ZPPSV(3F) ZPPSV(3F)
ZPPSV - compute the solution to a complex system of linear equations A *
X = B,
SUBROUTINE ZPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, N, NRHS
COMPLEX*16 AP( * ), B( LDB, * )
ZPPSV computes the solution to a complex system of linear equations
A * X = B, where A is an N-by-N Hermitian positive definite matrix
stored in packed format 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 matrix and L is a lower triangular matrix.
The factored form of A is then used to solve the system of equations A *
X = B.
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 + (j1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2nj)/2)
= A(i,j) for j<=i<=n. See below for further details.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H, in the same storage
format as A.
Page 1
ZPPSV(3F) ZPPSV(3F)
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, 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 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 ]
ZPPSV(3F) ZPPSV(3F)
ZPPSV - compute the solution to a complex system of linear equations A *
X = B,
SUBROUTINE ZPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, N, NRHS
COMPLEX*16 AP( * ), B( LDB, * )
ZPPSV computes the solution to a complex system of linear equations
A * X = B, where A is an N-by-N Hermitian positive definite matrix
stored in packed format 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 matrix and L is a lower triangular matrix.
The factored form of A is then used to solve the system of equations A *
X = B.
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 + (j1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2nj)/2)
= A(i,j) for j<=i<=n. See below for further details.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H, in the same storage
format as A.
Page 1
ZPPSV(3F) ZPPSV(3F)
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, 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 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 ]
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