Annotation of rpl/lapack/lapack/dgttrf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGTTRF( 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: DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DGTTRF computes an LU factorization of a real 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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: DOUBLE PRECISION FACT, TEMP
! 81: * ..
! 82: * .. Intrinsic Functions ..
! 83: INTRINSIC ABS
! 84: * ..
! 85: * .. External Subroutines ..
! 86: EXTERNAL XERBLA
! 87: * ..
! 88: * .. Executable Statements ..
! 89: *
! 90: INFO = 0
! 91: IF( N.LT.0 ) THEN
! 92: INFO = -1
! 93: CALL XERBLA( 'DGTTRF', -INFO )
! 94: RETURN
! 95: END IF
! 96: *
! 97: * Quick return if possible
! 98: *
! 99: IF( N.EQ.0 )
! 100: $ RETURN
! 101: *
! 102: * Initialize IPIV(i) = i and DU2(I) = 0
! 103: *
! 104: DO 10 I = 1, N
! 105: IPIV( I ) = I
! 106: 10 CONTINUE
! 107: DO 20 I = 1, N - 2
! 108: DU2( I ) = ZERO
! 109: 20 CONTINUE
! 110: *
! 111: DO 30 I = 1, N - 2
! 112: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
! 113: *
! 114: * No row interchange required, eliminate DL(I)
! 115: *
! 116: IF( D( I ).NE.ZERO ) THEN
! 117: FACT = DL( I ) / D( I )
! 118: DL( I ) = FACT
! 119: D( I+1 ) = D( I+1 ) - FACT*DU( I )
! 120: END IF
! 121: ELSE
! 122: *
! 123: * Interchange rows I and I+1, eliminate DL(I)
! 124: *
! 125: FACT = D( I ) / DL( I )
! 126: D( I ) = DL( I )
! 127: DL( I ) = FACT
! 128: TEMP = DU( I )
! 129: DU( I ) = D( I+1 )
! 130: D( I+1 ) = TEMP - FACT*D( I+1 )
! 131: DU2( I ) = DU( I+1 )
! 132: DU( I+1 ) = -FACT*DU( I+1 )
! 133: IPIV( I ) = I + 1
! 134: END IF
! 135: 30 CONTINUE
! 136: IF( N.GT.1 ) THEN
! 137: I = N - 1
! 138: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
! 139: IF( D( I ).NE.ZERO ) THEN
! 140: FACT = DL( I ) / D( I )
! 141: DL( I ) = FACT
! 142: D( I+1 ) = D( I+1 ) - FACT*DU( I )
! 143: END IF
! 144: ELSE
! 145: FACT = D( I ) / DL( I )
! 146: D( I ) = DL( I )
! 147: DL( I ) = FACT
! 148: TEMP = DU( I )
! 149: DU( I ) = D( I+1 )
! 150: D( I+1 ) = TEMP - FACT*D( I+1 )
! 151: IPIV( I ) = I + 1
! 152: END IF
! 153: END IF
! 154: *
! 155: * Check for a zero on the diagonal of U.
! 156: *
! 157: DO 40 I = 1, N
! 158: IF( D( I ).EQ.ZERO ) THEN
! 159: INFO = I
! 160: GO TO 50
! 161: END IF
! 162: 40 CONTINUE
! 163: 50 CONTINUE
! 164: *
! 165: RETURN
! 166: *
! 167: * End of DGTTRF
! 168: *
! 169: END
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