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

.in +1c
.ti -1c
.RI "subroutine \fBcpbtrs\fP (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)"
.br
.RI "\fBCPBTRS\fP "
.ti -1c
.RI "subroutine \fBdpbtrs\fP (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)"
.br
.RI "\fBDPBTRS\fP "
.ti -1c
.RI "subroutine \fBspbtrs\fP (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)"
.br
.RI "\fBSPBTRS\fP "
.ti -1c
.RI "subroutine \fBzpbtrs\fP (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)"
.br
.RI "\fBZPBTRS\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cpbtrs (character uplo, integer n, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBCPBTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CPBTRS solves a system of linear equations A*X = B with a Hermitian
!> positive definite band matrix A using the Cholesky factorization
!> A = U**H*U or A = L*L**H computed by CPBTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangular factor stored in AB;
!>          = 'L':  Lower triangular factor stored in AB\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'\&.  KD >= 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
\fIAB\fP 
.PP
.nf
!>          AB is COMPLEX array, dimension (LDAB,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**H*U or A = L*L**H of the band matrix A, stored in the
!>          first KD+1 rows of the array\&.  The j-th column of U or L is
!>          stored in the j-th column of the array AB as follows:
!>          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd)\&.
!> 
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
!>          LDAB is INTEGER
!>          The leading dimension of the array AB\&.  LDAB >= KD+1\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the 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
!> 
.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

.PP
Definition at line \fB120\fP of file \fBcpbtrs\&.f\fP\&.
.SS "subroutine dpbtrs (character uplo, integer n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBDPBTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DPBTRS solves a system of linear equations A*X = B with a symmetric
!> positive definite band matrix A using the Cholesky factorization
!> A = U**T*U or A = L*L**T computed by DPBTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangular factor stored in AB;
!>          = 'L':  Lower triangular factor stored in AB\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'\&.  KD >= 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
\fIAB\fP 
.PP
.nf
!>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**T*U or A = L*L**T of the band matrix A, stored in the
!>          first KD+1 rows of the array\&.  The j-th column of U or L is
!>          stored in the j-th column of the array AB as follows:
!>          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd)\&.
!> 
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
!>          LDAB is INTEGER
!>          The leading dimension of the array AB\&.  LDAB >= KD+1\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the 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
!> 
.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

.PP
Definition at line \fB120\fP of file \fBdpbtrs\&.f\fP\&.
.SS "subroutine spbtrs (character uplo, integer n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBSPBTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SPBTRS solves a system of linear equations A*X = B with a symmetric
!> positive definite band matrix A using the Cholesky factorization
!> A = U**T*U or A = L*L**T computed by SPBTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangular factor stored in AB;
!>          = 'L':  Lower triangular factor stored in AB\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'\&.  KD >= 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
\fIAB\fP 
.PP
.nf
!>          AB is REAL array, dimension (LDAB,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**T*U or A = L*L**T of the band matrix A, stored in the
!>          first KD+1 rows of the array\&.  The j-th column of U or L is
!>          stored in the j-th column of the array AB as follows:
!>          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd)\&.
!> 
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
!>          LDAB is INTEGER
!>          The leading dimension of the array AB\&.  LDAB >= KD+1\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the 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
!> 
.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

.PP
Definition at line \fB120\fP of file \fBspbtrs\&.f\fP\&.
.SS "subroutine zpbtrs (character uplo, integer n, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBZPBTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZPBTRS solves a system of linear equations A*X = B with a Hermitian
!> positive definite band matrix A using the Cholesky factorization
!> A = U**H *U or A = L*L**H computed by ZPBTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangular factor stored in AB;
!>          = 'L':  Lower triangular factor stored in AB\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'\&.  KD >= 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
\fIAB\fP 
.PP
.nf
!>          AB is COMPLEX*16 array, dimension (LDAB,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**H *U or A = L*L**H of the band matrix A, stored in the
!>          first KD+1 rows of the array\&.  The j-th column of U or L is
!>          stored in the j-th column of the array AB as follows:
!>          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd)\&.
!> 
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
!>          LDAB is INTEGER
!>          The leading dimension of the array AB\&.  LDAB >= KD+1\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the 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
!> 
.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

.PP
Definition at line \fB120\fP of file \fBzpbtrs\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.