'ZGEQPF', -INFO )
! 123: RETURN
! 124: END IF
! 125: *
! 126: MN = MIN( M, N )
! 127: TOL3Z = SQRT(DLAMCH('Epsilon'))
! 128: *
! 129: * Move initial columns up front
! 130: *
! 131: ITEMP = 1
! 132: DO 10 I = 1, N
! 133: IF( JPVT( I ).NE.0 ) THEN
! 134: IF( I.NE.ITEMP ) THEN
! 135: CALL ZSWAP( M, A( 1, I ), 1, A( 1, ITEMP ), 1 )
! 136: JPVT( I ) = JPVT( ITEMP )
! 137: JPVT( ITEMP ) = I
! 138: ELSE
! 139: JPVT( I ) = I
! 140: END IF
! 141: ITEMP = ITEMP + 1
! 142: ELSE
! 143: JPVT( I ) = I
! 144: END IF
! 145: 10 CONTINUE
! 146: ITEMP = ITEMP - 1
! 147: *
! 148: * Compute the QR factorization and update remaining columns
! 149: *
! 150: IF( ITEMP.GT.0 ) THEN
! 151: MA = MIN( ITEMP, M )
! 152: CALL ZGEQR2( M, MA, A, LDA, TAU, WORK, INFO )
! 153: IF( MA.LT.N ) THEN
! 154: CALL ZUNM2R( 'Left', 'Conjugate transpose', M, N-MA, MA, A,
! 155: $ LDA, TAU, A( 1, MA+1 ), LDA, WORK, INFO )
! 156: END IF
! 157: END IF
! 158: *
! 159: IF( ITEMP.LT.MN ) THEN
! 160: *
! 161: * Initialize partial column norms. The first n elements of
! 162: * work store the exact column norms.
! 163: *
! 164: DO 20 I = ITEMP + 1, N
! 165: RWORK( I ) = DZNRM2( M-ITEMP, A( ITEMP+1, I ), 1 )
! 166: RWORK( N+I ) = RWORK( I )
! 167: 20 CONTINUE
! 168: *
! 169: * Compute factorization
! 170: *
! 171: DO 40 I = ITEMP + 1, MN
! 172: *
! 173: * Determine ith pivot column and swap if necessary
! 174: *
! 175: PVT = ( I-1 ) + IDAMAX( N-I+1, RWORK( I ), 1 )
! 176: *
! 177: IF( PVT.NE.I ) THEN
! 178: CALL ZSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 )
! 179: ITEMP = JPVT( PVT )
! 180: JPVT( PVT ) = JPVT( I )
! 181: JPVT( I ) = ITEMP
! 182: RWORK( PVT ) = RWORK( I )
! 183: RWORK( N+PVT ) = RWORK( N+I )
! 184: END IF
! 185: *
! 186: * Generate elementary reflector H(i)
! 187: *
! 188: AII = A( I, I )
! 189: CALL ZLARFP( M-I+1, AII, A( MIN( I+1, M ), I ), 1,
! 190: $ TAU( I ) )
! 191: A( I, I ) = AII
! 192: *
! 193: IF( I.LT.N ) THEN
! 194: *
! 195: * Apply H(i) to A(i:m,i+1:n) from the left
! 196: *
! 197: AII = A( I, I )
! 198: A( I, I ) = DCMPLX( ONE )
! 199: CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
! 200: $ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
! 201: A( I, I ) = AII
! 202: END IF
! 203: *
! 204: * Update partial column norms
! 205: *
! 206: DO 30 J = I + 1, N
! 207: IF( RWORK( J ).NE.ZERO ) THEN
! 208: *
! 209: * NOTE: The following 4 lines follow from the analysis in
! 210: * Lapack Working Note 176.
! 211: *
! 212: TEMP = ABS( A( I, J ) ) / RWORK( J )
! 213: TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) )
! 214: TEMP2 = TEMP*( RWORK( J ) / RWORK( N+J ) )**2
! 215: IF( TEMP2 .LE. TOL3Z ) THEN
! 216: IF( M-I.GT.0 ) THEN
! 217: RWORK( J ) = DZNRM2( M-I, A( I+1, J ), 1 )
! 218: RWORK( N+J ) = RWORK( J )
! 219: ELSE
! 220: RWORK( J ) = ZERO
! 221: RWORK( N+J ) = ZERO
! 222: END IF
! 223: ELSE
! 224: RWORK( J ) = RWORK( J )*SQRT( TEMP )
! 225: END IF
! 226: END IF
! 227: 30 CONTINUE
! 228: *
! 229: 40 CONTINUE
! 230: END IF
! 231: RETURN
! 232: *
! 233: * End of ZGEQPF
! 234: *
! 235: END
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