Provided by: liblapack-doc_3.12.1-6build1_all 
NAME
tptrs - tptrs: triangular solve
SYNOPSIS
Functions
subroutine ctptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
CTPTRS
subroutine dtptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
DTPTRS
subroutine stptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
STPTRS
subroutine ztptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
ZTPTRS
Detailed Description
Function Documentation
subroutine ctptrs (character uplo, character trans, character diag, integer n, integer nrhs, complex,
dimension( * ) ap, complex, dimension( ldb, * ) b, integer ldb, integer info)
CTPTRS
Purpose:
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.
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.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS
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)
DIAG
DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AP
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.
B
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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)
DTPTRS
Purpose:
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.
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.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS
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)
DIAG
DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AP
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.
B
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.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine stptrs (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension(
* ) ap, real, dimension( ldb, * ) b, integer ldb, integer info)
STPTRS
Purpose:
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.
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.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS
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)
DIAG
DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AP
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.
B
B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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)
ZTPTRS
Purpose:
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.
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.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
TRANS
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)
DIAG
DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AP
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.
B
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.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author
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Version 3.12.0 Thu Aug 28 2025 19:20:45 tptrs(3)