Annotation of rpl/lapack/lapack/zgttrf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, 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, N
! 10: * ..
! 11: * .. Array Arguments ..
! 12: INTEGER IPIV( * )
! 13: COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * ZGTTRF computes an LU factorization of a complex tridiagonal matrix A
! 20: * using elimination with partial pivoting and row interchanges.
! 21: *
! 22: * The factorization has the form
! 23: * A = L * U
! 24: * where L is a product of permutation and unit lower bidiagonal
! 25: * matrices and U is upper triangular with nonzeros in only the main
! 26: * diagonal and first two superdiagonals.
! 27: *
! 28: * Arguments
! 29: * =========
! 30: *
! 31: * N (input) INTEGER
! 32: * The order of the matrix A.
! 33: *
! 34: * DL (input/output) COMPLEX*16 array, dimension (N-1)
! 35: * On entry, DL must contain the (n-1) sub-diagonal elements of
! 36: * A.
! 37: *
! 38: * On exit, DL is overwritten by the (n-1) multipliers that
! 39: * define the matrix L from the LU factorization of A.
! 40: *
! 41: * D (input/output) COMPLEX*16 array, dimension (N)
! 42: * On entry, D must contain the diagonal elements of A.
! 43: *
! 44: * On exit, D is overwritten by the n diagonal elements of the
! 45: * upper triangular matrix U from the LU factorization of A.
! 46: *
! 47: * DU (input/output) COMPLEX*16 array, dimension (N-1)
! 48: * On entry, DU must contain the (n-1) super-diagonal elements
! 49: * of A.
! 50: *
! 51: * On exit, DU is overwritten by the (n-1) elements of the first
! 52: * super-diagonal of U.
! 53: *
! 54: * DU2 (output) COMPLEX*16 array, dimension (N-2)
! 55: * On exit, DU2 is overwritten by the (n-2) elements of the
! 56: * second super-diagonal of U.
! 57: *
! 58: * IPIV (output) INTEGER array, dimension (N)
! 59: * The pivot indices; for 1 <= i <= n, row i of the matrix was
! 60: * interchanged with row IPIV(i). IPIV(i) will always be either
! 61: * i or i+1; IPIV(i) = i indicates a row interchange was not
! 62: * required.
! 63: *
! 64: * INFO (output) INTEGER
! 65: * = 0: successful exit
! 66: * < 0: if INFO = -k, the k-th argument had an illegal value
! 67: * > 0: if INFO = k, U(k,k) is exactly zero. The factorization
! 68: * has been completed, but the factor U is exactly
! 69: * singular, and division by zero will occur if it is used
! 70: * to solve a system of equations.
! 71: *
! 72: * =====================================================================
! 73: *
! 74: * .. Parameters ..
! 75: DOUBLE PRECISION ZERO
! 76: PARAMETER ( ZERO = 0.0D+0 )
! 77: * ..
! 78: * .. Local Scalars ..
! 79: INTEGER I
! 80: COMPLEX*16 FACT, TEMP, ZDUM
! 81: * ..
! 82: * .. External Subroutines ..
! 83: EXTERNAL XERBLA
! 84: * ..
! 85: * .. Intrinsic Functions ..
! 86: INTRINSIC ABS, DBLE, DIMAG
! 87: * ..
! 88: * .. Statement Functions ..
! 89: DOUBLE PRECISION CABS1
! 90: * ..
! 91: * .. Statement Function definitions ..
! 92: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 93: * ..
! 94: * .. Executable Statements ..
! 95: *
! 96: INFO = 0
! 97: IF( N.LT.0 ) THEN
! 98: INFO = -1
! 99: CALL XERBLA( 'ZGTTRF', -INFO )
! 100: RETURN
! 101: END IF
! 102: *
! 103: * Quick return if possible
! 104: *
! 105: IF( N.EQ.0 )
! 106: $ RETURN
! 107: *
! 108: * Initialize IPIV(i) = i and DU2(i) = 0
! 109: *
! 110: DO 10 I = 1, N
! 111: IPIV( I ) = I
! 112: 10 CONTINUE
! 113: DO 20 I = 1, N - 2
! 114: DU2( I ) = ZERO
! 115: 20 CONTINUE
! 116: *
! 117: DO 30 I = 1, N - 2
! 118: IF( CABS1( D( I ) ).GE.CABS1( DL( I ) ) ) THEN
! 119: *
! 120: * No row interchange required, eliminate DL(I)
! 121: *
! 122: IF( CABS1( D( I ) ).NE.ZERO ) THEN
! 123: FACT = DL( I ) / D( I )
! 124: DL( I ) = FACT
! 125: D( I+1 ) = D( I+1 ) - FACT*DU( I )
! 126: END IF
! 127: ELSE
! 128: *
! 129: * Interchange rows I and I+1, eliminate DL(I)
! 130: *
! 131: FACT = D( I ) / DL( I )
! 132: D( I ) = DL( I )
! 133: DL( I ) = FACT
! 134: TEMP = DU( I )
! 135: DU( I ) = D( I+1 )
! 136: D( I+1 ) = TEMP - FACT*D( I+1 )
! 137: DU2( I ) = DU( I+1 )
! 138: DU( I+1 ) = -FACT*DU( I+1 )
! 139: IPIV( I ) = I + 1
! 140: END IF
! 141: 30 CONTINUE
! 142: IF( N.GT.1 ) THEN
! 143: I = N - 1
! 144: IF( CABS1( D( I ) ).GE.CABS1( DL( I ) ) ) THEN
! 145: IF( CABS1( D( I ) ).NE.ZERO ) THEN
! 146: FACT = DL( I ) / D( I )
! 147: DL( I ) = FACT
! 148: D( I+1 ) = D( I+1 ) - FACT*DU( I )
! 149: END IF
! 150: ELSE
! 151: FACT = D( I ) / DL( I )
! 152: D( I ) = DL( I )
! 153: DL( I ) = FACT
! 154: TEMP = DU( I )
! 155: DU( I ) = D( I+1 )
! 156: D( I+1 ) = TEMP - FACT*D( I+1 )
! 157: IPIV( I ) = I + 1
! 158: END IF
! 159: END IF
! 160: *
! 161: * Check for a zero on the diagonal of U.
! 162: *
! 163: DO 40 I = 1, N
! 164: IF( CABS1( D( I ) ).EQ.ZERO ) THEN
! 165: INFO = I
! 166: GO TO 50
! 167: END IF
! 168: 40 CONTINUE
! 169: 50 CONTINUE
! 170: *
! 171: RETURN
! 172: *
! 173: * End of ZGTTRF
! 174: *
! 175: END
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