hetf2(3)

NAME
hetf2 - {he,sy}tf2: triangular factor, level 2

SYNOPSIS

  Functions
subroutine chetf2 (uplo, n, a, lda, ipiv, info)
CHETF2 computes the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm calling Level 2 BLAS).
subroutine csytf2 (uplo, n, a, lda, ipiv, info)
CSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).
subroutine dsytf2 (uplo, n, a, lda, ipiv, info)
DSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).
subroutine ssytf2 (uplo, n, a, lda, ipiv, info)
SSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).
subroutine zhetf2 (uplo, n, a, lda, ipiv, info)
ZHETF2 computes the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm, calling Level 2 BLAS).
subroutine zsytf2 (uplo, n, a, lda, ipiv, info)
ZSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).

Detailed Description

Function Documentation

  subroutine chetf2 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

CHETF2 computes the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm calling Level 2 BLAS).

Purpose:

     CHETF2 computes the factorization of a complex Hermitian matrix A
     using the Bunch-Kaufman diagonal pivoting method:
        A = U*D*U**H  or  A = L*D*L**H
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, U**H is the conjugate transpose of U, and D is
     Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
     This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters
    UPLO

              UPLO is CHARACTER*1
              Specifies whether the upper or lower triangular part of the
              Hermitian matrix A is stored:
              = 'U':  Upper triangular
              = 'L':  Lower triangular

    N

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

    A

              A is COMPLEX array, dimension (LDA,N)
              On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
              n-by-n upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading n-by-n lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, the block diagonal matrix D and the multipliers used
              to obtain the factor U or L (see below for further details).

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              Details of the interchanges and the block structure of D.
              If UPLO = 'U':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k-1) < 0, then rows and columns
                 k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
                 is a 2-by-2 diagonal block.
              If UPLO = 'L':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k+1) < 0, then rows and columns
                 k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
                 is a 2-by-2 diagonal block.

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -k, the k-th argument had an illegal value
              > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, and division by zero will occur if it
                   is used to solve a system of equations.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      09-29-06 - patch from
        Bobby Cheng, MathWorks
        Replace l.210 and l.392
             IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
        by
             IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
      01-01-96 - Based on modifications by
        J. Lewis, Boeing Computer Services Company
        A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
      If UPLO = 'U', then A = U*D*U**H, where
         U = P(n)*U(n)* ... *P(k)U(k)* ...,
      i.e., U is a product of terms P(k)*U(k), where k decreases from n to
      1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    v    0   )   k-s
         U(k) =  (   0    I    0   )   s
                 (   0    0    I   )   n-k
                    k-s   s   n-k
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
      If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
      and A(k,k), and v overwrites A(1:k-2,k-1:k).
      If UPLO = 'L', then A = L*D*L**H, where
         L = P(1)*L(1)* ... *P(k)*L(k)* ...,
      i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
      n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    0     0   )  k-1
         L(k) =  (   0    I     0   )  s
                 (   0    v     I   )  n-k-s+1
                    k-1   s  n-k-s+1
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
      If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
      and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

Definition at line 185 of file chetf2.f.

  subroutine csytf2 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

CSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).

Purpose:

     CSYTF2 computes the factorization of a complex symmetric matrix A
     using the Bunch-Kaufman diagonal pivoting method:
        A = U*D*U**T  or  A = L*D*L**T
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, U**T is the transpose of U, and D is symmetric and
     block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
     This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters
    UPLO

              UPLO is CHARACTER*1
              Specifies whether the upper or lower triangular part of the
              symmetric matrix A is stored:
              = 'U':  Upper triangular
              = 'L':  Lower triangular

    N

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

    A

              A is COMPLEX array, dimension (LDA,N)
              On entry, the symmetric matrix A.  If UPLO = 'U', the leading
              n-by-n upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading n-by-n lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, the block diagonal matrix D and the multipliers used
              to obtain the factor U or L (see below for further details).

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              Details of the interchanges and the block structure of D.
              If UPLO = 'U':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k-1) < 0, then rows and columns
                 k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
                 is a 2-by-2 diagonal block.
              If UPLO = 'L':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k+1) < 0, then rows and columns
                 k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
                 is a 2-by-2 diagonal block.

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -k, the k-th argument had an illegal value
              > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, and division by zero will occur if it
                   is used to solve a system of equations.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      If UPLO = 'U', then A = U*D*U**T, where
         U = P(n)*U(n)* ... *P(k)U(k)* ...,
      i.e., U is a product of terms P(k)*U(k), where k decreases from n to
      1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    v    0   )   k-s
         U(k) =  (   0    I    0   )   s
                 (   0    0    I   )   n-k
                    k-s   s   n-k
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
      If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
      and A(k,k), and v overwrites A(1:k-2,k-1:k).
      If UPLO = 'L', then A = L*D*L**T, where
         L = P(1)*L(1)* ... *P(k)*L(k)* ...,
      i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
      n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    0     0   )  k-1
         L(k) =  (   0    I     0   )  s
                 (   0    v     I   )  n-k-s+1
                    k-1   s  n-k-s+1
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
      If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
      and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

Contributors:

      09-29-06 - patch from
        Bobby Cheng, MathWorks
        Replace l.209 and l.377
             IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
        by
             IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
      1-96 - Based on modifications by J. Lewis, Boeing Computer Services
             Company

Definition at line 190 of file csytf2.f.

  subroutine dsytf2 (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

DSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).

Purpose:

     DSYTF2 computes the factorization of a real symmetric matrix A using
     the Bunch-Kaufman diagonal pivoting method:
        A = U*D*U**T  or  A = L*D*L**T
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, U**T is the transpose of U, and D is symmetric and
     block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
     This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters
    UPLO

              UPLO is CHARACTER*1
              Specifies whether the upper or lower triangular part of the
              symmetric matrix A is stored:
              = 'U':  Upper triangular
              = 'L':  Lower triangular

    N

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

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the symmetric matrix A.  If UPLO = 'U', the leading
              n-by-n upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading n-by-n lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, the block diagonal matrix D and the multipliers used
              to obtain the factor U or L (see below for further details).

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              Details of the interchanges and the block structure of D.
              If UPLO = 'U':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k-1) < 0, then rows and columns
                 k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
                 is a 2-by-2 diagonal block.
              If UPLO = 'L':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k+1) < 0, then rows and columns
                 k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
                 is a 2-by-2 diagonal block.

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -k, the k-th argument had an illegal value
              > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, and division by zero will occur if it
                   is used to solve a system of equations.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      If UPLO = 'U', then A = U*D*U**T, where
         U = P(n)*U(n)* ... *P(k)U(k)* ...,
      i.e., U is a product of terms P(k)*U(k), where k decreases from n to
      1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    v    0   )   k-s
         U(k) =  (   0    I    0   )   s
                 (   0    0    I   )   n-k
                    k-s   s   n-k
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
      If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
      and A(k,k), and v overwrites A(1:k-2,k-1:k).
      If UPLO = 'L', then A = L*D*L**T, where
         L = P(1)*L(1)* ... *P(k)*L(k)* ...,
      i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
      n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    0     0   )  k-1
         L(k) =  (   0    I     0   )  s
                 (   0    v     I   )  n-k-s+1
                    k-1   s  n-k-s+1
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
      If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
      and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

Contributors:

      09-29-06 - patch from
        Bobby Cheng, MathWorks
        Replace l.204 and l.372
             IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
        by
             IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
      01-01-96 - Based on modifications by
        J. Lewis, Boeing Computer Services Company
        A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
      1-96 - Based on modifications by J. Lewis, Boeing Computer Services
             Company

Definition at line 193 of file dsytf2.f.

  subroutine ssytf2 (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

SSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).

Purpose:

     SSYTF2 computes the factorization of a real symmetric matrix A using
     the Bunch-Kaufman diagonal pivoting method:
        A = U*D*U**T  or  A = L*D*L**T
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, U**T is the transpose of U, and D is symmetric and
     block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
     This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters
    UPLO

              UPLO is CHARACTER*1
              Specifies whether the upper or lower triangular part of the
              symmetric matrix A is stored:
              = 'U':  Upper triangular
              = 'L':  Lower triangular

    N

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

    A

              A is REAL array, dimension (LDA,N)
              On entry, the symmetric matrix A.  If UPLO = 'U', the leading
              n-by-n upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading n-by-n lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, the block diagonal matrix D and the multipliers used
              to obtain the factor U or L (see below for further details).

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              Details of the interchanges and the block structure of D.
              If UPLO = 'U':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k-1) < 0, then rows and columns
                 k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
                 is a 2-by-2 diagonal block.
              If UPLO = 'L':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k+1) < 0, then rows and columns
                 k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
                 is a 2-by-2 diagonal block.

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -k, the k-th argument had an illegal value
              > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, and division by zero will occur if it
                   is used to solve a system of equations.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      If UPLO = 'U', then A = U*D*U**T, where
         U = P(n)*U(n)* ... *P(k)U(k)* ...,
      i.e., U is a product of terms P(k)*U(k), where k decreases from n to
      1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    v    0   )   k-s
         U(k) =  (   0    I    0   )   s
                 (   0    0    I   )   n-k
                    k-s   s   n-k
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
      If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
      and A(k,k), and v overwrites A(1:k-2,k-1:k).
      If UPLO = 'L', then A = L*D*L**T, where
         L = P(1)*L(1)* ... *P(k)*L(k)* ...,
      i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
      n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    0     0   )  k-1
         L(k) =  (   0    I     0   )  s
                 (   0    v     I   )  n-k-s+1
                    k-1   s  n-k-s+1
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
      If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
      and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

Contributors:

      09-29-06 - patch from
        Bobby Cheng, MathWorks
        Replace l.204 and l.372
             IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
        by
             IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
      01-01-96 - Based on modifications by
        J. Lewis, Boeing Computer Services Company
        A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
      1-96 - Based on modifications by J. Lewis, Boeing Computer Services
             Company

Definition at line 194 of file ssytf2.f.

  subroutine zhetf2 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

ZHETF2 computes the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm, calling Level 2 BLAS).

Purpose:

     ZHETF2 computes the factorization of a complex Hermitian matrix A
     using the Bunch-Kaufman diagonal pivoting method:
        A = U*D*U**H  or  A = L*D*L**H
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, U**H is the conjugate transpose of U, and D is
     Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
     This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters
    UPLO

              UPLO is CHARACTER*1
              Specifies whether the upper or lower triangular part of the
              Hermitian matrix A is stored:
              = 'U':  Upper triangular
              = 'L':  Lower triangular

    N

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

    A

              A is COMPLEX*16 array, dimension (LDA,N)
              On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
              n-by-n upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading n-by-n lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, the block diagonal matrix D and the multipliers used
              to obtain the factor U or L (see below for further details).

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              Details of the interchanges and the block structure of D.
              If UPLO = 'U':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k-1) < 0, then rows and columns
                 k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
                 is a 2-by-2 diagonal block.
              If UPLO = 'L':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k+1) < 0, then rows and columns
                 k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
                 is a 2-by-2 diagonal block.

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -k, the k-th argument had an illegal value
              > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, and division by zero will occur if it
                   is used to solve a system of equations.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      If UPLO = 'U', then A = U*D*U**H, where
         U = P(n)*U(n)* ... *P(k)U(k)* ...,
      i.e., U is a product of terms P(k)*U(k), where k decreases from n to
      1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    v    0   )   k-s
         U(k) =  (   0    I    0   )   s
                 (   0    0    I   )   n-k
                    k-s   s   n-k
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
      If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
      and A(k,k), and v overwrites A(1:k-2,k-1:k).
      If UPLO = 'L', then A = L*D*L**H, where
         L = P(1)*L(1)* ... *P(k)*L(k)* ...,
      i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
      n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    0     0   )  k-1
         L(k) =  (   0    I     0   )  s
                 (   0    v     I   )  n-k-s+1
                    k-1   s  n-k-s+1
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
      If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
      and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

Contributors:

      09-29-06 - patch from
        Bobby Cheng, MathWorks
        Replace l.210 and l.393
             IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
        by
             IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
      01-01-96 - Based on modifications by
        J. Lewis, Boeing Computer Services Company
        A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Definition at line 190 of file zhetf2.f.

  subroutine zsytf2 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

ZSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).

Purpose:

     ZSYTF2 computes the factorization of a complex symmetric matrix A
     using the Bunch-Kaufman diagonal pivoting method:
        A = U*D*U**T  or  A = L*D*L**T
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, U**T is the transpose of U, and D is symmetric and
     block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
     This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters
    UPLO

              UPLO is CHARACTER*1
              Specifies whether the upper or lower triangular part of the
              symmetric matrix A is stored:
              = 'U':  Upper triangular
              = 'L':  Lower triangular

    N

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

    A

              A is COMPLEX*16 array, dimension (LDA,N)
              On entry, the symmetric matrix A.  If UPLO = 'U', the leading
              n-by-n upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading n-by-n lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, the block diagonal matrix D and the multipliers used
              to obtain the factor U or L (see below for further details).

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              Details of the interchanges and the block structure of D.
              If UPLO = 'U':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k-1) < 0, then rows and columns
                 k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
                 is a 2-by-2 diagonal block.
              If UPLO = 'L':
                 If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) = IPIV(k+1) < 0, then rows and columns
                 k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
                 is a 2-by-2 diagonal block.

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -k, the k-th argument had an illegal value
              > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, and division by zero will occur if it
                   is used to solve a system of equations.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      If UPLO = 'U', then A = U*D*U**T, where
         U = P(n)*U(n)* ... *P(k)U(k)* ...,
      i.e., U is a product of terms P(k)*U(k), where k decreases from n to
      1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    v    0   )   k-s
         U(k) =  (   0    I    0   )   s
                 (   0    0    I   )   n-k
                    k-s   s   n-k
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
      If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
      and A(k,k), and v overwrites A(1:k-2,k-1:k).
      If UPLO = 'L', then A = L*D*L**T, where
         L = P(1)*L(1)* ... *P(k)*L(k)* ...,
      i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
      n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
      and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
      defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
      that if the diagonal block D(k) is of order s (s = 1 or 2), then
                 (   I    0     0   )  k-1
         L(k) =  (   0    I     0   )  s
                 (   0    v     I   )  n-k-s+1
                    k-1   s  n-k-s+1
      If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
      If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
      and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

Contributors:

      09-29-06 - patch from
        Bobby Cheng, MathWorks
        Replace l.209 and l.377
             IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
        by
             IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
      1-96 - Based on modifications by J. Lewis, Boeing Computer Services
             Company

Definition at line 190 of file zsytf2.f.

Author

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