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SUBROUTINE <a name="DSYRK.1"></a><a href="dsyrk.f.html#DSYRK.1">DSYRK</a>(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
<span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> DOUBLE PRECISION ALPHA,BETA
INTEGER K,LDA,LDC,N
CHARACTER TRANS,UPLO
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE PRECISION A(LDA,*),C(LDC,*)
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DSYRK.14"></a><a href="dsyrk.f.html#DSYRK.1">DSYRK</a> performs one of the symmetric rank k operations
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C := alpha*A*A' + beta*C,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> or
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C := alpha*A'*A + beta*C,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where alpha and beta are scalars, C is an n by n symmetric matrix
</span><span class="comment">*</span><span class="comment"> and A is an n by k matrix in the first case and a k by n matrix
</span><span class="comment">*</span><span class="comment"> in the second case.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> ==========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO - CHARACTER*1.
</span><span class="comment">*</span><span class="comment"> On entry, UPLO specifies whether the upper or lower
</span><span class="comment">*</span><span class="comment"> triangular part of the array C is to be referenced as
</span><span class="comment">*</span><span class="comment"> follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO = 'U' or 'u' Only the upper triangular part of C
</span><span class="comment">*</span><span class="comment"> is to be referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO = 'L' or 'l' Only the lower triangular part of C
</span><span class="comment">*</span><span class="comment"> is to be referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS - CHARACTER*1.
</span><span class="comment">*</span><span class="comment"> On entry, TRANS specifies the operation to be performed as
</span><span class="comment">*</span><span class="comment"> follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS = 'N' or 'n' C := alpha*A*A' + beta*C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS = 'T' or 't' C := alpha*A'*A + beta*C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS = 'C' or 'c' C := alpha*A'*A + beta*C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, N specifies the order of the matrix C. N must be
</span><span class="comment">*</span><span class="comment"> at least zero.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> K - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry with TRANS = 'N' or 'n', K specifies the number
</span><span class="comment">*</span><span class="comment"> of columns of the matrix A, and on entry with
</span><span class="comment">*</span><span class="comment"> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
</span><span class="comment">*</span><span class="comment"> of rows of the matrix A. K must be at least zero.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ALPHA - DOUBLE PRECISION.
</span><span class="comment">*</span><span class="comment"> On entry, ALPHA specifies the scalar alpha.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
</span><span class="comment">*</span><span class="comment"> k when TRANS = 'N' or 'n', and is n otherwise.
</span><span class="comment">*</span><span class="comment"> Before entry with TRANS = 'N' or 'n', the leading n by k
</span><span class="comment">*</span><span class="comment"> part of the array A must contain the matrix A, otherwise
</span><span class="comment">*</span><span class="comment"> the leading k by n part of the array A must contain the
</span><span class="comment">*</span><span class="comment"> matrix A.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, LDA specifies the first dimension of A as declared
</span><span class="comment">*</span><span class="comment"> in the calling (sub) program. When TRANS = 'N' or 'n'
</span><span class="comment">*</span><span class="comment"> then LDA must be at least max( 1, n ), otherwise LDA must
</span><span class="comment">*</span><span class="comment"> be at least max( 1, k ).
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> BETA - DOUBLE PRECISION.
</span><span class="comment">*</span><span class="comment"> On entry, BETA specifies the scalar beta.
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
</span><span class="comment">*</span><span class="comment"> Before entry with UPLO = 'U' or 'u', the leading n by n
</span><span class="comment">*</span><span class="comment"> upper triangular part of the array C must contain the upper
</span><span class="comment">*</span><span class="comment"> triangular part of the symmetric matrix and the strictly
</span><span class="comment">*</span><span class="comment"> lower triangular part of C is not referenced. On exit, the
</span><span class="comment">*</span><span class="comment"> upper triangular part of the array C is overwritten by the
</span><span class="comment">*</span><span class="comment"> upper triangular part of the updated matrix.
</span><span class="comment">*</span><span class="comment"> Before entry with UPLO = 'L' or 'l', the leading n by n
</span><span class="comment">*</span><span class="comment"> lower triangular part of the array C must contain the lower
</span><span class="comment">*</span><span class="comment"> triangular part of the symmetric matrix and the strictly
</span><span class="comment">*</span><span class="comment"> upper triangular part of C is not referenced. On exit, the
</span><span class="comment">*</span><span class="comment"> lower triangular part of the array C is overwritten by the
</span><span class="comment">*</span><span class="comment"> lower triangular part of the updated matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDC - INTEGER.
</span><span class="comment">*</span><span class="comment"> On entry, LDC specifies the first dimension of C as declared
</span><span class="comment">*</span><span class="comment"> in the calling (sub) program. LDC must be at least
</span><span class="comment">*</span><span class="comment"> max( 1, n ).
</span><span class="comment">*</span><span class="comment"> Unchanged on exit.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Level 3 Blas routine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- Written on 8-February-1989.
</span><span class="comment">*</span><span class="comment"> Jack Dongarra, Argonne National Laboratory.
</span><span class="comment">*</span><span class="comment"> Iain Duff, AERE Harwell.
</span><span class="comment">*</span><span class="comment"> Jeremy Du Croz, Numerical Algorithms Group Ltd.
</span><span class="comment">*</span><span class="comment"> Sven Hammarling, Numerical Algorithms Group Ltd.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.120"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.121"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="XERBLA.124"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> DOUBLE PRECISION TEMP
INTEGER I,INFO,J,L,NROWA
LOGICAL UPPER
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ONE,ZERO
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span> IF (<a name="LSAME.141"></a><a href="lsame.f.html#LSAME.1">LSAME</a>(TRANS,<span class="string">'N'</span>)) THEN
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