Annotation of rpl/lapack/lapack/dgtsv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGTSV( 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: DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * )
! 13: * ..
! 14: *
! 15: * Purpose
! 16: * =======
! 17: *
! 18: * DGTSV 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) DOUBLE PRECISION array, dimension (N-1)
! 39: * On entry, DL must contain the (n-1) sub-diagonal elements of
! 40: * A.
! 41: *
! 42: * On exit, DL is overwritten by the (n-2) elements of the
! 43: * second super-diagonal of the upper triangular matrix U from
! 44: * the LU factorization of A, in DL(1), ..., DL(n-2).
! 45: *
! 46: * D (input/output) DOUBLE PRECISION array, dimension (N)
! 47: * On entry, D must contain the diagonal elements of A.
! 48: *
! 49: * On exit, D is overwritten by the n diagonal elements of U.
! 50: *
! 51: * DU (input/output) DOUBLE PRECISION array, dimension (N-1)
! 52: * On entry, DU must contain the (n-1) super-diagonal elements
! 53: * of A.
! 54: *
! 55: * On exit, DU is overwritten by the (n-1) elements of the first
! 56: * super-diagonal of U.
! 57: *
! 58: * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
! 59: * On entry, the N by NRHS matrix of right hand side matrix B.
! 60: * On exit, if INFO = 0, the N by NRHS solution matrix X.
! 61: *
! 62: * LDB (input) INTEGER
! 63: * The leading dimension of the array B. LDB >= max(1,N).
! 64: *
! 65: * INFO (output) INTEGER
! 66: * = 0: successful exit
! 67: * < 0: if INFO = -i, the i-th argument had an illegal value
! 68: * > 0: if INFO = i, U(i,i) is exactly zero, and the solution
! 69: * has not been computed. The factorization has not been
! 70: * completed unless i = N.
! 71: *
! 72: * =====================================================================
! 73: *
! 74: * .. Parameters ..
! 75: DOUBLE PRECISION ZERO
! 76: PARAMETER ( ZERO = 0.0D+0 )
! 77: * ..
! 78: * .. Local Scalars ..
! 79: INTEGER I, J
! 80: DOUBLE PRECISION FACT, TEMP
! 81: * ..
! 82: * .. Intrinsic Functions ..
! 83: INTRINSIC ABS, MAX
! 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: ELSE IF( NRHS.LT.0 ) THEN
! 94: INFO = -2
! 95: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 96: INFO = -7
! 97: END IF
! 98: IF( INFO.NE.0 ) THEN
! 99: CALL XERBLA( 'DGTSV ', -INFO )
! 100: RETURN
! 101: END IF
! 102: *
! 103: IF( N.EQ.0 )
! 104: $ RETURN
! 105: *
! 106: IF( NRHS.EQ.1 ) THEN
! 107: DO 10 I = 1, N - 2
! 108: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
! 109: *
! 110: * No row interchange required
! 111: *
! 112: IF( D( I ).NE.ZERO ) THEN
! 113: FACT = DL( I ) / D( I )
! 114: D( I+1 ) = D( I+1 ) - FACT*DU( I )
! 115: B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 )
! 116: ELSE
! 117: INFO = I
! 118: RETURN
! 119: END IF
! 120: DL( I ) = ZERO
! 121: ELSE
! 122: *
! 123: * Interchange rows I and I+1
! 124: *
! 125: FACT = D( I ) / DL( I )
! 126: D( I ) = DL( I )
! 127: TEMP = D( I+1 )
! 128: D( I+1 ) = DU( I ) - FACT*TEMP
! 129: DL( I ) = DU( I+1 )
! 130: DU( I+1 ) = -FACT*DL( I )
! 131: DU( I ) = TEMP
! 132: TEMP = B( I, 1 )
! 133: B( I, 1 ) = B( I+1, 1 )
! 134: B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 )
! 135: END IF
! 136: 10 CONTINUE
! 137: IF( N.GT.1 ) THEN
! 138: I = N - 1
! 139: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
! 140: IF( D( I ).NE.ZERO ) THEN
! 141: FACT = DL( I ) / D( I )
! 142: D( I+1 ) = D( I+1 ) - FACT*DU( I )
! 143: B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 )
! 144: ELSE
! 145: INFO = I
! 146: RETURN
! 147: END IF
! 148: ELSE
! 149: FACT = D( I ) / DL( I )
! 150: D( I ) = DL( I )
! 151: TEMP = D( I+1 )
! 152: D( I+1 ) = DU( I ) - FACT*TEMP
! 153: DU( I ) = TEMP
! 154: TEMP = B( I, 1 )
! 155: B( I, 1 ) = B( I+1, 1 )
! 156: B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 )
! 157: END IF
! 158: END IF
! 159: IF( D( N ).EQ.ZERO ) THEN
! 160: INFO = N
! 161: RETURN
! 162: END IF
! 163: ELSE
! 164: DO 40 I = 1, N - 2
! 165: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
! 166: *
! 167: * No row interchange required
! 168: *
! 169: IF( D( I ).NE.ZERO ) THEN
! 170: FACT = DL( I ) / D( I )
! 171: D( I+1 ) = D( I+1 ) - FACT*DU( I )
! 172: DO 20 J = 1, NRHS
! 173: B( I+1, J ) = B( I+1, J ) - FACT*B( I, J )
! 174: 20 CONTINUE
! 175: ELSE
! 176: INFO = I
! 177: RETURN
! 178: END IF
! 179: DL( I ) = ZERO
! 180: ELSE
! 181: *
! 182: * Interchange rows I and I+1
! 183: *
! 184: FACT = D( I ) / DL( I )
! 185: D( I ) = DL( I )
! 186: TEMP = D( I+1 )
! 187: D( I+1 ) = DU( I ) - FACT*TEMP
! 188: DL( I ) = DU( I+1 )
! 189: DU( I+1 ) = -FACT*DL( I )
! 190: DU( I ) = TEMP
! 191: DO 30 J = 1, NRHS
! 192: TEMP = B( I, J )
! 193: B( I, J ) = B( I+1, J )
! 194: B( I+1, J ) = TEMP - FACT*B( I+1, J )
! 195: 30 CONTINUE
! 196: END IF
! 197: 40 CONTINUE
! 198: IF( N.GT.1 ) THEN
! 199: I = N - 1
! 200: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
! 201: IF( D( I ).NE.ZERO ) THEN
! 202: FACT = DL( I ) / D( I )
! 203: D( I+1 ) = D( I+1 ) - FACT*DU( I )
! 204: DO 50 J = 1, NRHS
! 205: B( I+1, J ) = B( I+1, J ) - FACT*B( I, J )
! 206: 50 CONTINUE
! 207: ELSE
! 208: INFO = I
! 209: RETURN
! 210: END IF
! 211: ELSE
! 212: FACT = D( I ) / DL( I )
! 213: D( I ) = DL( I )
! 214: TEMP = D( I+1 )
! 215: D( I+1 ) = DU( I ) - FACT*TEMP
! 216: DU( I ) = TEMP
! 217: DO 60 J = 1, NRHS
! 218: TEMP = B( I, J )
! 219: B( I, J ) = B( I+1, J )
! 220: B( I+1, J ) = TEMP - FACT*B( I+1, J )
! 221: 60 CONTINUE
! 222: END IF
! 223: END IF
! 224: IF( D( N ).EQ.ZERO ) THEN
! 225: INFO = N
! 226: RETURN
! 227: END IF
! 228: END IF
! 229: *
! 230: * Back solve with the matrix U from the factorization.
! 231: *
! 232: IF( NRHS.LE.2 ) THEN
! 233: J = 1
! 234: 70 CONTINUE
! 235: B( N, J ) = B( N, J ) / D( N )
! 236: IF( N.GT.1 )
! 237: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
! 238: DO 80 I = N - 2, 1, -1
! 239: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )*
! 240: $ B( I+2, J ) ) / D( I )
! 241: 80 CONTINUE
! 242: IF( J.LT.NRHS ) THEN
! 243: J = J + 1
! 244: GO TO 70
! 245: END IF
! 246: ELSE
! 247: DO 100 J = 1, NRHS
! 248: B( N, J ) = B( N, J ) / D( N )
! 249: IF( N.GT.1 )
! 250: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
! 251: $ D( N-1 )
! 252: DO 90 I = N - 2, 1, -1
! 253: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )*
! 254: $ B( I+2, J ) ) / D( I )
! 255: 90 CONTINUE
! 256: 100 CONTINUE
! 257: END IF
! 258: *
! 259: RETURN
! 260: *
! 261: * End of DGTSV
! 262: *
! 263: END
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