diff options
author | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
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committer | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
commit | baba851215b44ac3b60b9248eb02bcce7eb76247 (patch) | |
tree | 8c0f5c006875532a30d4409f5e94b0f310ff00a7 /SRC/dgttrf.f |
Move LAPACK trunk into position.
Diffstat (limited to 'SRC/dgttrf.f')
-rw-r--r-- | SRC/dgttrf.f | 168 |
1 files changed, 168 insertions, 0 deletions
diff --git a/SRC/dgttrf.f b/SRC/dgttrf.f new file mode 100644 index 00000000..b39527ef --- /dev/null +++ b/SRC/dgttrf.f @@ -0,0 +1,168 @@ + SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + INTEGER INFO, N +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * ) +* .. +* +* Purpose +* ======= +* +* DGTTRF computes an LU factorization of a real tridiagonal matrix A +* using elimination with partial pivoting and row interchanges. +* +* The factorization has the form +* A = L * U +* where L is a product of permutation and unit lower bidiagonal +* matrices and U is upper triangular with nonzeros in only the main +* diagonal and first two superdiagonals. +* +* Arguments +* ========= +* +* N (input) INTEGER +* The order of the matrix A. +* +* 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-1) multipliers that +* define the matrix L from the LU factorization of A. +* +* 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 the +* upper triangular matrix U from the LU factorization of A. +* +* 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. +* +* DU2 (output) DOUBLE PRECISION array, dimension (N-2) +* On exit, DU2 is overwritten by the (n-2) elements of the +* second super-diagonal of U. +* +* IPIV (output) INTEGER array, dimension (N) +* The pivot indices; for 1 <= i <= n, row i of the matrix was +* interchanged with row IPIV(i). IPIV(i) will always be either +* i or i+1; IPIV(i) = i indicates a row interchange was not +* required. +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -k, the k-th argument had an illegal value +* > 0: if INFO = k, U(k,k) is exactly zero. The factorization +* has been completed, but the factor U is exactly +* singular, and division by zero will occur if it is used +* to solve a system of equations. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I + DOUBLE PRECISION FACT, TEMP +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Executable Statements .. +* + INFO = 0 + IF( N.LT.0 ) THEN + INFO = -1 + CALL XERBLA( 'DGTTRF', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Initialize IPIV(i) = i and DU2(I) = 0 +* + DO 10 I = 1, N + IPIV( I ) = I + 10 CONTINUE + DO 20 I = 1, N - 2 + DU2( I ) = ZERO + 20 CONTINUE +* + DO 30 I = 1, N - 2 + IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN +* +* No row interchange required, eliminate DL(I) +* + IF( D( I ).NE.ZERO ) THEN + FACT = DL( I ) / D( I ) + DL( I ) = FACT + D( I+1 ) = D( I+1 ) - FACT*DU( I ) + END IF + ELSE +* +* Interchange rows I and I+1, eliminate DL(I) +* + FACT = D( I ) / DL( I ) + D( I ) = DL( I ) + DL( I ) = FACT + TEMP = DU( I ) + DU( I ) = D( I+1 ) + D( I+1 ) = TEMP - FACT*D( I+1 ) + DU2( I ) = DU( I+1 ) + DU( I+1 ) = -FACT*DU( I+1 ) + IPIV( I ) = I + 1 + END IF + 30 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 ) + DL( I ) = FACT + D( I+1 ) = D( I+1 ) - FACT*DU( I ) + END IF + ELSE + FACT = D( I ) / DL( I ) + D( I ) = DL( I ) + DL( I ) = FACT + TEMP = DU( I ) + DU( I ) = D( I+1 ) + D( I+1 ) = TEMP - FACT*D( I+1 ) + IPIV( I ) = I + 1 + END IF + END IF +* +* Check for a zero on the diagonal of U. +* + DO 40 I = 1, N + IF( D( I ).EQ.ZERO ) THEN + INFO = I + GO TO 50 + END IF + 40 CONTINUE + 50 CONTINUE +* + RETURN +* +* End of DGTTRF +* + END |