Annotation of rpl/lapack/lapack/zpttrf.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPTTRF( N, D, E, 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: DOUBLE PRECISION D( * )
! 13: COMPLEX*16 E( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * ZPTTRF computes the L*D*L' factorization of a complex Hermitian
! 20: * positive definite tridiagonal matrix A. The factorization may also
! 21: * be regarded as having the form A = U'*D*U.
! 22: *
! 23: * Arguments
! 24: * =========
! 25: *
! 26: * N (input) INTEGER
! 27: * The order of the matrix A. N >= 0.
! 28: *
! 29: * D (input/output) DOUBLE PRECISION array, dimension (N)
! 30: * On entry, the n diagonal elements of the tridiagonal matrix
! 31: * A. On exit, the n diagonal elements of the diagonal matrix
! 32: * D from the L*D*L' factorization of A.
! 33: *
! 34: * E (input/output) COMPLEX*16 array, dimension (N-1)
! 35: * On entry, the (n-1) subdiagonal elements of the tridiagonal
! 36: * matrix A. On exit, the (n-1) subdiagonal elements of the
! 37: * unit bidiagonal factor L from the L*D*L' factorization of A.
! 38: * E can also be regarded as the superdiagonal of the unit
! 39: * bidiagonal factor U from the U'*D*U factorization of A.
! 40: *
! 41: * INFO (output) INTEGER
! 42: * = 0: successful exit
! 43: * < 0: if INFO = -k, the k-th argument had an illegal value
! 44: * > 0: if INFO = k, the leading minor of order k is not
! 45: * positive definite; if k < N, the factorization could not
! 46: * be completed, while if k = N, the factorization was
! 47: * completed, but D(N) <= 0.
! 48: *
! 49: * =====================================================================
! 50: *
! 51: * .. Parameters ..
! 52: DOUBLE PRECISION ZERO
! 53: PARAMETER ( ZERO = 0.0D+0 )
! 54: * ..
! 55: * .. Local Scalars ..
! 56: INTEGER I, I4
! 57: DOUBLE PRECISION EII, EIR, F, G
! 58: * ..
! 59: * .. External Subroutines ..
! 60: EXTERNAL XERBLA
! 61: * ..
! 62: * .. Intrinsic Functions ..
! 63: INTRINSIC DBLE, DCMPLX, DIMAG, MOD
! 64: * ..
! 65: * .. Executable Statements ..
! 66: *
! 67: * Test the input parameters.
! 68: *
! 69: INFO = 0
! 70: IF( N.LT.0 ) THEN
! 71: INFO = -1
! 72: CALL XERBLA( 'ZPTTRF', -INFO )
! 73: RETURN
! 74: END IF
! 75: *
! 76: * Quick return if possible
! 77: *
! 78: IF( N.EQ.0 )
! 79: $ RETURN
! 80: *
! 81: * Compute the L*D*L' (or U'*D*U) factorization of A.
! 82: *
! 83: I4 = MOD( N-1, 4 )
! 84: DO 10 I = 1, I4
! 85: IF( D( I ).LE.ZERO ) THEN
! 86: INFO = I
! 87: GO TO 30
! 88: END IF
! 89: EIR = DBLE( E( I ) )
! 90: EII = DIMAG( E( I ) )
! 91: F = EIR / D( I )
! 92: G = EII / D( I )
! 93: E( I ) = DCMPLX( F, G )
! 94: D( I+1 ) = D( I+1 ) - F*EIR - G*EII
! 95: 10 CONTINUE
! 96: *
! 97: DO 20 I = I4 + 1, N - 4, 4
! 98: *
! 99: * Drop out of the loop if d(i) <= 0: the matrix is not positive
! 100: * definite.
! 101: *
! 102: IF( D( I ).LE.ZERO ) THEN
! 103: INFO = I
! 104: GO TO 30
! 105: END IF
! 106: *
! 107: * Solve for e(i) and d(i+1).
! 108: *
! 109: EIR = DBLE( E( I ) )
! 110: EII = DIMAG( E( I ) )
! 111: F = EIR / D( I )
! 112: G = EII / D( I )
! 113: E( I ) = DCMPLX( F, G )
! 114: D( I+1 ) = D( I+1 ) - F*EIR - G*EII
! 115: *
! 116: IF( D( I+1 ).LE.ZERO ) THEN
! 117: INFO = I + 1
! 118: GO TO 30
! 119: END IF
! 120: *
! 121: * Solve for e(i+1) and d(i+2).
! 122: *
! 123: EIR = DBLE( E( I+1 ) )
! 124: EII = DIMAG( E( I+1 ) )
! 125: F = EIR / D( I+1 )
! 126: G = EII / D( I+1 )
! 127: E( I+1 ) = DCMPLX( F, G )
! 128: D( I+2 ) = D( I+2 ) - F*EIR - G*EII
! 129: *
! 130: IF( D( I+2 ).LE.ZERO ) THEN
! 131: INFO = I + 2
! 132: GO TO 30
! 133: END IF
! 134: *
! 135: * Solve for e(i+2) and d(i+3).
! 136: *
! 137: EIR = DBLE( E( I+2 ) )
! 138: EII = DIMAG( E( I+2 ) )
! 139: F = EIR / D( I+2 )
! 140: G = EII / D( I+2 )
! 141: E( I+2 ) = DCMPLX( F, G )
! 142: D( I+3 ) = D( I+3 ) - F*EIR - G*EII
! 143: *
! 144: IF( D( I+3 ).LE.ZERO ) THEN
! 145: INFO = I + 3
! 146: GO TO 30
! 147: END IF
! 148: *
! 149: * Solve for e(i+3) and d(i+4).
! 150: *
! 151: EIR = DBLE( E( I+3 ) )
! 152: EII = DIMAG( E( I+3 ) )
! 153: F = EIR / D( I+3 )
! 154: G = EII / D( I+3 )
! 155: E( I+3 ) = DCMPLX( F, G )
! 156: D( I+4 ) = D( I+4 ) - F*EIR - G*EII
! 157: 20 CONTINUE
! 158: *
! 159: * Check d(n) for positive definiteness.
! 160: *
! 161: IF( D( N ).LE.ZERO )
! 162: $ INFO = N
! 163: *
! 164: 30 CONTINUE
! 165: RETURN
! 166: *
! 167: * End of ZPTTRF
! 168: *
! 169: END
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