tptrs(3)

Library Functions Manual

tptrs(3)

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 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 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 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.

Definition at line 134 of file ctptrs.f.

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 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 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 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.

Definition at line 134 of file dtptrs.f.

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 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 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 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.

Definition at line 134 of file stptrs.f.

subroutine ztptrs (character uplo, character trans, character diag, integer n, integer nrhs, complex16, dimension( ) ap, complex16, 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 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 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 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.

Definition at line 134 of file ztptrs.f.

Author

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