Annotation of rpl/lapack/lapack/zgetc2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
! 2: *
! 3: * -- LAPACK auxiliary 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, N
! 10: * ..
! 11: * .. Array Arguments ..
! 12: INTEGER IPIV( * ), JPIV( * )
! 13: COMPLEX*16 A( LDA, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * ZGETC2 computes an LU factorization, using complete pivoting, of the
! 20: * n-by-n matrix A. The factorization has the form A = P * L * U * Q,
! 21: * where P and Q are permutation matrices, L is lower triangular with
! 22: * unit diagonal elements and U is upper triangular.
! 23: *
! 24: * This is a level 1 BLAS version of the algorithm.
! 25: *
! 26: * Arguments
! 27: * =========
! 28: *
! 29: * N (input) INTEGER
! 30: * The order of the matrix A. N >= 0.
! 31: *
! 32: * A (input/output) COMPLEX*16 array, dimension (LDA, N)
! 33: * On entry, the n-by-n matrix to be factored.
! 34: * On exit, the factors L and U from the factorization
! 35: * A = P*L*U*Q; the unit diagonal elements of L are not stored.
! 36: * If U(k, k) appears to be less than SMIN, U(k, k) is given the
! 37: * value of SMIN, giving a nonsingular perturbed system.
! 38: *
! 39: * LDA (input) INTEGER
! 40: * The leading dimension of the array A. LDA >= max(1, N).
! 41: *
! 42: * IPIV (output) INTEGER array, dimension (N).
! 43: * The pivot indices; for 1 <= i <= N, row i of the
! 44: * matrix has been interchanged with row IPIV(i).
! 45: *
! 46: * JPIV (output) INTEGER array, dimension (N).
! 47: * The pivot indices; for 1 <= j <= N, column j of the
! 48: * matrix has been interchanged with column JPIV(j).
! 49: *
! 50: * INFO (output) INTEGER
! 51: * = 0: successful exit
! 52: * > 0: if INFO = k, U(k, k) is likely to produce overflow if
! 53: * one tries to solve for x in Ax = b. So U is perturbed
! 54: * to avoid the overflow.
! 55: *
! 56: * Further Details
! 57: * ===============
! 58: *
! 59: * Based on contributions by
! 60: * Bo Kagstrom and Peter Poromaa, Department of Computing Science,
! 61: * Umea University, S-901 87 Umea, Sweden.
! 62: *
! 63: * =====================================================================
! 64: *
! 65: * .. Parameters ..
! 66: DOUBLE PRECISION ZERO, ONE
! 67: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 68: * ..
! 69: * .. Local Scalars ..
! 70: INTEGER I, IP, IPV, J, JP, JPV
! 71: DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX
! 72: * ..
! 73: * .. External Subroutines ..
! 74: EXTERNAL ZGERU, ZSWAP
! 75: * ..
! 76: * .. External Functions ..
! 77: DOUBLE PRECISION DLAMCH
! 78: EXTERNAL DLAMCH
! 79: * ..
! 80: * .. Intrinsic Functions ..
! 81: INTRINSIC ABS, DCMPLX, MAX
! 82: * ..
! 83: * .. Executable Statements ..
! 84: *
! 85: * Set constants to control overflow
! 86: *
! 87: INFO = 0
! 88: EPS = DLAMCH( 'P' )
! 89: SMLNUM = DLAMCH( 'S' ) / EPS
! 90: BIGNUM = ONE / SMLNUM
! 91: CALL DLABAD( SMLNUM, BIGNUM )
! 92: *
! 93: * Factorize A using complete pivoting.
! 94: * Set pivots less than SMIN to SMIN
! 95: *
! 96: DO 40 I = 1, N - 1
! 97: *
! 98: * Find max element in matrix A
! 99: *
! 100: XMAX = ZERO
! 101: DO 20 IP = I, N
! 102: DO 10 JP = I, N
! 103: IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN
! 104: XMAX = ABS( A( IP, JP ) )
! 105: IPV = IP
! 106: JPV = JP
! 107: END IF
! 108: 10 CONTINUE
! 109: 20 CONTINUE
! 110: IF( I.EQ.1 )
! 111: $ SMIN = MAX( EPS*XMAX, SMLNUM )
! 112: *
! 113: * Swap rows
! 114: *
! 115: IF( IPV.NE.I )
! 116: $ CALL ZSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
! 117: IPIV( I ) = IPV
! 118: *
! 119: * Swap columns
! 120: *
! 121: IF( JPV.NE.I )
! 122: $ CALL ZSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 )
! 123: JPIV( I ) = JPV
! 124: *
! 125: * Check for singularity
! 126: *
! 127: IF( ABS( A( I, I ) ).LT.SMIN ) THEN
! 128: INFO = I
! 129: A( I, I ) = DCMPLX( SMIN, ZERO )
! 130: END IF
! 131: DO 30 J = I + 1, N
! 132: A( J, I ) = A( J, I ) / A( I, I )
! 133: 30 CONTINUE
! 134: CALL ZGERU( N-I, N-I, -DCMPLX( ONE ), A( I+1, I ), 1,
! 135: $ A( I, I+1 ), LDA, A( I+1, I+1 ), LDA )
! 136: 40 CONTINUE
! 137: *
! 138: IF( ABS( A( N, N ) ).LT.SMIN ) THEN
! 139: INFO = N
! 140: A( N, N ) = DCMPLX( SMIN, ZERO )
! 141: END IF
! 142: RETURN
! 143: *
! 144: * End of ZGETC2
! 145: *
! 146: END
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