.TH "hptri" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME hptri \- {hp,sp}tri: triangular inverse .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBchptri\fP (uplo, n, ap, ipiv, work, info)" .br .RI "\fBCHPTRI\fP " .ti -1c .RI "subroutine \fBcsptri\fP (uplo, n, ap, ipiv, work, info)" .br .RI "\fBCSPTRI\fP " .ti -1c .RI "subroutine \fBdsptri\fP (uplo, n, ap, ipiv, work, info)" .br .RI "\fBDSPTRI\fP " .ti -1c .RI "subroutine \fBssptri\fP (uplo, n, ap, ipiv, work, info)" .br .RI "\fBSSPTRI\fP " .ti -1c .RI "subroutine \fBzhptri\fP (uplo, n, ap, ipiv, work, info)" .br .RI "\fBZHPTRI\fP " .ti -1c .RI "subroutine \fBzsptri\fP (uplo, n, ap, ipiv, work, info)" .br .RI "\fBZSPTRI\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine chptri (character uplo, integer n, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer info)" .PP \fBCHPTRI\fP .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIAP\fP .PP .nf 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\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHPTRF\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "subroutine csptri (character uplo, integer n, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer info)" .PP \fBCSPTRI\fP .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIAP\fP .PP .nf 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\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSPTRF\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "subroutine dsptri (character uplo, integer n, double precision, dimension( * ) ap, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer info)" .PP \fBDSPTRI\fP .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIAP\fP .PP .nf 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\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by DSPTRF\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "subroutine ssptri (character uplo, integer n, real, dimension( * ) ap, integer, dimension( * ) ipiv, real, dimension( * ) work, integer info)" .PP \fBSSPTRI\fP .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIAP\fP .PP .nf 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\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by SSPTRF\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "subroutine zhptri (character uplo, integer n, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)" .PP \fBZHPTRI\fP .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIAP\fP .PP .nf 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\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHPTRF\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "subroutine zsptri (character uplo, integer n, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)" .PP \fBZSPTRI\fP .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIAP\fP .PP .nf 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\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSPTRF\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.