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hptrs(3) LAPACK hptrs(3)

NAME

hptrs - {hp,sp}trs: triangular solve using factor

SYNOPSIS

Functions


subroutine chptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
CHPTRS subroutine csptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
CSPTRS subroutine dsptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
DSPTRS subroutine ssptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
SSPTRS subroutine zhptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
ZHPTRS subroutine zsptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
ZSPTRS

Detailed Description

Function Documentation

subroutine chptrs (character uplo, integer n, integer nrhs, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)

CHPTRS

Purpose:

!>
!> CHPTRS solves a system of linear equations A*X = B with a complex
!> Hermitian matrix A stored in packed format using the factorization
!> A = U*D*U**H or A = L*D*L**H computed by CHPTRF.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**H;
!>          = 'L':  Lower triangular, form is A = L*D*L**H.
!>

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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CHPTRF, stored as a
!>          packed triangular matrix.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CHPTRF.
!>

B

!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, 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
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine csptrs (character uplo, integer n, integer nrhs, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)

CSPTRS

Purpose:

!>
!> CSPTRS solves a system of linear equations A*X = B with a complex
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by CSPTRF.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>

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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CSPTRF, stored as a
!>          packed triangular matrix.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CSPTRF.
!>

B

!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, 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
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dsptrs (character uplo, integer n, integer nrhs, double precision, dimension( * ) ap, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DSPTRS

Purpose:

!>
!> DSPTRS solves a system of linear equations A*X = B with a real
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by DSPTRF.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>

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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by DSPTRF, stored as a
!>          packed triangular matrix.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by DSPTRF.
!>

B

!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, 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
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ssptrs (character uplo, integer n, integer nrhs, real, dimension( * ) ap, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, integer info)

SSPTRS

Purpose:

!>
!> SSPTRS solves a system of linear equations A*X = B with a real
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by SSPTRF.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>

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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by SSPTRF, stored as a
!>          packed triangular matrix.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by SSPTRF.
!>

B

!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, 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
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zhptrs (character uplo, integer n, integer nrhs, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZHPTRS

Purpose:

!>
!> ZHPTRS solves a system of linear equations A*X = B with a complex
!> Hermitian matrix A stored in packed format using the factorization
!> A = U*D*U**H or A = L*D*L**H computed by ZHPTRF.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**H;
!>          = 'L':  Lower triangular, form is A = L*D*L**H.
!>

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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZHPTRF, stored as a
!>          packed triangular matrix.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZHPTRF.
!>

B

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, 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
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zsptrs (character uplo, integer n, integer nrhs, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZSPTRS

Purpose:

!>
!> ZSPTRS solves a system of linear equations A*X = B with a complex
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.
!>

Parameters

UPLO 

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>

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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZSPTRF, stored as a
!>          packed triangular matrix.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZSPTRF.
!>

B

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, 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
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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