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

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subroutinechpr(characteruplo,integern,realalpha,complex,dimension(*)x,integerincx,complex,dimension(*)ap)CHPRPurpose: 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. ParametersUPLO 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 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 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 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. FurtherDetails: 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. subroutinecspr(characteruplo,integern,complexalpha,complex,dimension(*)x,integerincx,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. ParametersUPLO 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 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 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 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. subroutinedspr(characteruplo,integern,doubleprecisionalpha,doubleprecision,dimension(*)x,integerincx,doubleprecision,dimension(*)ap)DSPRPurpose: 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. ParametersUPLO 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 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 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 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. FurtherDetails: 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. subroutinesspr(characteruplo,integern,realalpha,real,dimension(*)x,integerincx,real,dimension(*)ap)SSPRPurpose: 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. ParametersUPLO 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 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 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 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. FurtherDetails: 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. subroutinezhpr(characteruplo,integern,doubleprecisionalpha,complex*16,dimension(*)x,integerincx,complex*16,dimension(*)ap)ZHPRPurpose: 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. ParametersUPLO 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 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 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 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. FurtherDetails: 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. subroutinezspr(characteruplo,integern,complex*16alpha,complex*16,dimension(*)x,integerincx,complex*16,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. ParametersUPLO 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 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 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 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.

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

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.