This routine is available only to users of the COS operating system

NOTE

CSYMM

is a

level 3 Basic Linear Algebra Subprogram (BLAS 3),

SR-Ol13

4-44

D

CSYR2K (3COS ) CSYR2K(3COS)

NAME

CSYR2K - Performs symmetric rank 2k update of a complex symmetric matrix SYNOPSIS

CALL CSYR2K(uplo,trans,n,k,a/pha,a,lda.b.ldb,beta,c.ldc) DESCRIPTION

SR-01l3

CSYR2K performs one of the following symmetric rank 2k operations:

c := alpha*a*b' +alplul*b*a' +beta*c or

c := alpha*a'*b+alpha*b'*a+beta*c

Arguments alpha and beta are scalars. and c is an n-by-n symmetric matrix. Arguments a and b are n-by·k matrices in the first operation listed previously, and k-by-n matrices in the second.

uplo Type charac~I.

trans Type character* 1.

On entry, trans specifies the operation to be performed as follows:

If trans

=

'N' or 'n',

C := alpha*a*b' +alpha*b*a' +heta*c If trans = 'T' or 't',

c := aipha*a'*b+alplul*b'*a+beta*c On exit, trans is unchanged

On entry, alpha specifies the scalar alpha.

On exit. alpha is unchanged.

4-45 D

CSYR2K(3COS) CSYR2K(3COS)

a Type complex.

Array of dimension (Ida, ka).

Argument lea is k if trans

=

'N' or 'n', and is n otherwise.

Otherwise. Idb must be at least max(l. k).

On exit, ldb is unchanged.

beta Type complex.

On entry, beta specifies the scalar beta.

On exit, beta is unchanged.

e Type complex.

Array of dimension (Ide, n).

Before entry with up[o = 'U' or 'u', the leading n-by-n upper triangular part of array c must contain the upper triangular part of the symmetric matrix.

The strictly lower triangular part of

e

is not referenced.

On exit, the upper triangular part of array c is overwritten by the upper triangular part of the updated matrix.

Before entry with uplo :;;;; 'L' or 'I'. the leading n-by-n lower triangular part of array e must contain the lower triangular part of the symmetric matrix.

The strictly upper triangular part of e is not referenced.

On exit, the lower triangular part of array e is overwritten by the lower triangular part of the

CS YR2K (3COS) CSYR.2K (3COS )

NOTE

CSYR2K is a level 3 Basic Linear Algebra Subprogram (BLAS 3).

SR-Ol13 ^4-47 D

CSYRK(3COS) CSYRK.(3COS)

CSYRK perfonns one of the following symmetric rank k operations:

e := alpha*a*a' +beta*c or

c := alpha*a' *a+beta*c

Arguments alpha and beta are

scalars,

and c

is an

n-by-n symmetric matrix. Argument a is

an

n-by-k matrix in the

first

operation listed previously. and a k-by-n matrix in the second.

uplo

Type

character"'1.

On entry, uplo specifies whether the upper or lower triangular part of array e is to be

CSYRK(3COS) CSYRK(3COS)

a Type complex.

Array of dimension (ida, ka).

Argument ka is k if trans

=

'N' or 'n', and is n otherwise.

Before entry with trans

=

'N' or 'n', the leading n-by-k part of array a must contain matrix a.

Otherwise, the leading k-by-n part of array a must contain matrix a.

On exit, a is unchanged.

Ida Type integer.

On entry, Ida specifies the first dimension of a as declared in the calling (sllb)program.

If trans = 'N' or 'n', Ida must be at least max(l, n).

Otherwise, Ida must be at least max(l, k).

On exit, Ida is unchanged.

beta Type complex.

On entry, beta specifies the scalar beta.

On exit, bela is unchanged.

e Type complex.

Array of dimension (Ide, n).

Before entry

with

uplo ;;;;

'u'

or 'u', the leading n-by-n upper triangular part of array c must contain the upper triangular part of the symmetric matrix.

The strictly lower triangular part of e is not referenced.

On exit, the upper triangular part of array e is overwritten by the upper triangular pan of the updated matrix.

Before entry with uplo

=

^{'L' or "1',} the leading n-by-n lower triangular part of array e must contain the lower triangular part of the symmetric matrix.

The strictly upper triangular part of c is not referenced.

On exit, the lower triangular part of array c is overwritten by the lower triangular pan of the updated matrix.

Ide Type integer.

On entry, Ide specifies the first dimension of e as declared in the calling (sub)program.

Argumentlde must be at least max(l. n).

On exit, Ide is unchanged.

IMPLEMENTATION

This routine is available only to users of the

cos

operating system.

NOTE

CSYRK is a level 3 Basic Linear AJgebra Subprogram (BLAS 3).

SR-Ol13 4-49 D

CTBMV (3COS ) CTBMV (3COS)

NAME

CTBMV - Multiplies a complex vector by a complex triangular band matrix SYNOPSIS

CALL CTBMV(uplo, trans ,diag ,n,k,a,lda.x,incx) DESCRIPTION

SR-01l3

CTBMV performs one of the following matrix~vector operations:

x:= a*x or x := a'·x or x := conjg(a')"'x

Argument x is an n element vector, and a is an n-by-n unit, or non-unit, upper or lower triangular band matrix. with (k+ 1) diagonals.

uplo Type character'" 1.

On entry, uplo specifies whether the matrix is an upper or lower triangular matrix

as

follows:

If uplo

=

^{'U' or} 'u', a is an upper triangular matrix.

If uplo

=

'L' or '1', a is a lower triangular matrix.

On exit, uplo is unchanged.

trans Type character "'I.

On entry, trans specifies the operation to be perfonned as follows:

If trans

=

'N' or 'n'. x := a"'x.

CTBMV (3COS ) CTBMV (3COS)

The following program segment will transfer

an

upper triangular band matrix from conven-tional full matrix storage to band storage:

DO 20, J

=

I, N

The following program segment will transfer a lower triangular band matrix from conventional full matrix storage to band storage:

CTBMV(3COS) CTBMV (3COS )

NOTE

CTBMV is a level 2 Basic Linear Algebra Subprogram (BLAS 2).

SR-OI13 4-52 D

crBSV (3CaS) crBSV (3CaS )

NAME

crBSV - Solves a complex triangular banded system of equations SYNOPSIS

CALL CTBSV(uplo,trafls,diog,n.k,a,lda.x,incx) DESCRIYfION

SR-Ol13

crBSV solves one of the following systems of equations:

o"'x=b

diag Type character "'I.

On entry, diag specifies whether or not a is Wlit triangular as follows:

CTBSV(3COS) CTBSV(3COS)

a Type complex.

Array of dimension (Ida, n).

Before entry with uplo

=

^'U' or 'u', the leading (k+l)-by-n part of array a must contain the upper triangular band part of the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row (k+l) of the array, the first superdiagonal starting at posi-tion 2 in row k, and so on. The top left k-by-k triangle of array a is not referenced.

The following program segment will transfer an upper triangular band matrix from conven-tional full matrix storage to band storage:

The following program segment will transfer a lower triangular band matrix from conventional full matrix storage to band storage:

DO 20, J = 1, N

CTBSV(3COS) CfBSV (3eOS)

NOTES

SR-01l3

No tests for singularity or near-singularity are included in CTBSV.

Such

tests must be performed before

calling

this

routine.

CTBSV is a level 2 Basic Linear Algebra

Subprogram

(BLAS 2).

4-55 D

CTRMM (3CaS) CfRMM (3CaS)

NAME

Im Dokument SR-0113 D (Seite 164-176)