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

.in +1c
.ti -1c
.RI "subroutine \fBctptrs\fP (uplo, trans, diag, n, nrhs, ap, b, ldb, info)"
.br
.RI "\fBCTPTRS\fP "
.ti -1c
.RI "subroutine \fBdtptrs\fP (uplo, trans, diag, n, nrhs, ap, b, ldb, info)"
.br
.RI "\fBDTPTRS\fP "
.ti -1c
.RI "subroutine \fBstptrs\fP (uplo, trans, diag, n, nrhs, ap, b, ldb, info)"
.br
.RI "\fBSTPTRS\fP "
.ti -1c
.RI "subroutine \fBztptrs\fP (uplo, trans, diag, n, nrhs, ap, b, ldb, info)"
.br
.RI "\fBZTPTRS\fP "
.in -1c
.SH "Detailed Description"
.PP 

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

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

.PP
.nf
 CTPTRS solves a triangular system of the form

    A * X = B,  A**T * X = B,  or  A**H * X = B,

 where A is a triangular matrix of order N stored in packed format,
 and B is an N-by-NRHS matrix\&.  A check is made to verify that A is
 nonsingular\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose)
.fi
.PP
.br
\fIDIAG\fP 
.PP
.nf
          DIAG is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          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)
          The upper or lower triangular 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)*(2*n-j)/2) = A(i,j) for j<=i<=n\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B\&.
          On exit, if INFO = 0, 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
          > 0:  if INFO = i, the i-th diagonal element of A is zero,
                indicating that the matrix is singular and the
                solutions X have 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

.PP
Definition at line \fB129\fP of file \fBctptrs\&.f\fP\&.
.SS "subroutine dtptrs (character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( * ) ap, double precision, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 DTPTRS solves a triangular system of the form

    A * X = B  or  A**T * X = B,

 where A is a triangular matrix of order N stored in packed format,
 and B is an N-by-NRHS matrix\&.  A check is made to verify that A is
 nonsingular\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A * X = B  (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
.fi
.PP
.br
\fIDIAG\fP 
.PP
.nf
          DIAG is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          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)
          The upper or lower triangular 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)*(2*n-j)/2) = A(i,j) for j<=i<=n\&.
.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, if INFO = 0, 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
          > 0:  if INFO = i, the i-th diagonal element of A is zero,
                indicating that the matrix is singular and the
                solutions X have 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

.PP
Definition at line \fB129\fP of file \fBdtptrs\&.f\fP\&.
.SS "subroutine stptrs (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 STPTRS solves a triangular system of the form

    A * X = B  or  A**T * X = B,

 where A is a triangular matrix of order N stored in packed format,
 and B is an N-by-NRHS matrix\&.  A check is made to verify that A is
 nonsingular\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A * X = B  (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
.fi
.PP
.br
\fIDIAG\fP 
.PP
.nf
          DIAG is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          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)
          The upper or lower triangular 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)*(2*n-j)/2) = A(i,j) for j<=i<=n\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B\&.
          On exit, if INFO = 0, 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
          > 0:  if INFO = i, the i-th diagonal element of A is zero,
                indicating that the matrix is singular and the
                solutions X have 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

.PP
Definition at line \fB129\fP of file \fBstptrs\&.f\fP\&.
.SS "subroutine ztptrs (character uplo, character trans, character diag, integer n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 ZTPTRS solves a triangular system of the form

    A * X = B,  A**T * X = B,  or  A**H * X = B,

 where A is a triangular matrix of order N stored in packed format,
 and B is an N-by-NRHS matrix\&.  A check is made to verify that A is
 nonsingular\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose)
.fi
.PP
.br
\fIDIAG\fP 
.PP
.nf
          DIAG is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          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)
          The upper or lower triangular 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)*(2*n-j)/2) = A(i,j) for j<=i<=n\&.
.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, if INFO = 0, 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
          > 0:  if INFO = i, the i-th diagonal element of A is zero,
                indicating that the matrix is singular and the
                solutions X have 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

.PP
Definition at line \fB129\fP of file \fBztptrs\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.