Man page - hptri(3)

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Manual

hptri(3) LAPACK hptri(3)

hptri - {hp,sp}tri: triangular inverse


subroutine chptri (uplo, n, ap, ipiv, work, info)
CHPTRI subroutine csptri (uplo, n, ap, ipiv, work, info)
CSPTRI subroutine dsptri (uplo, n, ap, ipiv, work, info)
DSPTRI subroutine ssptri (uplo, n, ap, ipiv, work, info)
SSPTRI subroutine zhptri (uplo, n, ap, ipiv, work, info)
ZHPTRI subroutine zsptri (uplo, n, ap, ipiv, work, info)
ZSPTRI

CHPTRI

Purpose:



 CHPTRI computes the inverse of a complex Hermitian indefinite matrix


 A in packed storage 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.

AP



          AP is COMPLEX array, dimension (N*(N+1)/2)


          On entry, 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.


          On exit, if INFO = 0, the (Hermitian) inverse of the original


          matrix, stored as a packed triangular matrix. The j-th column


          of inv(A) is stored in the array AP as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;


          if UPLO = 'L',


             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

IPIV



          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D


          as determined by CHPTRF.

WORK



          WORK is COMPLEX array, dimension (N)

INFO



          INFO is INTEGER


          = 0: successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value


          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its


               inverse could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

CSPTRI

Purpose:



 CSPTRI computes the inverse of a complex symmetric indefinite matrix


 A in packed storage 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.

AP



          AP is COMPLEX array, dimension (N*(N+1)/2)


          On entry, 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.


          On exit, if INFO = 0, the (symmetric) inverse of the original


          matrix, stored as a packed triangular matrix. The j-th column


          of inv(A) is stored in the array AP as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;


          if UPLO = 'L',


             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

IPIV



          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D


          as determined by CSPTRF.

WORK



          WORK is COMPLEX array, dimension (N)

INFO



          INFO is INTEGER


          = 0: successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value


          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its


               inverse could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

DSPTRI

Purpose:



 DSPTRI computes the inverse of a real symmetric indefinite matrix


 A in packed storage 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.

AP



          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)


          On entry, 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.


          On exit, if INFO = 0, the (symmetric) inverse of the original


          matrix, stored as a packed triangular matrix. The j-th column


          of inv(A) is stored in the array AP as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;


          if UPLO = 'L',


             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

IPIV



          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D


          as determined by DSPTRF.

WORK



          WORK is DOUBLE PRECISION array, dimension (N)

INFO



          INFO is INTEGER


          = 0: successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value


          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its


               inverse could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

SSPTRI

Purpose:



 SSPTRI computes the inverse of a real symmetric indefinite matrix


 A in packed storage 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.

AP



          AP is REAL array, dimension (N*(N+1)/2)


          On entry, 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.


          On exit, if INFO = 0, the (symmetric) inverse of the original


          matrix, stored as a packed triangular matrix. The j-th column


          of inv(A) is stored in the array AP as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;


          if UPLO = 'L',


             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

IPIV



          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D


          as determined by SSPTRF.

WORK



          WORK is REAL array, dimension (N)

INFO



          INFO is INTEGER


          = 0: successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value


          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its


               inverse could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

ZHPTRI

Purpose:



 ZHPTRI computes the inverse of a complex Hermitian indefinite matrix


 A in packed storage 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.

AP



          AP is COMPLEX*16 array, dimension (N*(N+1)/2)


          On entry, 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.


          On exit, if INFO = 0, the (Hermitian) inverse of the original


          matrix, stored as a packed triangular matrix. The j-th column


          of inv(A) is stored in the array AP as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;


          if UPLO = 'L',


             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

IPIV



          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D


          as determined by ZHPTRF.

WORK



          WORK is COMPLEX*16 array, dimension (N)

INFO



          INFO is INTEGER


          = 0: successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value


          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its


               inverse could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

ZSPTRI

Purpose:



 ZSPTRI computes the inverse of a complex symmetric indefinite matrix


 A in packed storage 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.

AP



          AP is COMPLEX*16 array, dimension (N*(N+1)/2)


          On entry, 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.


          On exit, if INFO = 0, the (symmetric) inverse of the original


          matrix, stored as a packed triangular matrix. The j-th column


          of inv(A) is stored in the array AP as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;


          if UPLO = 'L',


             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

IPIV



          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D


          as determined by ZSPTRF.

WORK



          WORK is COMPLEX*16 array, dimension (N)

INFO



          INFO is INTEGER


          = 0: successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value


          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its


               inverse could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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