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