.TH "SRC/chpsv.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/chpsv.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBchpsv\fP (uplo, n, nrhs, ap, ipiv, b, ldb, info)"
.br
.RI "\fB CHPSV computes the solution to system of linear equations A * X = B for OTHER matrices\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine chpsv (character uplo, integer n, integer nrhs, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fB CHPSV computes the solution to system of linear equations A * X = B for OTHER matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CHPSV 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of linear equations, i\&.e\&., the order of the
!>          matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of columns
!>          of the matrix B\&.  NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX 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 CHPTRF, stored as
!>          a packed triangular matrix in the same storage format as A\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D, as
!>          determined by CHPTRF\&.  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\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is 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\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

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.nf
!>
!>  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 ]
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB161\fP of file \fBchpsv\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.