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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/zgtsvx.f | |
download | lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.gz lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.bz2 lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.zip |
Move LAPACK trunk into position.
Diffstat (limited to 'SRC/zgtsvx.f')
-rw-r--r-- | SRC/zgtsvx.f | 292 |
1 files changed, 292 insertions, 0 deletions
diff --git a/SRC/zgtsvx.f b/SRC/zgtsvx.f new file mode 100644 index 00000000..6ecebb07 --- /dev/null +++ b/SRC/zgtsvx.f @@ -0,0 +1,292 @@ + SUBROUTINE ZGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, + $ DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, + $ WORK, RWORK, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER FACT, TRANS + INTEGER INFO, LDB, LDX, N, NRHS + DOUBLE PRECISION RCOND +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * ) + COMPLEX*16 B( LDB, * ), D( * ), DF( * ), DL( * ), + $ DLF( * ), DU( * ), DU2( * ), DUF( * ), + $ WORK( * ), X( LDX, * ) +* .. +* +* Purpose +* ======= +* +* ZGTSVX uses the LU factorization to compute the solution to a complex +* system of linear equations A * X = B, A**T * X = B, or A**H * X = B, +* where A is a tridiagonal matrix of order N and X and B are N-by-NRHS +* matrices. +* +* Error bounds on the solution and a condition estimate are also +* provided. +* +* Description +* =========== +* +* The following steps are performed: +* +* 1. If FACT = 'N', the LU decomposition is used to factor the matrix A +* as 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. +* +* 2. If some U(i,i)=0, so that U is exactly singular, then the routine +* returns with INFO = i. Otherwise, the factored form of A is used +* to estimate the condition number of the matrix A. If the +* reciprocal of the condition number is less than machine precision, +* INFO = N+1 is returned as a warning, but the routine still goes on +* to solve for X and compute error bounds as described below. +* +* 3. The system of equations is solved for X using the factored form +* of A. +* +* 4. Iterative refinement is applied to improve the computed solution +* matrix and calculate error bounds and backward error estimates +* for it. +* +* Arguments +* ========= +* +* FACT (input) CHARACTER*1 +* Specifies whether or not the factored form of A has been +* supplied on entry. +* = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored form +* of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not +* be modified. +* = 'N': The matrix will be copied to DLF, DF, and DUF +* and factored. +* +* TRANS (input) CHARACTER*1 +* Specifies the form of the system of equations: +* = 'N': A * X = B (No transpose) +* = 'T': A**T * X = B (Transpose) +* = 'C': A**H * X = B (Conjugate transpose) +* +* 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) COMPLEX*16 array, dimension (N-1) +* The (n-1) subdiagonal elements of A. +* +* D (input) COMPLEX*16 array, dimension (N) +* The n diagonal elements of A. +* +* DU (input) COMPLEX*16 array, dimension (N-1) +* The (n-1) superdiagonal elements of A. +* +* DLF (input or output) COMPLEX*16 array, dimension (N-1) +* If FACT = 'F', then DLF is an input argument and on entry +* contains the (n-1) multipliers that define the matrix L from +* the LU factorization of A as computed by ZGTTRF. +* +* If FACT = 'N', then DLF is an output argument and on exit +* contains the (n-1) multipliers that define the matrix L from +* the LU factorization of A. +* +* DF (input or output) COMPLEX*16 array, dimension (N) +* If FACT = 'F', then DF is an input argument and on entry +* contains the n diagonal elements of the upper triangular +* matrix U from the LU factorization of A. +* +* If FACT = 'N', then DF is an output argument and on exit +* contains the n diagonal elements of the upper triangular +* matrix U from the LU factorization of A. +* +* DUF (input or output) COMPLEX*16 array, dimension (N-1) +* If FACT = 'F', then DUF is an input argument and on entry +* contains the (n-1) elements of the first superdiagonal of U. +* +* If FACT = 'N', then DUF is an output argument and on exit +* contains the (n-1) elements of the first superdiagonal of U. +* +* DU2 (input or output) COMPLEX*16 array, dimension (N-2) +* If FACT = 'F', then DU2 is an input argument and on entry +* contains the (n-2) elements of the second superdiagonal of +* U. +* +* If FACT = 'N', then DU2 is an output argument and on exit +* contains the (n-2) elements of the second superdiagonal of +* U. +* +* IPIV (input or output) INTEGER array, dimension (N) +* If FACT = 'F', then IPIV is an input argument and on entry +* contains the pivot indices from the LU factorization of A as +* computed by ZGTTRF. +* +* If FACT = 'N', then IPIV is an output argument and on exit +* contains the pivot indices from the LU factorization of A; +* 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. +* +* B (input) COMPLEX*16 array, dimension (LDB,NRHS) +* The N-by-NRHS right hand side matrix B. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* X (output) COMPLEX*16 array, dimension (LDX,NRHS) +* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. +* +* LDX (input) INTEGER +* The leading dimension of the array X. LDX >= max(1,N). +* +* RCOND (output) DOUBLE PRECISION +* The estimate of the reciprocal condition number of the matrix +* A. If RCOND is less than the machine precision (in +* particular, if RCOND = 0), the matrix is singular to working +* precision. This condition is indicated by a return code of +* INFO > 0. +* +* FERR (output) DOUBLE PRECISION array, dimension (NRHS) +* The estimated forward error bound for each solution vector +* X(j) (the j-th column of the solution matrix X). +* If XTRUE is the true solution corresponding to X(j), FERR(j) +* is an estimated upper bound for the magnitude of the largest +* element in (X(j) - XTRUE) divided by the magnitude of the +* largest element in X(j). The estimate is as reliable as +* the estimate for RCOND, and is almost always a slight +* overestimate of the true error. +* +* BERR (output) DOUBLE PRECISION array, dimension (NRHS) +* The componentwise relative backward error of each solution +* vector X(j) (i.e., the smallest relative change in +* any element of A or B that makes X(j) an exact solution). +* +* WORK (workspace) COMPLEX*16 array, dimension (2*N) +* +* RWORK (workspace) DOUBLE PRECISION array, dimension (N) +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: if INFO = i, and i is +* <= N: U(i,i) is exactly zero. The factorization +* has not been completed unless i = N, but the +* factor U is exactly singular, so the solution +* and error bounds could not be computed. +* RCOND = 0 is returned. +* = N+1: U is nonsingular, but RCOND is less than machine +* precision, meaning that the matrix is singular +* to working precision. Nevertheless, the +* solution and error bounds are computed because +* there are a number of situations where the +* computed solution can be more accurate than the +* value of RCOND would suggest. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL NOFACT, NOTRAN + CHARACTER NORM + DOUBLE PRECISION ANORM +* .. +* .. External Functions .. + LOGICAL LSAME + DOUBLE PRECISION DLAMCH, ZLANGT + EXTERNAL LSAME, DLAMCH, ZLANGT +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZCOPY, ZGTCON, ZGTRFS, ZGTTRF, ZGTTRS, + $ ZLACPY +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* + INFO = 0 + NOFACT = LSAME( FACT, 'N' ) + NOTRAN = LSAME( TRANS, 'N' ) + IF( .NOT.NOFACT .AND. .NOT.LSAME( FACT, 'F' ) ) THEN + INFO = -1 + ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. + $ LSAME( TRANS, 'C' ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -4 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -14 + ELSE IF( LDX.LT.MAX( 1, N ) ) THEN + INFO = -16 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZGTSVX', -INFO ) + RETURN + END IF +* + IF( NOFACT ) THEN +* +* Compute the LU factorization of A. +* + CALL ZCOPY( N, D, 1, DF, 1 ) + IF( N.GT.1 ) THEN + CALL ZCOPY( N-1, DL, 1, DLF, 1 ) + CALL ZCOPY( N-1, DU, 1, DUF, 1 ) + END IF + CALL ZGTTRF( N, DLF, DF, DUF, DU2, IPIV, INFO ) +* +* Return if INFO is non-zero. +* + IF( INFO.GT.0 )THEN + RCOND = ZERO + RETURN + END IF + END IF +* +* Compute the norm of the matrix A. +* + IF( NOTRAN ) THEN + NORM = '1' + ELSE + NORM = 'I' + END IF + ANORM = ZLANGT( NORM, N, DL, D, DU ) +* +* Compute the reciprocal of the condition number of A. +* + CALL ZGTCON( NORM, N, DLF, DF, DUF, DU2, IPIV, ANORM, RCOND, WORK, + $ INFO ) +* +* Compute the solution vectors X. +* + CALL ZLACPY( 'Full', N, NRHS, B, LDB, X, LDX ) + CALL ZGTTRS( TRANS, N, NRHS, DLF, DF, DUF, DU2, IPIV, X, LDX, + $ INFO ) +* +* Use iterative refinement to improve the computed solutions and +* compute error bounds and backward error estimates for them. +* + CALL ZGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, + $ B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO ) +* +* Set INFO = N+1 if the matrix is singular to working precision. +* + IF( RCOND.LT.DLAMCH( 'Epsilon' ) ) + $ INFO = N + 1 +* + RETURN +* +* End of ZGTSVX +* + END |