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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/cpbsv.f | |
download | lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.gz lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.bz2 lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.zip |
Move LAPACK trunk into position.
Diffstat (limited to 'SRC/cpbsv.f')
-rw-r--r-- | SRC/cpbsv.f | 151 |
1 files changed, 151 insertions, 0 deletions
diff --git a/SRC/cpbsv.f b/SRC/cpbsv.f new file mode 100644 index 00000000..4a7f62f8 --- /dev/null +++ b/SRC/cpbsv.f @@ -0,0 +1,151 @@ + SUBROUTINE CPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) +* +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, KD, LDAB, LDB, N, NRHS +* .. +* .. Array Arguments .. + COMPLEX AB( LDAB, * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* CPBSV computes the solution to a complex system of linear equations +* A * X = B, +* where A is an N-by-N Hermitian positive definite band matrix and X +* and B are N-by-NRHS matrices. +* +* The Cholesky decomposition is used to factor A as +* A = U**H * U, if UPLO = 'U', or +* A = L * L**H, if UPLO = 'L', +* where U is an upper triangular band matrix, and L is a lower +* triangular band matrix, with the same number of superdiagonals or +* subdiagonals as A. The factored form of A is then used to solve the +* system of equations A * X = B. +* +* Arguments +* ========= +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangle of A is stored; +* = 'L': Lower triangle of A is stored. +* +* N (input) INTEGER +* The number of linear equations, i.e., the order of the +* matrix A. N >= 0. +* +* KD (input) INTEGER +* The number of superdiagonals of the matrix A if UPLO = 'U', +* or the number of subdiagonals if UPLO = 'L'. KD >= 0. +* +* NRHS (input) INTEGER +* The number of right hand sides, i.e., the number of columns +* of the matrix B. NRHS >= 0. +* +* AB (input/output) COMPLEX array, dimension (LDAB,N) +* On entry, the upper or lower triangle of the Hermitian band +* matrix A, stored in the first KD+1 rows of the array. The +* j-th column of A is stored in the j-th column of the array AB +* as follows: +* if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; +* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). +* See below for further details. +* +* On exit, if INFO = 0, the triangular factor U or L from the +* Cholesky factorization A = U**H*U or A = L*L**H of the band +* matrix A, in the same storage format as A. +* +* LDAB (input) INTEGER +* The leading dimension of the array AB. LDAB >= KD+1. +* +* B (input/output) COMPLEX array, dimension (LDB,NRHS) +* On entry, the N-by-NRHS 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, the leading minor of order i of A is not +* positive definite, so the factorization could not be +* completed, and the solution has not been computed. +* +* Further Details +* =============== +* +* The band storage scheme is illustrated by the following example, when +* N = 6, KD = 2, and UPLO = 'U': +* +* On entry: On exit: +* +* * * a13 a24 a35 a46 * * u13 u24 u35 u46 +* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 +* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 +* +* Similarly, if UPLO = 'L' the format of A is as follows: +* +* On entry: On exit: +* +* a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 +* a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * +* a31 a42 a53 a64 * * l31 l42 l53 l64 * * +* +* Array elements marked * are not used by the routine. +* +* ===================================================================== +* +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL CPBTRF, CPBTRS, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( KD.LT.0 ) THEN + INFO = -3 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -4 + ELSE IF( LDAB.LT.KD+1 ) THEN + INFO = -6 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CPBSV ', -INFO ) + RETURN + END IF +* +* Compute the Cholesky factorization A = U'*U or A = L*L'. +* + CALL CPBTRF( UPLO, N, KD, AB, LDAB, INFO ) + IF( INFO.EQ.0 ) THEN +* +* Solve the system A*X = B, overwriting B with X. +* + CALL CPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) +* + END IF + RETURN +* +* End of CPBSV +* + END |