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

.in +1c
.ti -1c
.RI "subroutine \fBctrtrs\fP (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)"
.br
.RI "\fBCTRTRS\fP "
.ti -1c
.RI "subroutine \fBdtrtrs\fP (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)"
.br
.RI "\fBDTRTRS\fP "
.ti -1c
.RI "subroutine \fBstrtrs\fP (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)"
.br
.RI "\fBSTRTRS\fP "
.ti -1c
.RI "subroutine \fBztrtrs\fP (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)"
.br
.RI "\fBZTRTRS\fP "
.in -1c
.SH "Detailed Description"
.PP 

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

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

.PP
.nf
!>
!> CTRTRS 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, and B is an N-by-NRHS matrix\&.
!>
!> This subroutine verifies that A is nonsingular, but callers should note that only exact
!> singularity is detected\&. It is conceivable for one or more diagonal elements of A to be
!> subnormally tiny numbers without this subroutine signalling an error\&.
!>
!> If a possible loss of numerical precision due to near-singular matrices is a concern, the
!> caller should verify that A is nonsingular within some tolerance before calling this subroutine\&.
!> 
.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
\fIA\fP 
.PP
.nf
!>          A is COMPLEX array, dimension (LDA,N)
!>          The triangular matrix A\&.  If UPLO = 'U', the leading N-by-N
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced\&.  If UPLO = 'L', the leading N-by-N lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced\&.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,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 exactly 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 \fB144\fP of file \fBctrtrs\&.f\fP\&.
.SS "subroutine dtrtrs (character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
!>
!> DTRTRS solves a triangular system of the form
!>
!>    A * X = B  or  A**T * X = B,
!>
!> where A is a triangular matrix of order N, and B is an N-by-NRHS matrix\&.
!>
!> This subroutine verifies that A is nonsingular, but callers should note that only exact
!> singularity is detected\&. It is conceivable for one or more diagonal elements of A to be
!> subnormally tiny numbers without this subroutine signalling an error\&.
!>
!> If a possible loss of numerical precision due to near-singular matrices is a concern, the
!> caller should verify that A is nonsingular within some tolerance before calling this subroutine\&.
!> 
.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
\fIA\fP 
.PP
.nf
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The triangular matrix A\&.  If UPLO = 'U', the leading N-by-N
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced\&.  If UPLO = 'L', the leading N-by-N lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced\&.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,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 exactly 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 \fB144\fP of file \fBdtrtrs\&.f\fP\&.
.SS "subroutine strtrs (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
!>
!> STRTRS solves a triangular system of the form
!>
!>    A * X = B  or  A**T * X = B,
!>
!> where A is a triangular matrix of order N, and B is an N-by-NRHS matrix\&.
!>
!> This subroutine verifies that A is nonsingular, but callers should note that only exact
!> singularity is detected\&. It is conceivable for one or more diagonal elements of A to be
!> subnormally tiny numbers without this subroutine signalling an error\&.
!>
!> If a possible loss of numerical precision due to near-singular matrices is a concern, the
!> caller should verify that A is nonsingular within some tolerance before calling this subroutine\&.
!> 
.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
\fIA\fP 
.PP
.nf
!>          A is REAL array, dimension (LDA,N)
!>          The triangular matrix A\&.  If UPLO = 'U', the leading N-by-N
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced\&.  If UPLO = 'L', the leading N-by-N lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced\&.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,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 exactly 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 \fB144\fP of file \fBstrtrs\&.f\fP\&.
.SS "subroutine ztrtrs (character uplo, character trans, character diag, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
!>
!> ZTRTRS 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, and B is an N-by-NRHS matrix\&.
!>
!> This subroutine verifies that A is nonsingular, but callers should note that only exact
!> singularity is detected\&. It is conceivable for one or more diagonal elements of A to be
!> subnormally tiny numbers without this subroutine signalling an error\&.
!>
!> If a possible loss of numerical precision due to near-singular matrices is a concern, the
!> caller should verify that A is nonsingular within some tolerance before calling this subroutine\&.
!> 
.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
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The triangular matrix A\&.  If UPLO = 'U', the leading N-by-N
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced\&.  If UPLO = 'L', the leading N-by-N lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced\&.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,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 exactly 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 \fB144\fP of file \fBztrtrs\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.