pbtf2(3)

NAME
pbtf2 - pbtf2: triangular factor panel, level 2

SYNOPSIS

  Functions

subroutine cpbtf2 (uplo, n, kd, ab, ldab, info)
CPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).
subroutine dpbtf2 (uplo, n, kd, ab, ldab, info)
DPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).
subroutine spbtf2 (uplo, n, kd, ab, ldab, info)
SPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).
subroutine zpbtf2 (uplo, n, kd, ab, ldab, info)
ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Detailed Description

Function Documentation

  subroutine cpbtf2 (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, integer info)

CPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Purpose:

    !>
    !> CPBTF2 computes the Cholesky factorization of a complex Hermitian
    !> positive definite band matrix A.
    !>
    !> 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, U**H is the conjugate transpose
    !> of U, and L is lower triangular.
    !>
    !> 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.
    !>

    KD

    !>          KD is INTEGER
    !>          The number of super-diagonals of the matrix A if UPLO = 'U',
    !>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
    !>

    AB

    !>          AB is COMPLEX array, dimension (LDAB,N)
    !>          On entry, the upper or lower triangle of the Hermitian band
    !>          matrix A, stored in the first KD+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>
    !>          On exit, if INFO = 0, the triangular factor U or L from the
    !>          Cholesky factorization A = U**H *U or A = L*L**H of the band
    !>          matrix A, in the same storage format as A.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD+1.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -k, the k-th argument had an illegal value
    !>          > 0: if INFO = k, the leading principal minor of order k
    !>               is not positive, and the factorization could not be
    !>               completed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The band storage scheme is illustrated by the following example, when
    !>  N = 6, KD = 2, and UPLO = 'U':
    !>
    !>  On entry:                       On exit:
    !>
    !>      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
    !>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
    !>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    !>
    !>  Similarly, if UPLO = 'L' the format of A is as follows:
    !>
    !>  On entry:                       On exit:
    !>
    !>     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
    !>     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
    !>     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
    !>
    !>  Array elements marked * are not used by the routine.
    !>

  subroutine dpbtf2 (character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, integer info)

DPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Purpose:

    !>
    !> DPBTF2 computes the Cholesky factorization of a real symmetric
    !> positive definite band matrix A.
    !>
    !> 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, U**T is the transpose of U, and
    !> L is lower triangular.
    !>
    !> 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.
    !>

    KD

    !>          KD is INTEGER
    !>          The number of super-diagonals of the matrix A if UPLO = 'U',
    !>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
    !>

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
    !>          On entry, the upper or lower triangle of the symmetric band
    !>          matrix A, stored in the first KD+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>
    !>          On exit, if INFO = 0, the triangular factor U or L from the
    !>          Cholesky factorization A = U**T*U or A = L*L**T of the band
    !>          matrix A, in the same storage format as A.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD+1.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -k, the k-th argument had an illegal value
    !>          > 0: if INFO = k, the leading principal minor of order k
    !>               is not positive, and the factorization could not be
    !>               completed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The band storage scheme is illustrated by the following example, when
    !>  N = 6, KD = 2, and UPLO = 'U':
    !>
    !>  On entry:                       On exit:
    !>
    !>      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
    !>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
    !>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    !>
    !>  Similarly, if UPLO = 'L' the format of A is as follows:
    !>
    !>  On entry:                       On exit:
    !>
    !>     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
    !>     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
    !>     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
    !>
    !>  Array elements marked * are not used by the routine.
    !>

  subroutine spbtf2 (character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, integer info)

SPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Purpose:

    !>
    !> SPBTF2 computes the Cholesky factorization of a real symmetric
    !> positive definite band matrix A.
    !>
    !> 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, U**T is the transpose of U, and
    !> L is lower triangular.
    !>
    !> 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.
    !>

    KD

    !>          KD is INTEGER
    !>          The number of super-diagonals of the matrix A if UPLO = 'U',
    !>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
    !>

    AB

    !>          AB is REAL array, dimension (LDAB,N)
    !>          On entry, the upper or lower triangle of the symmetric band
    !>          matrix A, stored in the first KD+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>
    !>          On exit, if INFO = 0, the triangular factor U or L from the
    !>          Cholesky factorization A = U**T*U or A = L*L**T of the band
    !>          matrix A, in the same storage format as A.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD+1.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -k, the k-th argument had an illegal value
    !>          > 0: if INFO = k, the leading principal minor of order k
    !>               is not positive, and the factorization could not be
    !>               completed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The band storage scheme is illustrated by the following example, when
    !>  N = 6, KD = 2, and UPLO = 'U':
    !>
    !>  On entry:                       On exit:
    !>
    !>      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
    !>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
    !>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    !>
    !>  Similarly, if UPLO = 'L' the format of A is as follows:
    !>
    !>  On entry:                       On exit:
    !>
    !>     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
    !>     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
    !>     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
    !>
    !>  Array elements marked * are not used by the routine.
    !>

  subroutine zpbtf2 (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, integer info)

ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Purpose:

    !>
    !> ZPBTF2 computes the Cholesky factorization of a complex Hermitian
    !> positive definite band matrix A.
    !>
    !> 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, U**H is the conjugate transpose
    !> of U, and L is lower triangular.
    !>
    !> 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.
    !>

    KD

    !>          KD is INTEGER
    !>          The number of super-diagonals of the matrix A if UPLO = 'U',
    !>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
    !>

    AB

    !>          AB is COMPLEX*16 array, dimension (LDAB,N)
    !>          On entry, the upper or lower triangle of the Hermitian band
    !>          matrix A, stored in the first KD+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>
    !>          On exit, if INFO = 0, the triangular factor U or L from the
    !>          Cholesky factorization A = U**H *U or A = L*L**H of the band
    !>          matrix A, in the same storage format as A.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD+1.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -k, the k-th argument had an illegal value
    !>          > 0: if INFO = k, the leading principal minor of order k
    !>               is not positive, and the factorization could not be
    !>               completed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The band storage scheme is illustrated by the following example, when
    !>  N = 6, KD = 2, and UPLO = 'U':
    !>
    !>  On entry:                       On exit:
    !>
    !>      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
    !>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
    !>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    !>
    !>  Similarly, if UPLO = 'L' the format of A is as follows:
    !>
    !>  On entry:                       On exit:
    !>
    !>     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
    !>     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
    !>     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
    !>
    !>  Array elements marked * are not used by the routine.
    !>

Author

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