Annotation of rpl/lapack/lapack/zgtsv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, 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, LDB, N, NRHS
! 10: * ..
! 11: * .. Array Arguments ..
! 12: COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * )
! 13: * ..
! 14: *
! 15: * Purpose
! 16: * =======
! 17: *
! 18: * ZGTSV solves the equation
! 19: *
! 20: * A*X = B,
! 21: *
! 22: * where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
! 23: * partial pivoting.
! 24: *
! 25: * Note that the equation A'*X = B may be solved by interchanging the
! 26: * order of the arguments DU and DL.
! 27: *
! 28: * Arguments
! 29: * =========
! 30: *
! 31: * N (input) INTEGER
! 32: * The order of the matrix A. N >= 0.
! 33: *
! 34: * NRHS (input) INTEGER
! 35: * The number of right hand sides, i.e., the number of columns
! 36: * of the matrix B. NRHS >= 0.
! 37: *
! 38: * DL (input/output) COMPLEX*16 array, dimension (N-1)
! 39: * On entry, DL must contain the (n-1) subdiagonal elements of
! 40: * A.
! 41: * On exit, DL is overwritten by the (n-2) elements of the
! 42: * second superdiagonal of the upper triangular matrix U from
! 43: * the LU factorization of A, in DL(1), ..., DL(n-2).
! 44: *
! 45: * D (input/output) COMPLEX*16 array, dimension (N)
! 46: * On entry, D must contain the diagonal elements of A.
! 47: * On exit, D is overwritten by the n diagonal elements of U.
! 48: *
! 49: * DU (input/output) COMPLEX*16 array, dimension (N-1)
! 50: * On entry, DU must contain the (n-1) superdiagonal elements
! 51: * of A.
! 52: * On exit, DU is overwritten by the (n-1) elements of the first
! 53: * superdiagonal of U.
! 54: *
! 55: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
! 56: * On entry, the N-by-NRHS right hand side matrix B.
! 57: * On exit, if INFO = 0, the N-by-NRHS solution matrix X.
! 58: *
! 59: * LDB (input) INTEGER
! 60: * The leading dimension of the array B. LDB >= max(1,N).
! 61: *
! 62: * INFO (output) INTEGER
! 63: * = 0: successful exit
! 64: * < 0: if INFO = -i, the i-th argument had an illegal value
! 65: * > 0: if INFO = i, U(i,i) is exactly zero, and the solution
! 66: * has not been computed. The factorization has not been
! 67: * completed unless i = N.
! 68: *
! 69: * =====================================================================
! 70: *
! 71: * .. Parameters ..
! 72: COMPLEX*16 ZERO
! 73: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
! 74: * ..
! 75: * .. Local Scalars ..
! 76: INTEGER J, K
! 77: COMPLEX*16 MULT, TEMP, ZDUM
! 78: * ..
! 79: * .. Intrinsic Functions ..
! 80: INTRINSIC ABS, DBLE, DIMAG, MAX
! 81: * ..
! 82: * .. External Subroutines ..
! 83: EXTERNAL XERBLA
! 84: * ..
! 85: * .. Statement Functions ..
! 86: DOUBLE PRECISION CABS1
! 87: * ..
! 88: * .. Statement Function definitions ..
! 89: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 90: * ..
! 91: * .. Executable Statements ..
! 92: *
! 93: INFO = 0
! 94: IF( N.LT.0 ) THEN
! 95: INFO = -1
! 96: ELSE IF( NRHS.LT.0 ) THEN
! 97: INFO = -2
! 98: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 99: INFO = -7
! 100: END IF
! 101: IF( INFO.NE.0 ) THEN
! 102: CALL XERBLA( 'ZGTSV ', -INFO )
! 103: RETURN
! 104: END IF
! 105: *
! 106: IF( N.EQ.0 )
! 107: $ RETURN
! 108: *
! 109: DO 30 K = 1, N - 1
! 110: IF( DL( K ).EQ.ZERO ) THEN
! 111: *
! 112: * Subdiagonal is zero, no elimination is required.
! 113: *
! 114: IF( D( K ).EQ.ZERO ) THEN
! 115: *
! 116: * Diagonal is zero: set INFO = K and return; a unique
! 117: * solution can not be found.
! 118: *
! 119: INFO = K
! 120: RETURN
! 121: END IF
! 122: ELSE IF( CABS1( D( K ) ).GE.CABS1( DL( K ) ) ) THEN
! 123: *
! 124: * No row interchange required
! 125: *
! 126: MULT = DL( K ) / D( K )
! 127: D( K+1 ) = D( K+1 ) - MULT*DU( K )
! 128: DO 10 J = 1, NRHS
! 129: B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
! 130: 10 CONTINUE
! 131: IF( K.LT.( N-1 ) )
! 132: $ DL( K ) = ZERO
! 133: ELSE
! 134: *
! 135: * Interchange rows K and K+1
! 136: *
! 137: MULT = D( K ) / DL( K )
! 138: D( K ) = DL( K )
! 139: TEMP = D( K+1 )
! 140: D( K+1 ) = DU( K ) - MULT*TEMP
! 141: IF( K.LT.( N-1 ) ) THEN
! 142: DL( K ) = DU( K+1 )
! 143: DU( K+1 ) = -MULT*DL( K )
! 144: END IF
! 145: DU( K ) = TEMP
! 146: DO 20 J = 1, NRHS
! 147: TEMP = B( K, J )
! 148: B( K, J ) = B( K+1, J )
! 149: B( K+1, J ) = TEMP - MULT*B( K+1, J )
! 150: 20 CONTINUE
! 151: END IF
! 152: 30 CONTINUE
! 153: IF( D( N ).EQ.ZERO ) THEN
! 154: INFO = N
! 155: RETURN
! 156: END IF
! 157: *
! 158: * Back solve with the matrix U from the factorization.
! 159: *
! 160: DO 50 J = 1, NRHS
! 161: B( N, J ) = B( N, J ) / D( N )
! 162: IF( N.GT.1 )
! 163: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
! 164: DO 40 K = N - 2, 1, -1
! 165: B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
! 166: $ B( K+2, J ) ) / D( K )
! 167: 40 CONTINUE
! 168: 50 CONTINUE
! 169: *
! 170: RETURN
! 171: *
! 172: * End of ZGTSV
! 173: *
! 174: END
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