.TH "hpr2" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME hpr2 \- {hp,sp}r2: Hermitian/symmetric rank-2 update .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBchpr2\fP (uplo, n, alpha, x, incx, y, incy, ap)" .br .RI "\fBCHPR2\fP " .ti -1c .RI "subroutine \fBdspr2\fP (uplo, n, alpha, x, incx, y, incy, ap)" .br .RI "\fBDSPR2\fP " .ti -1c .RI "subroutine \fBsspr2\fP (uplo, n, alpha, x, incx, y, incy, ap)" .br .RI "\fBSSPR2\fP " .ti -1c .RI "subroutine \fBzhpr2\fP (uplo, n, alpha, x, incx, y, incy, ap)" .br .RI "\fBZHPR2\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine chpr2 (character uplo, integer n, complex alpha, complex, dimension(*) x, integer incx, complex, dimension(*) y, integer incy, complex, dimension(*) ap)" .PP \fBCHPR2\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CHPR2 performs the hermitian rank 2 operation A := alpha*x*y**H + conjg( alpha )*y*x**H + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIX\fP .PP .nf 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\&. .fi .PP .br \fIINCX\fP .PP .nf INCX is INTEGER On entry, INCX specifies the increment for the elements of X\&. INCX must not be zero\&. .fi .PP .br \fIY\fP .PP .nf Y is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) )\&. Before entry, the incremented array Y must contain the n element vector y\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .br \fIAP\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP .SS "subroutine dspr2 (character uplo, integer n, double precision alpha, double precision, dimension(*) x, integer incx, double precision, dimension(*) y, integer incy, double precision, dimension(*) ap)" .PP \fBDSPR2\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSPR2 performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is DOUBLE PRECISION\&. On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIX\fP .PP .nf 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\&. .fi .PP .br \fIINCX\fP .PP .nf INCX is INTEGER On entry, INCX specifies the increment for the elements of X\&. INCX must not be zero\&. .fi .PP .br \fIY\fP .PP .nf Y is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) )\&. Before entry, the incremented array Y must contain the n element vector y\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .br \fIAP\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP .SS "subroutine sspr2 (character uplo, integer n, real alpha, real, dimension(*) x, integer incx, real, dimension(*) y, integer incy, real, dimension(*) ap)" .PP \fBSSPR2\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSPR2 performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is REAL On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIX\fP .PP .nf 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\&. .fi .PP .br \fIINCX\fP .PP .nf INCX is INTEGER On entry, INCX specifies the increment for the elements of X\&. INCX must not be zero\&. .fi .PP .br \fIY\fP .PP .nf Y is REAL array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) )\&. Before entry, the incremented array Y must contain the n element vector y\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .br \fIAP\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP .SS "subroutine zhpr2 (character uplo, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(*) ap)" .PP \fBZHPR2\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZHPR2 performs the hermitian rank 2 operation A := alpha*x*y**H + conjg( alpha )*y*x**H + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix A\&. N must be at least zero\&. .fi .PP .br \fIALPHA\fP .PP .nf ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha\&. .fi .PP .br \fIX\fP .PP .nf 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\&. .fi .PP .br \fIINCX\fP .PP .nf INCX is INTEGER On entry, INCX specifies the increment for the elements of X\&. INCX must not be zero\&. .fi .PP .br \fIY\fP .PP .nf Y is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) )\&. Before entry, the incremented array Y must contain the n element vector y\&. .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER On entry, INCY specifies the increment for the elements of Y\&. INCY must not be zero\&. .fi .PP .br \fIAP\fP .PP .nf 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\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.