149 lines
4.9 KiB
FortranFixed
149 lines
4.9 KiB
FortranFixed
SUBROUTINE ZHPSV( UPLO, N, NRHS, AP, IPIV, 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, LDB, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IPIV( * )
|
|
COMPLEX*16 AP( * ), B( LDB, * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* ZHPSV computes the solution to a complex system of linear equations
|
|
* A * X = B,
|
|
* where A is an N-by-N Hermitian matrix stored in packed format and X
|
|
* and B are N-by-NRHS matrices.
|
|
*
|
|
* The diagonal pivoting method is used to factor A as
|
|
* A = U * D * U**H, if UPLO = 'U', or
|
|
* A = L * D * L**H, if UPLO = 'L',
|
|
* where U (or L) is a product of permutation and unit upper (lower)
|
|
* triangular matrices, D is Hermitian and block diagonal with 1-by-1
|
|
* and 2-by-2 diagonal blocks. 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.
|
|
*
|
|
* NRHS (input) INTEGER
|
|
* The number of right hand sides, i.e., the number of columns
|
|
* of the matrix B. NRHS >= 0.
|
|
*
|
|
* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
|
|
* On entry, the upper or lower triangle of the Hermitian matrix
|
|
* A, packed columnwise in a linear array. The j-th column of A
|
|
* is stored in the array AP as follows:
|
|
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
|
|
* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
|
|
* See below for further details.
|
|
*
|
|
* On exit, the block diagonal matrix D and the multipliers used
|
|
* to obtain the factor U or L from the factorization
|
|
* A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as
|
|
* a packed triangular matrix in the same storage format as A.
|
|
*
|
|
* IPIV (output) INTEGER array, dimension (N)
|
|
* Details of the interchanges and the block structure of D, as
|
|
* determined by ZHPTRF. If IPIV(k) > 0, then rows and columns
|
|
* k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
|
|
* diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
|
|
* then rows and columns k-1 and -IPIV(k) were interchanged and
|
|
* D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
|
|
* IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
|
|
* -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
|
|
* diagonal block.
|
|
*
|
|
* B (input/output) COMPLEX*16 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, D(i,i) is exactly zero. The factorization
|
|
* has been completed, but the block diagonal matrix D is
|
|
* exactly singular, so the solution could not be
|
|
* computed.
|
|
*
|
|
* Further Details
|
|
* ===============
|
|
*
|
|
* The packed storage scheme is illustrated by the following example
|
|
* when N = 4, UPLO = 'U':
|
|
*
|
|
* Two-dimensional storage of the Hermitian matrix A:
|
|
*
|
|
* a11 a12 a13 a14
|
|
* a22 a23 a24
|
|
* a33 a34 (aij = conjg(aji))
|
|
* a44
|
|
*
|
|
* Packed storage of the upper triangle of A:
|
|
*
|
|
* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL XERBLA, ZHPTRF, ZHPTRS
|
|
* ..
|
|
* .. 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( NRHS.LT.0 ) THEN
|
|
INFO = -3
|
|
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
|
|
INFO = -7
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'ZHPSV ', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Compute the factorization A = U*D*U' or A = L*D*L'.
|
|
*
|
|
CALL ZHPTRF( UPLO, N, AP, IPIV, INFO )
|
|
IF( INFO.EQ.0 ) THEN
|
|
*
|
|
* Solve the system A*X = B, overwriting B with X.
|
|
*
|
|
CALL ZHPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
|
|
*
|
|
END IF
|
|
RETURN
|
|
*
|
|
* End of ZHPSV
|
|
*
|
|
END
|