CPPTRF computes the Cholesky factorization of a complex Hermitian


 positive definite matrix A stored in packed format.


 The factorization has the form


    A = U**H * U,  if UPLO = 'U', or


    A = L  * L**H,  if UPLO = 'L',


 where U is an upper triangular matrix and L is lower triangular.

UPLO

          UPLO is CHARACTER*1


          = '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.

AP

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


          On entry, the upper or lower triangle of the Hermitian matrix


          A, packed columnwise in a linear array.  The j-th column of A


          is stored in the array AP as follows:


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


          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.


          See below for further details.


          On exit, if INFO = 0, the triangular factor U or L from the


          Cholesky factorization A = U**H*U or A = L*L**H, in the same


          storage format as A.

INFO

          INFO is INTEGER


          = 0:  successful exit


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


          > 0:  if INFO = i, the leading principal minor of order i


                is not positive definite, and the factorization could


                not be completed.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  The packed storage scheme is illustrated by the following example


  when N = 4, UPLO = 'U':


  Two-dimensional storage of the Hermitian matrix A:


     a11 a12 a13 a14


         a22 a23 a24


             a33 a34     (aij = conjg(aji))


                 a44


  Packed storage of the upper triangle of A:


  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

 DPPTRF computes the Cholesky factorization of a real symmetric


 positive definite matrix A stored in packed format.


 The factorization has the form


    A = U**T * U,  if UPLO = 'U', or


    A = L  * L**T,  if UPLO = 'L',


 where U is an upper triangular matrix and L is lower triangular.

UPLO

          UPLO is CHARACTER*1


          = '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.

AP

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


          On entry, the upper or lower triangle of the symmetric matrix


          A, packed columnwise in a linear array.  The j-th column of A


          is stored in the array AP as follows:


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


          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.


          See below for further details.


          On exit, if INFO = 0, the triangular factor U or L from the


          Cholesky factorization A = U**T*U or A = L*L**T, in the same


          storage format as A.

INFO

          INFO is INTEGER


          = 0:  successful exit


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


          > 0:  if INFO = i, the leading principal minor of order i


                is not positive, and the factorization could not be


                completed.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  The packed storage scheme is illustrated by the following example


  when N = 4, UPLO = 'U':


  Two-dimensional storage of the symmetric matrix A:


     a11 a12 a13 a14


         a22 a23 a24


             a33 a34     (aij = aji)


                 a44


  Packed storage of the upper triangle of A:


  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

 SPPTRF computes the Cholesky factorization of a real symmetric


 positive definite matrix A stored in packed format.


 The factorization has the form


    A = U**T * U,  if UPLO = 'U', or


    A = L  * L**T,  if UPLO = 'L',


 where U is an upper triangular matrix and L is lower triangular.

UPLO

          UPLO is CHARACTER*1


          = '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.

AP

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


          On entry, the upper or lower triangle of the symmetric matrix


          A, packed columnwise in a linear array.  The j-th column of A


          is stored in the array AP as follows:


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


          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.


          See below for further details.


          On exit, if INFO = 0, the triangular factor U or L from the


          Cholesky factorization A = U**T*U or A = L*L**T, in the same


          storage format as A.

INFO

          INFO is INTEGER


          = 0:  successful exit


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


          > 0:  if INFO = i, the leading principal minor of order i


                is not positive, and the factorization could not be


                completed.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  The packed storage scheme is illustrated by the following example


  when N = 4, UPLO = 'U':


  Two-dimensional storage of the symmetric matrix A:


     a11 a12 a13 a14


         a22 a23 a24


             a33 a34     (aij = aji)


                 a44


  Packed storage of the upper triangle of A:


  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

 ZPPTRF computes the Cholesky factorization of a complex Hermitian


 positive definite matrix A stored in packed format.


 The factorization has the form


    A = U**H * U,  if UPLO = 'U', or


    A = L  * L**H,  if UPLO = 'L',


 where U is an upper triangular matrix and L is lower triangular.

UPLO

          UPLO is CHARACTER*1


          = '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.

AP

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


          On entry, the upper or lower triangle of the Hermitian matrix


          A, packed columnwise in a linear array.  The j-th column of A


          is stored in the array AP as follows:


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


          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.


          See below for further details.


          On exit, if INFO = 0, the triangular factor U or L from the


          Cholesky factorization A = U**H*U or A = L*L**H, in the same


          storage format as A.

INFO

          INFO is INTEGER


          = 0:  successful exit


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


          > 0:  if INFO = i, the leading principal minor of order i


                is not positive, and the factorization could not be


                completed.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  The packed storage scheme is illustrated by the following example


  when N = 4, UPLO = 'U':


  Two-dimensional storage of the Hermitian matrix A:


     a11 a12 a13 a14


         a22 a23 a24


             a33 a34     (aij = conjg(aji))


                 a44


  Packed storage of the upper triangle of A:


  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]