ppsv(3)

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, integer info)

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 = 'U', or
    !>    A = L * L**H,  if UPLO = 'L',
    !> 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
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', 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 = 'U':
    !>
    !>  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, double precision, 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 = 'U', or
    !>    A = L * L**T,  if UPLO = 'L',
    !> 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
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', 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 = 'U':
    !>
    !>  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 = 'U', or
    !>    A = L * L**T,  if UPLO = 'L',
    !> 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
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', 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 = 'U':
    !>
    !>  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 = 'U', or
    !>    A = L * L**H,  if UPLO = 'L',
    !> 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
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', 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 = 'U':
    !>
    !>  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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