hetri_3x(3)

NAME
hetri_3x - {he,sy}tri_3x: inverse

SYNOPSIS

  Functions

subroutine chetri_3x (uplo, n, a, lda, e, ipiv, work, nb, info)
CHETRI_3X
subroutine csytri_3x (uplo, n, a, lda, e, ipiv, work, nb, info)
CSYTRI_3X
subroutine dsytri_3x (uplo, n, a, lda, e, ipiv, work, nb, info)
DSYTRI_3X
subroutine ssytri_3x (uplo, n, a, lda, e, ipiv, work, nb, info)
SSYTRI_3X
subroutine zhetri_3x (uplo, n, a, lda, e, ipiv, work, nb, info)
ZHETRI_3X
subroutine zsytri_3x (uplo, n, a, lda, e, ipiv, work, nb, info)
ZSYTRI_3X

Detailed Description

Function Documentation

  subroutine chetri_3x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( n+nb+1, * ) work, integer nb, integer info)

CHETRI_3X

Purpose:

    !> CHETRI_3X 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.
    !>
    !> This is the blocked version of the algorithm, calling Level 3 BLAS.
    !>

Parameters
    UPLO

    !>          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.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by CHETRF_RK or CHETRF_BK.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (N+NB+1,NB+3).
    !>

    NB

    !>          NB is INTEGER
    !>          Block size.
    !>

    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.

Contributors:

    !>
    !>  June 2017,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>

  subroutine csytri_3x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( n+nb+1, * ) work, integer nb, integer info)

CSYTRI_3X

Purpose:

    !> CSYTRI_3X 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.
    !>
    !> This is the blocked version of the algorithm, calling Level 3 BLAS.
    !>

Parameters
    UPLO

    !>          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.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by CSYTRF_RK or CSYTRF_BK.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (N+NB+1,NB+3).
    !>

    NB

    !>          NB is INTEGER
    !>          Block size.
    !>

    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.

Contributors:

    !>
    !>  June 2017,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>

  subroutine dsytri_3x (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) e, integer, dimension( * ) ipiv, double precision, dimension( n+nb+1, * ) work, integer nb, integer info)

DSYTRI_3X

Purpose:

    !> DSYTRI_3X 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.
    !>
    !> This is the blocked version of the algorithm, calling Level 3 BLAS.
    !>

Parameters
    UPLO

    !>          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.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by DSYTRF_RK or DSYTRF_BK.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (N+NB+1,NB+3).
    !>

    NB

    !>          NB is INTEGER
    !>          Block size.
    !>

    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.

Contributors:

    !>
    !>  June 2017,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>

  subroutine ssytri_3x (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv, real, dimension( n+nb+1, * ) work, integer nb, integer info)

SSYTRI_3X

Purpose:

    !> SSYTRI_3X 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.
    !>
    !> This is the blocked version of the algorithm, calling Level 3 BLAS.
    !>

Parameters
    UPLO

    !>          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.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, diagonal of the block diagonal matrix D and
    !>          factors U or L as computed by SYTRF_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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by SSYTRF_RK or SSYTRF_BK.
    !>

    WORK

    !>          WORK is REAL array, dimension (N+NB+1,NB+3).
    !>

    NB

    !>          NB is INTEGER
    !>          Block size.
    !>

    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.

Contributors:

    !>
    !>  June 2017,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>

  subroutine zhetri_3x (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( * ) ipiv, complex*16, dimension( n+nb+1, * ) work, integer nb, integer info)

ZHETRI_3X

Purpose:

    !> ZHETRI_3X 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.
    !>
    !> This is the blocked version of the algorithm, calling Level 3 BLAS.
    !>

Parameters
    UPLO

    !>          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.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by ZHETRF_RK or ZHETRF_BK.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3).
    !>

    NB

    !>          NB is INTEGER
    !>          Block size.
    !>

    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.

Contributors:

    !>
    !>  June 2017,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>

  subroutine zsytri_3x (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( * ) ipiv, complex*16, dimension( n+nb+1, * ) work, integer nb, integer info)

ZSYTRI_3X

Purpose:

    !> ZSYTRI_3X 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.
    !>
    !> This is the blocked version of the algorithm, calling Level 3 BLAS.
    !>

Parameters
    UPLO

    !>          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.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by ZSYTRF_RK or ZSYTRF_BK.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3).
    !>

    NB

    !>          NB is INTEGER
    !>          Block size.
    !>

    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.

Contributors:

    !>
    !>  June 2017,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>

Author

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