134 lines
4.0 KiB
FortranFixed
134 lines
4.0 KiB
FortranFixed
SUBROUTINE CPPSV( UPLO, N, NRHS, AP, 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, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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COMPLEX AP( * ), 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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* CPPSV 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 matrix stored in
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* packed format and X 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 matrix and L is a lower triangular
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* matrix. The factored form of A is then used to solve the system of
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* 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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* 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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* AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
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* On entry, the upper or lower triangle of the Hermitian matrix
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* A, packed columnwise in a linear array. The j-th column of A
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* is stored in the array AP as follows:
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* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
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* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
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* See below for further details.
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*
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* On exit, if INFO = 0, the factor U or L from the Cholesky
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* factorization A = U**H*U or A = L*L**H, in the same storage
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* format as A.
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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 packed storage scheme is illustrated by the following example
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* when N = 4, UPLO = 'U':
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*
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* Two-dimensional storage of the Hermitian matrix A:
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*
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* a11 a12 a13 a14
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* a22 a23 a24
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* a33 a34 (aij = conjg(aji))
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* a44
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*
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* Packed storage of the upper triangle of A:
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*
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* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
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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 CPPTRF, CPPTRS, 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( NRHS.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -6
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CPPSV ', -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 CPPTRF( UPLO, N, AP, 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 CPPTRS( UPLO, N, NRHS, AP, 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 CPPSV
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*
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END
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