Mercurial > forge
diff main/splines/dgtsv.f @ 0:6b33357c7561 octave-forge
Initial revision
| author | pkienzle |
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| date | Wed, 10 Oct 2001 19:54:49 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/splines/dgtsv.f Wed Oct 10 19:54:49 2001 +0000 @@ -0,0 +1,263 @@ + SUBROUTINE DGTSV( N, NRHS, DL, D, DU, B, LDB, INFO ) +* +* -- LAPACK routine (version 3.0) -- +* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., +* Courant Institute, Argonne National Lab, and Rice University +* October 31, 1999 +* +* .. Scalar Arguments .. + INTEGER INFO, LDB, N, NRHS +* .. +* .. Array Arguments .. + DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ) +* .. +* +* Purpose +* ======= +* +* DGTSV solves the equation +* +* A*X = B, +* +* where A is an n by n tridiagonal matrix, by Gaussian elimination with +* partial pivoting. +* +* Note that the equation A'*X = B may be solved by interchanging the +* order of the arguments DU and DL. +* +* Arguments +* ========= +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* NRHS (input) INTEGER +* The number of right hand sides, i.e., the number of columns +* of the matrix B. NRHS >= 0. +* +* DL (input/output) DOUBLE PRECISION array, dimension (N-1) +* On entry, DL must contain the (n-1) sub-diagonal elements of +* A. +* +* On exit, DL is overwritten by the (n-2) elements of the +* second super-diagonal of the upper triangular matrix U from +* the LU factorization of A, in DL(1), ..., DL(n-2). +* +* D (input/output) DOUBLE PRECISION array, dimension (N) +* On entry, D must contain the diagonal elements of A. +* +* On exit, D is overwritten by the n diagonal elements of U. +* +* DU (input/output) DOUBLE PRECISION array, dimension (N-1) +* On entry, DU must contain the (n-1) super-diagonal elements +* of A. +* +* On exit, DU is overwritten by the (n-1) elements of the first +* super-diagonal of U. +* +* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) +* On entry, the N by NRHS matrix of right hand side matrix B. +* On exit, if INFO = 0, the N by NRHS solution matrix X. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: if INFO = i, U(i,i) is exactly zero, and the solution +* has not been computed. The factorization has not been +* completed unless i = N. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J + DOUBLE PRECISION FACT, TEMP +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Executable Statements .. +* + INFO = 0 + IF( N.LT.0 ) THEN + INFO = -1 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -2 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DGTSV ', -INFO ) + RETURN + END IF +* + IF( N.EQ.0 ) + $ RETURN +* + IF( NRHS.EQ.1 ) THEN + DO 10 I = 1, N - 2 + IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN +* +* No row interchange required +* + IF( D( I ).NE.ZERO ) THEN + FACT = DL( I ) / D( I ) + D( I+1 ) = D( I+1 ) - FACT*DU( I ) + B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 ) + ELSE + INFO = I + RETURN + END IF + DL( I ) = ZERO + ELSE +* +* Interchange rows I and I+1 +* + FACT = D( I ) / DL( I ) + D( I ) = DL( I ) + TEMP = D( I+1 ) + D( I+1 ) = DU( I ) - FACT*TEMP + DL( I ) = DU( I+1 ) + DU( I+1 ) = -FACT*DL( I ) + DU( I ) = TEMP + TEMP = B( I, 1 ) + B( I, 1 ) = B( I+1, 1 ) + B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 ) + END IF + 10 CONTINUE + IF( N.GT.1 ) THEN + I = N - 1 + IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN + IF( D( I ).NE.ZERO ) THEN + FACT = DL( I ) / D( I ) + D( I+1 ) = D( I+1 ) - FACT*DU( I ) + B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 ) + ELSE + INFO = I + RETURN + END IF + ELSE + FACT = D( I ) / DL( I ) + D( I ) = DL( I ) + TEMP = D( I+1 ) + D( I+1 ) = DU( I ) - FACT*TEMP + DU( I ) = TEMP + TEMP = B( I, 1 ) + B( I, 1 ) = B( I+1, 1 ) + B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 ) + END IF + END IF + IF( D( N ).EQ.ZERO ) THEN + INFO = N + RETURN + END IF + ELSE + DO 40 I = 1, N - 2 + IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN +* +* No row interchange required +* + IF( D( I ).NE.ZERO ) THEN + FACT = DL( I ) / D( I ) + D( I+1 ) = D( I+1 ) - FACT*DU( I ) + DO 20 J = 1, NRHS + B( I+1, J ) = B( I+1, J ) - FACT*B( I, J ) + 20 CONTINUE + ELSE + INFO = I + RETURN + END IF + DL( I ) = ZERO + ELSE +* +* Interchange rows I and I+1 +* + FACT = D( I ) / DL( I ) + D( I ) = DL( I ) + TEMP = D( I+1 ) + D( I+1 ) = DU( I ) - FACT*TEMP + DL( I ) = DU( I+1 ) + DU( I+1 ) = -FACT*DL( I ) + DU( I ) = TEMP + DO 30 J = 1, NRHS + TEMP = B( I, J ) + B( I, J ) = B( I+1, J ) + B( I+1, J ) = TEMP - FACT*B( I+1, J ) + 30 CONTINUE + END IF + 40 CONTINUE + IF( N.GT.1 ) THEN + I = N - 1 + IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN + IF( D( I ).NE.ZERO ) THEN + FACT = DL( I ) / D( I ) + D( I+1 ) = D( I+1 ) - FACT*DU( I ) + DO 50 J = 1, NRHS + B( I+1, J ) = B( I+1, J ) - FACT*B( I, J ) + 50 CONTINUE + ELSE + INFO = I + RETURN + END IF + ELSE + FACT = D( I ) / DL( I ) + D( I ) = DL( I ) + TEMP = D( I+1 ) + D( I+1 ) = DU( I ) - FACT*TEMP + DU( I ) = TEMP + DO 60 J = 1, NRHS + TEMP = B( I, J ) + B( I, J ) = B( I+1, J ) + B( I+1, J ) = TEMP - FACT*B( I+1, J ) + 60 CONTINUE + END IF + END IF + IF( D( N ).EQ.ZERO ) THEN + INFO = N + RETURN + END IF + END IF +* +* Back solve with the matrix U from the factorization. +* + IF( NRHS.LE.2 ) THEN + J = 1 + 70 CONTINUE + B( N, J ) = B( N, J ) / D( N ) + IF( N.GT.1 ) + $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 ) + DO 80 I = N - 2, 1, -1 + B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )* + $ B( I+2, J ) ) / D( I ) + 80 CONTINUE + IF( J.LT.NRHS ) THEN + J = J + 1 + GO TO 70 + END IF + ELSE + DO 100 J = 1, NRHS + B( N, J ) = B( N, J ) / D( N ) + IF( N.GT.1 ) + $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / + $ D( N-1 ) + DO 90 I = N - 2, 1, -1 + B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )* + $ B( I+2, J ) ) / D( I ) + 90 CONTINUE + 100 CONTINUE + END IF +* + RETURN +* +* End of DGTSV +* + END