.TH "ppsv" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
ppsv \- ppsv: factor and solve
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcppsv\fP (uplo, n, nrhs, ap, b, ldb, info)"
.br
.RI "\fB CPPSV computes the solution to system of linear equations A * X = B for OTHER matrices\fP "
.ti -1c
.RI "subroutine \fBdppsv\fP (uplo, n, nrhs, ap, b, ldb, info)"
.br
.RI "\fB DPPSV computes the solution to system of linear equations A * X = B for OTHER matrices\fP "
.ti -1c
.RI "subroutine \fBsppsv\fP (uplo, n, nrhs, ap, b, ldb, info)"
.br
.RI "\fB SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices\fP "
.ti -1c
.RI "subroutine \fBzppsv\fP (uplo, n, nrhs, ap, b, ldb, info)"
.br
.RI "\fB ZPPSV computes the solution to system of linear equations A * X = B for OTHER matrices\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cppsv (character uplo, integer n, integer nrhs, complex, dimension( * ) ap, complex, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
!>
!> CPPSV 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\&.
!> 
.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, 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\&.
!> 
.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, the leading principal minor of order i
!>                of A is not positive, so the factorization could not
!>                be completed, and the solution has not been 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

.PP
.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 \fB143\fP of file \fBcppsv\&.f\fP\&.
.SS "subroutine dppsv (character uplo, integer n, integer nrhs, double precision, dimension( * ) ap, double precision, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
!>
!> DPPSV computes the solution to a real system of linear equations
!>    A * X = B,
!> where A is an N-by-N symmetric 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**T* U,  if UPLO = 'U', or
!>    A = L * L**T,  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\&.
!> 
.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 DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          On entry, the upper or lower triangle of the symmetric 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, if INFO = 0, the factor U or L from the Cholesky
!>          factorization A = U**T*U or A = L*L**T, in the same storage
!>          format as A\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is DOUBLE PRECISION 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, the leading principal minor of order i
!>                of A is not positive, so the factorization could not
!>                be completed, and the solution has not been 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

.PP
.nf
!>
!>  The packed storage scheme is illustrated by the following example
!>  when N = 4, UPLO = 'U':
!>
!>  Two-dimensional storage of the symmetric 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 \fB143\fP of file \fBdppsv\&.f\fP\&.
.SS "subroutine sppsv (character uplo, integer n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
!>
!> SPPSV computes the solution to a real system of linear equations
!>    A * X = B,
!> where A is an N-by-N symmetric 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**T* U,  if UPLO = 'U', or
!>    A = L * L**T,  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\&.
!> 
.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 REAL array, dimension (N*(N+1)/2)
!>          On entry, the upper or lower triangle of the symmetric 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, if INFO = 0, the factor U or L from the Cholesky
!>          factorization A = U**T*U or A = L*L**T, in the same storage
!>          format as A\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is REAL 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, the leading principal minor of order i
!>                of A is not positive, so the factorization could not
!>                be completed, and the solution has not been 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

.PP
.nf
!>
!>  The packed storage scheme is illustrated by the following example
!>  when N = 4, UPLO = 'U':
!>
!>  Two-dimensional storage of the symmetric 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 \fB143\fP of file \fBsppsv\&.f\fP\&.
.SS "subroutine zppsv (character uplo, integer n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
!>
!> 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\&.
!> 
.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*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, 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\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is 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\&.
!> 
.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, the leading principal minor of order i
!>                of A is not positive, so the factorization could not
!>                be completed, and the solution has not been 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

.PP
.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 \fB143\fP of file \fBzppsv\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.