Man page - ppsv(3)

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Manual

ppsv

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cppsv (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, complex, dimension( ldb, * ) b, integer ldb, integerinfo)
subroutine dppsv (character uplo, integer n, integer nrhs, doubleprecision, dimension( * ) ap, double precision, dimension( ldb, * ) b,integer ldb, integer info)
subroutine sppsv (character uplo, integer n, integer nrhs, real, dimension(* ) ap, real, dimension( ldb, * ) b, integer ldb, integer info)
subroutine zppsv (character uplo, integer n, integer nrhs, complex*16,dimension( * ) ap, complex*16, dimension( ldb, * ) b, integer ldb,integer info)
Author

NAME

ppsv - ppsv: factor and solve

SYNOPSIS

Functions

subroutine cppsv (uplo, n, nrhs, ap, b, ldb, info)
CPPSV computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine dppsv (uplo, n, nrhs, ap, b, ldb, info)
DPPSV computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine sppsv (uplo, n, nrhs, ap, b, ldb, info)
SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine zppsv (uplo, n, nrhs, ap, b, ldb, info)
ZPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Detailed Description

Function Documentation

subroutine cppsv (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, complex, dimension( ldb, * ) b, integer ldb, integerinfo)

CPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

CPPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as
A = U**H * U, if UPLO = ā€™Uā€™, or
A = L * L**H, if UPLO = ā€™Lā€™,
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., 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)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.

On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H, in the same storage
format as A.

B

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS 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 leading principal minor of order i
of A is not positive, so the factorization could not
be completed, and the solution has not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = ā€™Uā€™:

Two-dimensional storage of the Hermitian matrix A:

a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = conjg(aji))
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

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

DPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

DPPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as
A = U**T* U, if UPLO = ā€™Uā€™, or
A = L * L**T, if UPLO = ā€™Lā€™,
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., 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)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.

On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T, in the same storage
format as A.

B

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS 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 leading principal minor of order i
of A is not positive, so the factorization could not
be completed, and the solution has not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = ā€™Uā€™:

Two-dimensional storage of the symmetric matrix A:

a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = conjg(aji))
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

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

SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

SPPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as
A = U**T* U, if UPLO = ā€™Uā€™, or
A = L * L**T, if UPLO = ā€™Lā€™,
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., 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)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.

On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T, in the same storage
format as A.

B

B is REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS 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 leading principal minor of order i
of A is not positive, so the factorization could not
be completed, and the solution has not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = ā€™Uā€™:

Two-dimensional storage of the symmetric matrix A:

a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = conjg(aji))
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

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

ZPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

ZPPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as
A = U**H * U, if UPLO = ā€™Uā€™, or
A = L * L**H, if UPLO = ā€™Lā€™,
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., 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)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.

On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H, in the same storage
format as A.

B

B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS 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 leading principal minor of order i
of A is not positive, so the factorization could not
be completed, and the solution has not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = ā€™Uā€™:

Two-dimensional storage of the Hermitian matrix A:

a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = conjg(aji))
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Author

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