.TH "hetri_3" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME hetri_3 \- {he,sy}tri_3: inverse .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBchetri_3\fP (uplo, n, a, lda, e, ipiv, work, lwork, info)" .br .RI "\fBCHETRI_3\fP " .ti -1c .RI "subroutine \fBcsytri_3\fP (uplo, n, a, lda, e, ipiv, work, lwork, info)" .br .RI "\fBCSYTRI_3\fP " .ti -1c .RI "subroutine \fBdsytri_3\fP (uplo, n, a, lda, e, ipiv, work, lwork, info)" .br .RI "\fBDSYTRI_3\fP " .ti -1c .RI "subroutine \fBssytri_3\fP (uplo, n, a, lda, e, ipiv, work, lwork, info)" .br .RI "\fBSSYTRI_3\fP " .ti -1c .RI "subroutine \fBzhetri_3\fP (uplo, n, a, lda, e, ipiv, work, lwork, info)" .br .RI "\fBZHETRI_3\fP " .ti -1c .RI "subroutine \fBzsytri_3\fP (uplo, n, a, lda, e, ipiv, work, lwork, info)" .br .RI "\fBZSYTRI_3\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine chetri_3 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)" .PP \fBCHETRI_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> CHETRI_3 computes the inverse of a complex Hermitian indefinite !> matrix A using the factorization computed by CHETRF_RK or CHETRF_BK: !> !> A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T), !> !> where U (or L) is unit upper (or lower) triangular matrix, !> U**H (or L**H) is the conjugate of U (or L), P is a permutation !> matrix, P**T is the transpose of P, and D is Hermitian and block !> diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. !> !> CHETRI_3 sets the leading dimension of the workspace before calling !> CHETRI_3X that actually computes the inverse\&. This is the blocked !> version of the algorithm, calling Level 3 BLAS\&. !> .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 triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> On entry, diagonal of the block diagonal matrix D and !> factors U or L as computed by CHETRF_RK and CHETRF_BK: !> a) ONLY diagonal elements of the Hermitian block diagonal !> matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); !> (superdiagonal (or subdiagonal) elements of D !> should be provided on entry in array E), and !> b) If UPLO = 'U': factor U in the superdiagonal part of A\&. !> If UPLO = 'L': factor L in the subdiagonal part of A\&. !> !> On exit, if INFO = 0, the Hermitian inverse of the original !> matrix\&. !> If UPLO = 'U': the upper triangular part of the inverse !> is formed and the part of A below the diagonal is not !> referenced; !> If UPLO = 'L': the lower triangular part of the inverse !> is formed and the part of A above the diagonal is not !> referenced\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is COMPLEX array, dimension (N) !> On entry, contains the superdiagonal (or subdiagonal) !> elements of the Hermitian block diagonal matrix D !> with 1-by-1 or 2-by-2 diagonal blocks, where !> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; !> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. !> !> NOTE: For 1-by-1 diagonal block D(k), where !> 1 <= k <= N, the element E(k) is not referenced in both !> UPLO = 'U' or UPLO = 'L' cases\&. !> .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 CHETRF_RK or CHETRF_BK\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX array, dimension (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. !> If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3)\&. !> !> If LWORK = -1, then a workspace query is assumed; !> the routine only calculates the optimal size of the optimal !> size of the WORK array, returns this value as the first !> entry of the WORK array, and no error message related to !> LWORK is issued by XERBLA\&. !> .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 \fBContributors:\fP .RS 4 .PP .nf !> !> November 2017, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> .fi .PP .RE .PP .PP Definition at line \fB169\fP of file \fBchetri_3\&.f\fP\&. .SS "subroutine csytri_3 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)" .PP \fBCSYTRI_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> CSYTRI_3 computes the inverse of a complex symmetric indefinite !> matrix A using the factorization computed by CSYTRF_RK or CSYTRF_BK: !> !> A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), !> !> where U (or L) is unit upper (or lower) triangular matrix, !> U**T (or L**T) is the transpose of U (or L), P is a permutation !> matrix, P**T is the transpose of P, and D is symmetric and block !> diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. !> !> CSYTRI_3 sets the leading dimension of the workspace before calling !> CSYTRI_3X that actually computes the inverse\&. This is the blocked !> version of the algorithm, calling Level 3 BLAS\&. !> .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 triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> On entry, diagonal of the block diagonal matrix D and !> factors U or L as computed by CSYTRF_RK and CSYTRF_BK: !> a) ONLY diagonal elements of the symmetric block diagonal !> matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); !> (superdiagonal (or subdiagonal) elements of D !> should be provided on entry in array E), and !> b) If UPLO = 'U': factor U in the superdiagonal part of A\&. !> If UPLO = 'L': factor L in the subdiagonal part of A\&. !> !> On exit, if INFO = 0, the symmetric inverse of the original !> matrix\&. !> If UPLO = 'U': the upper triangular part of the inverse !> is formed and the part of A below the diagonal is not !> referenced; !> If UPLO = 'L': the lower triangular part of the inverse !> is formed and the part of A above the diagonal is not !> referenced\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is COMPLEX array, dimension (N) !> On entry, contains the superdiagonal (or subdiagonal) !> elements of the symmetric block diagonal matrix D !> with 1-by-1 or 2-by-2 diagonal blocks, where !> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; !> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. !> !> NOTE: For 1-by-1 diagonal block D(k), where !> 1 <= k <= N, the element E(k) is not referenced in both !> UPLO = 'U' or UPLO = 'L' cases\&. !> .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 CSYTRF_RK or CSYTRF_BK\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX array, dimension (N+NB+1)*(NB+3)\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. LWORK >= (N+NB+1)*(NB+3)\&. !> !> If LDWORK = -1, then a workspace query is assumed; !> the routine only calculates the optimal size of the optimal !> size of the WORK array, returns this value as the first !> entry of the WORK array, and no error message related to !> LWORK is issued by XERBLA\&. !> .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 \fBContributors:\fP .RS 4 .PP .nf !> !> November 2017, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> .fi .PP .RE .PP .PP Definition at line \fB168\fP of file \fBcsytri_3\&.f\fP\&. .SS "subroutine dsytri_3 (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) e, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer lwork, integer info)" .PP \fBDSYTRI_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> DSYTRI_3 computes the inverse of a real symmetric indefinite !> matrix A using the factorization computed by DSYTRF_RK or DSYTRF_BK: !> !> A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), !> !> where U (or L) is unit upper (or lower) triangular matrix, !> U**T (or L**T) is the transpose of U (or L), P is a permutation !> matrix, P**T is the transpose of P, and D is symmetric and block !> diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. !> !> DSYTRI_3 sets the leading dimension of the workspace before calling !> DSYTRI_3X that actually computes the inverse\&. This is the blocked !> version of the algorithm, calling Level 3 BLAS\&. !> .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 triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, diagonal of the block diagonal matrix D and !> factors U or L as computed by DSYTRF_RK and DSYTRF_BK: !> a) ONLY diagonal elements of the symmetric block diagonal !> matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); !> (superdiagonal (or subdiagonal) elements of D !> should be provided on entry in array E), and !> b) If UPLO = 'U': factor U in the superdiagonal part of A\&. !> If UPLO = 'L': factor L in the subdiagonal part of A\&. !> !> On exit, if INFO = 0, the symmetric inverse of the original !> matrix\&. !> If UPLO = 'U': the upper triangular part of the inverse !> is formed and the part of A below the diagonal is not !> referenced; !> If UPLO = 'L': the lower triangular part of the inverse !> is formed and the part of A above the diagonal is not !> referenced\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is DOUBLE PRECISION array, dimension (N) !> On entry, contains the superdiagonal (or subdiagonal) !> elements of the symmetric block diagonal matrix D !> with 1-by-1 or 2-by-2 diagonal blocks, where !> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; !> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. !> !> NOTE: For 1-by-1 diagonal block D(k), where !> 1 <= k <= N, the element E(k) is not referenced in both !> UPLO = 'U' or UPLO = 'L' cases\&. !> .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 DSYTRF_RK or DSYTRF_BK\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. !> If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3)\&. !> !> If LWORK = -1, then a workspace query is assumed; !> the routine only calculates the optimal size of the optimal !> size of the WORK array, returns this value as the first !> entry of the WORK array, and no error message related to !> LWORK is issued by XERBLA\&. !> .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 \fBContributors:\fP .RS 4 .PP .nf !> !> November 2017, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> .fi .PP .RE .PP .PP Definition at line \fB169\fP of file \fBdsytri_3\&.f\fP\&. .SS "subroutine ssytri_3 (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv, real, dimension( * ) work, integer lwork, integer info)" .PP \fBSSYTRI_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> SSYTRI_3 computes the inverse of a real symmetric indefinite !> matrix A using the factorization computed by SSYTRF_RK or SSYTRF_BK: !> !> A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), !> !> where U (or L) is unit upper (or lower) triangular matrix, !> U**T (or L**T) is the transpose of U (or L), P is a permutation !> matrix, P**T is the transpose of P, and D is symmetric and block !> diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. !> !> SSYTRI_3 sets the leading dimension of the workspace before calling !> SSYTRI_3X that actually computes the inverse\&. This is the blocked !> version of the algorithm, calling Level 3 BLAS\&. !> .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 triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, dimension (LDA,N) !> On entry, diagonal of the block diagonal matrix D and !> factors U or L as computed by SSYTRF_RK and SSYTRF_BK: !> a) ONLY diagonal elements of the symmetric block diagonal !> matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); !> (superdiagonal (or subdiagonal) elements of D !> should be provided on entry in array E), and !> b) If UPLO = 'U': factor U in the superdiagonal part of A\&. !> If UPLO = 'L': factor L in the subdiagonal part of A\&. !> !> On exit, if INFO = 0, the symmetric inverse of the original !> matrix\&. !> If UPLO = 'U': the upper triangular part of the inverse !> is formed and the part of A below the diagonal is not !> referenced; !> If UPLO = 'L': the lower triangular part of the inverse !> is formed and the part of A above the diagonal is not !> referenced\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is REAL array, dimension (N) !> On entry, contains the superdiagonal (or subdiagonal) !> elements of the symmetric block diagonal matrix D !> with 1-by-1 or 2-by-2 diagonal blocks, where !> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; !> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. !> !> NOTE: For 1-by-1 diagonal block D(k), where !> 1 <= k <= N, the element E(k) is not referenced in both !> UPLO = 'U' or UPLO = 'L' cases\&. !> .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 SSYTRF_RK or SSYTRF_BK\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL array, dimension (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. !> If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3)\&. !> !> If LWORK = -1, then a workspace query is assumed; !> the routine only calculates the optimal size of the optimal !> size of the WORK array, returns this value as the first !> entry of the WORK array, and no error message related to !> LWORK is issued by XERBLA\&. !> .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 \fBContributors:\fP .RS 4 .PP .nf !> !> November 2017, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> .fi .PP .RE .PP .PP Definition at line \fB169\fP of file \fBssytri_3\&.f\fP\&. .SS "subroutine zhetri_3 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)" .PP \fBZHETRI_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> ZHETRI_3 computes the inverse of a complex Hermitian indefinite !> matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK: !> !> A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T), !> !> where U (or L) is unit upper (or lower) triangular matrix, !> U**H (or L**H) is the conjugate of U (or L), P is a permutation !> matrix, P**T is the transpose of P, and D is Hermitian and block !> diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. !> !> ZHETRI_3 sets the leading dimension of the workspace before calling !> ZHETRI_3X that actually computes the inverse\&. This is the blocked !> version of the algorithm, calling Level 3 BLAS\&. !> .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 triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, diagonal of the block diagonal matrix D and !> factors U or L as computed by ZHETRF_RK and ZHETRF_BK: !> a) ONLY diagonal elements of the Hermitian block diagonal !> matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); !> (superdiagonal (or subdiagonal) elements of D !> should be provided on entry in array E), and !> b) If UPLO = 'U': factor U in the superdiagonal part of A\&. !> If UPLO = 'L': factor L in the subdiagonal part of A\&. !> !> On exit, if INFO = 0, the Hermitian inverse of the original !> matrix\&. !> If UPLO = 'U': the upper triangular part of the inverse !> is formed and the part of A below the diagonal is not !> referenced; !> If UPLO = 'L': the lower triangular part of the inverse !> is formed and the part of A above the diagonal is not !> referenced\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is COMPLEX*16 array, dimension (N) !> On entry, contains the superdiagonal (or subdiagonal) !> elements of the Hermitian block diagonal matrix D !> with 1-by-1 or 2-by-2 diagonal blocks, where !> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; !> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. !> !> NOTE: For 1-by-1 diagonal block D(k), where !> 1 <= k <= N, the element E(k) is not referenced in both !> UPLO = 'U' or UPLO = 'L' cases\&. !> .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 ZHETRF_RK or ZHETRF_BK\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3)\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. LWORK >= (N+NB+1)*(NB+3)\&. !> !> If LDWORK = -1, then a workspace query is assumed; !> the routine only calculates the optimal size of the optimal !> size of the WORK array, returns this value as the first !> entry of the WORK array, and no error message related to !> LWORK is issued by XERBLA\&. !> .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 \fBContributors:\fP .RS 4 .PP .nf !> !> November 2017, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> .fi .PP .RE .PP .PP Definition at line \fB168\fP of file \fBzhetri_3\&.f\fP\&. .SS "subroutine zsytri_3 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)" .PP \fBZSYTRI_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> ZSYTRI_3 computes the inverse of a complex symmetric indefinite !> matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK: !> !> A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), !> !> where U (or L) is unit upper (or lower) triangular matrix, !> U**T (or L**T) is the transpose of U (or L), P is a permutation !> matrix, P**T is the transpose of P, and D is symmetric and block !> diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. !> !> ZSYTRI_3 sets the leading dimension of the workspace before calling !> ZSYTRI_3X that actually computes the inverse\&. This is the blocked !> version of the algorithm, calling Level 3 BLAS\&. !> .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 triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, diagonal of the block diagonal matrix D and !> factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK: !> a) ONLY diagonal elements of the symmetric block diagonal !> matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); !> (superdiagonal (or subdiagonal) elements of D !> should be provided on entry in array E), and !> b) If UPLO = 'U': factor U in the superdiagonal part of A\&. !> If UPLO = 'L': factor L in the subdiagonal part of A\&. !> !> On exit, if INFO = 0, the symmetric inverse of the original !> matrix\&. !> If UPLO = 'U': the upper triangular part of the inverse !> is formed and the part of A below the diagonal is not !> referenced; !> If UPLO = 'L': the lower triangular part of the inverse !> is formed and the part of A above the diagonal is not !> referenced\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIE\fP .PP .nf !> E is COMPLEX*16 array, dimension (N) !> On entry, contains the superdiagonal (or subdiagonal) !> elements of the symmetric block diagonal matrix D !> with 1-by-1 or 2-by-2 diagonal blocks, where !> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; !> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. !> !> NOTE: For 1-by-1 diagonal block D(k), where !> 1 <= k <= N, the element E(k) is not referenced in both !> UPLO = 'U' or UPLO = 'L' cases\&. !> .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 ZSYTRF_RK or ZSYTRF_BK\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3)\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. LWORK >= (N+NB+1)*(NB+3)\&. !> !> If LDWORK = -1, then a workspace query is assumed; !> the routine only calculates the optimal size of the optimal !> size of the WORK array, returns this value as the first !> entry of the WORK array, and no error message related to !> LWORK is issued by XERBLA\&. !> .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 \fBContributors:\fP .RS 4 .PP .nf !> !> November 2017, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> .fi .PP .RE .PP .PP Definition at line \fB168\fP of file \fBzsytri_3\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.