hpr(3)

Library Functions Manual

hpr(3)

NAME

hpr - {hp,sp}r: Hermitian/symmetric rank-1 update

SYNOPSIS

Functions

subroutine chpr (uplo, n, alpha, x, incx, ap)
CHPR subroutine dspr (uplo, n, alpha, x, incx, ap)
DSPR subroutine sspr (uplo, n, alpha, x, incx, ap)
SSPR subroutine zhpr (uplo, n, alpha, x, incx, ap)
ZHPR subroutine cspr (uplo, n, alpha, x, incx, ap)
CSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix. subroutine zspr (uplo, n, alpha, x, incx, ap)
ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

Detailed Description

Function Documentation

subroutine chpr (character uplo, integer n, real alpha, complex, dimension() x, integer incx, complex, dimension() ap)

CHPR

Purpose:

 CHPR    performs the hermitian rank 1 operation
    A := alpha*x*x**H + A,
 where alpha is a real scalar, x is an n element vector and A is an
 n by n hermitian matrix, supplied in packed form.

Parameters

UPLO

          UPLO is CHARACTER*1
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:
              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.
              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.

          N is INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.

ALPHA

          ALPHA is REAL
           On entry, ALPHA specifies the scalar alpha.

          X is COMPLEX array, dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.

INCX

          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.

          AP is COMPLEX array, dimension at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the hermitian matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on. On exit, the array
           AP is overwritten by the upper triangular part of the
           updated matrix.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the hermitian matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on. On exit, the array
           AP is overwritten by the lower triangular part of the
           updated matrix.
           Note that the imaginary parts of the diagonal elements need
           not be set, they are assumed to be zero, and on exit they
           are set to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  Level 2 Blas routine.
  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.

Definition at line 129 of file chpr.f.

subroutine cspr (character uplo, integer n, complex alpha, complex, dimension( * ) x, integer incx, complex, dimension( * ) ap)

CSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

Purpose:

 CSPR    performs the symmetric rank 1 operation
    A := alpha*x*x**H + A,
 where alpha is a complex scalar, x is an n element vector and A is an
 n by n symmetric matrix, supplied in packed form.

Parameters

UPLO

          UPLO is CHARACTER*1
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:
              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.
              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.
           Unchanged on exit.

          N is INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

ALPHA

          ALPHA is COMPLEX
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

          X is COMPLEX array, dimension at least
           ( 1 + ( N - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the N-
           element vector x.
           Unchanged on exit.

INCX

          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

          AP is COMPLEX array, dimension at least
           ( ( N*( N + 1 ) )/2 ).
           Before entry, with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on. On exit, the array
           AP is overwritten by the upper triangular part of the
           updated matrix.
           Before entry, with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on. On exit, the array
           AP is overwritten by the lower triangular part of the
           updated matrix.
           Note that the imaginary parts of the diagonal elements need
           not be set, they are assumed to be zero, and on exit they
           are set to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 131 of file cspr.f.

subroutine dspr (character uplo, integer n, double precision alpha, double precision, dimension() x, integer incx, double precision, dimension() ap)

DSPR

Purpose:

 DSPR    performs the symmetric rank 1 operation
    A := alpha*x*x**T + A,
 where alpha is a real scalar, x is an n element vector and A is an
 n by n symmetric matrix, supplied in packed form.

Parameters

UPLO

          UPLO is CHARACTER*1
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:
              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.
              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.

          N is INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.

ALPHA

          ALPHA is DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.

          X is DOUBLE PRECISION array, dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.

INCX

          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.

          AP is DOUBLE PRECISION array, dimension at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on. On exit, the array
           AP is overwritten by the upper triangular part of the
           updated matrix.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on. On exit, the array
           AP is overwritten by the lower triangular part of the
           updated matrix.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  Level 2 Blas routine.
  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.

Definition at line 126 of file dspr.f.

subroutine sspr (character uplo, integer n, real alpha, real, dimension() x, integer incx, real, dimension() ap)

SSPR

Purpose:

 SSPR    performs the symmetric rank 1 operation
    A := alpha*x*x**T + A,
 where alpha is a real scalar, x is an n element vector and A is an
 n by n symmetric matrix, supplied in packed form.

Parameters

UPLO

          UPLO is CHARACTER*1
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:
              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.
              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.

          N is INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.

ALPHA

          ALPHA is REAL
           On entry, ALPHA specifies the scalar alpha.

          X is REAL array, dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.

INCX

          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.

          AP is REAL array, dimension at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on. On exit, the array
           AP is overwritten by the upper triangular part of the
           updated matrix.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on. On exit, the array
           AP is overwritten by the lower triangular part of the
           updated matrix.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  Level 2 Blas routine.
  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.

Definition at line 126 of file sspr.f.

subroutine zhpr (character uplo, integer n, double precision alpha, complex16, dimension() x, integer incx, complex16, dimension() ap)

ZHPR

Purpose:

 ZHPR    performs the hermitian rank 1 operation
    A := alpha*x*x**H + A,
 where alpha is a real scalar, x is an n element vector and A is an
 n by n hermitian matrix, supplied in packed form.

Parameters

UPLO

          UPLO is CHARACTER*1
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:
              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.
              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.

          N is INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.

ALPHA

          ALPHA is DOUBLE PRECISION.
           On entry, ALPHA specifies the scalar alpha.

          X is COMPLEX*16 array, dimension at least
           ( 1 + ( n - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the n
           element vector x.

INCX

          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.

          AP is COMPLEX*16 array, dimension at least
           ( ( n*( n + 1 ) )/2 ).
           Before entry with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the hermitian matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on. On exit, the array
           AP is overwritten by the upper triangular part of the
           updated matrix.
           Before entry with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the hermitian matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on. On exit, the array
           AP is overwritten by the lower triangular part of the
           updated matrix.
           Note that the imaginary parts of the diagonal elements need
           not be set, they are assumed to be zero, and on exit they
           are set to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  Level 2 Blas routine.
  -- Written on 22-October-1986.
     Jack Dongarra, Argonne National Lab.
     Jeremy Du Croz, Nag Central Office.
     Sven Hammarling, Nag Central Office.
     Richard Hanson, Sandia National Labs.

Definition at line 129 of file zhpr.f.

subroutine zspr (character uplo, integer n, complex16 alpha, complex16, dimension( * ) x, integer incx, complex16, dimension( ) ap)

ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

Purpose:

 ZSPR    performs the symmetric rank 1 operation
    A := alpha*x*x**H + A,
 where alpha is a complex scalar, x is an n element vector and A is an
 n by n symmetric matrix, supplied in packed form.

Parameters

UPLO

          UPLO is CHARACTER*1
           On entry, UPLO specifies whether the upper or lower
           triangular part of the matrix A is supplied in the packed
           array AP as follows:
              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  supplied in AP.
              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  supplied in AP.
           Unchanged on exit.

          N is INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.

ALPHA

          ALPHA is COMPLEX*16
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

          X is COMPLEX*16 array, dimension at least
           ( 1 + ( N - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the N-
           element vector x.
           Unchanged on exit.

INCX

          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.

          AP is COMPLEX*16 array, dimension at least
           ( ( N*( N + 1 ) )/2 ).
           Before entry, with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
           and a( 2, 2 ) respectively, and so on. On exit, the array
           AP is overwritten by the upper triangular part of the
           updated matrix.
           Before entry, with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric matrix
           packed sequentially, column by column, so that AP( 1 )
           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
           and a( 3, 1 ) respectively, and so on. On exit, the array
           AP is overwritten by the lower triangular part of the
           updated matrix.
           Note that the imaginary parts of the diagonal elements need
           not be set, they are assumed to be zero, and on exit they
           are set to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 131 of file zspr.f.

Author

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