.TH "her2k" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME her2k \- {he,sy}r2k: Hermitian/symmetric rank-2k update .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcher2k\fP (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)" .br .RI "\fBCHER2K\fP " .ti -1c .RI "subroutine \fBcsyr2k\fP (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)" .br .RI "\fBCSYR2K\fP " .ti -1c .RI "subroutine \fBdsyr2k\fP (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)" .br .RI "\fBDSYR2K\fP " .ti -1c .RI "subroutine \fBssyr2k\fP (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)" .br .RI "\fBSSYR2K\fP " .ti -1c .RI "subroutine \fBzher2k\fP (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)" .br .RI "\fBZHER2K\fP " .ti -1c .RI "subroutine \fBzsyr2k\fP (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)" .br .RI "\fBZSYR2K\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cher2k (character uplo, character trans, integer n, integer k, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, real beta, complex, dimension(ldc,*) c, integer ldc)" .PP \fBCHER2K\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CHER2K performs one of the hermitian rank 2k operations C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, or C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, where alpha and beta are scalars with beta real, C is an n by n hermitian matrix and A and B are n by k matrices in the first case and k by n matrices in the second case\&. .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 array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced\&. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced\&. .fi .PP .br \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C\&. TRANS = 'C' or 'c' C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. .fi .PP .br \fIK\fP .PP .nf K is INTEGER On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'C' or 'c', K specifies the number of rows of the matrices A and B\&. K 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 \fIA\fP .PP .nf A is COMPLEX array, dimension ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k )\&. .fi .PP .br \fIB\fP .PP .nf B is COMPLEX array, dimension ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k )\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is REAL On entry, BETA specifies the scalar beta\&. .fi .PP .br \fIC\fP .PP .nf C is COMPLEX array, dimension ( LDC, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of C is not referenced\&. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix\&. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of C is not referenced\&. On exit, the lower triangular part of the array C 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 .br \fILDC\fP .PP .nf LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program\&. LDC must be at least max( 1, n )\&. .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 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1\&. Ed Anderson, Cray Research Inc\&. .fi .PP .RE .PP .SS "subroutine csyr2k (character uplo, character trans, integer n, integer k, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)" .PP \fBCSYR2K\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CSYR2K performs one of the symmetric rank 2k operations C := alpha*A*B**T + alpha*B*A**T + beta*C, or C := alpha*A**T*B + alpha*B**T*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case\&. .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 array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced\&. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced\&. .fi .PP .br \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + beta*C\&. TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + beta*C\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. .fi .PP .br \fIK\fP .PP .nf K is INTEGER On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'T' or 't', K specifies the number of rows of the matrices A and B\&. K 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 \fIA\fP .PP .nf A is COMPLEX array, dimension ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k )\&. .fi .PP .br \fIB\fP .PP .nf B is COMPLEX array, dimension ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k )\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is COMPLEX On entry, BETA specifies the scalar beta\&. .fi .PP .br \fIC\fP .PP .nf C is COMPLEX array, dimension ( LDC, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced\&. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix\&. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced\&. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix\&. .fi .PP .br \fILDC\fP .PP .nf LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program\&. LDC must be at least max( 1, n )\&. .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 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. .fi .PP .RE .PP .SS "subroutine dsyr2k (character uplo, character trans, integer n, integer k, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb,*) b, integer ldb, double precision beta, double precision, dimension(ldc,*) c, integer ldc)" .PP \fBDSYR2K\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSYR2K performs one of the symmetric rank 2k operations C := alpha*A*B**T + alpha*B*A**T + beta*C, or C := alpha*A**T*B + alpha*B**T*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case\&. .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 array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced\&. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced\&. .fi .PP .br \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + beta*C\&. TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + beta*C\&. TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + beta*C\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. .fi .PP .br \fIK\fP .PP .nf K is INTEGER On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrices A and B\&. K 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 \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k )\&. .fi .PP .br \fIB\fP .PP .nf B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k )\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is DOUBLE PRECISION\&. On entry, BETA specifies the scalar beta\&. .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension ( LDC, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced\&. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix\&. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced\&. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix\&. .fi .PP .br \fILDC\fP .PP .nf LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program\&. LDC must be at least max( 1, n )\&. .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 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. .fi .PP .RE .PP .SS "subroutine ssyr2k (character uplo, character trans, integer n, integer k, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(ldb,*) b, integer ldb, real beta, real, dimension(ldc,*) c, integer ldc)" .PP \fBSSYR2K\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSYR2K performs one of the symmetric rank 2k operations C := alpha*A*B**T + alpha*B*A**T + beta*C, or C := alpha*A**T*B + alpha*B**T*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case\&. .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 array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced\&. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced\&. .fi .PP .br \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + beta*C\&. TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + beta*C\&. TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + beta*C\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. .fi .PP .br \fIK\fP .PP .nf K is INTEGER On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrices A and B\&. K 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 \fIA\fP .PP .nf A is REAL array, dimension ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k )\&. .fi .PP .br \fIB\fP .PP .nf B is REAL array, dimension ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k )\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is REAL On entry, BETA specifies the scalar beta\&. .fi .PP .br \fIC\fP .PP .nf C is REAL array, dimension ( LDC, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced\&. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix\&. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced\&. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix\&. .fi .PP .br \fILDC\fP .PP .nf LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program\&. LDC must be at least max( 1, n )\&. .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 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. .fi .PP .RE .PP .SS "subroutine zher2k (character uplo, character trans, integer n, integer k, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, double precision beta, complex*16, dimension(ldc,*) c, integer ldc)" .PP \fBZHER2K\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZHER2K performs one of the hermitian rank 2k operations C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, or C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, where alpha and beta are scalars with beta real, C is an n by n hermitian matrix and A and B are n by k matrices in the first case and k by n matrices in the second case\&. .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 array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced\&. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced\&. .fi .PP .br \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C\&. TRANS = 'C' or 'c' C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. .fi .PP .br \fIK\fP .PP .nf K is INTEGER On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'C' or 'c', K specifies the number of rows of the matrices A and B\&. K 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 \fIA\fP .PP .nf A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k )\&. .fi .PP .br \fIB\fP .PP .nf B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k )\&. Unchanged on exit\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is DOUBLE PRECISION \&. On entry, BETA specifies the scalar beta\&. .fi .PP .br \fIC\fP .PP .nf C is COMPLEX*16 array, dimension ( LDC, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of C is not referenced\&. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix\&. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of C is not referenced\&. On exit, the lower triangular part of the array C 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 .br \fILDC\fP .PP .nf LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program\&. LDC must be at least max( 1, n )\&. .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 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1\&. Ed Anderson, Cray Research Inc\&. .fi .PP .RE .PP .SS "subroutine zsyr2k (character uplo, character trans, integer n, integer k, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta, complex*16, dimension(ldc,*) c, integer ldc)" .PP \fBZSYR2K\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZSYR2K performs one of the symmetric rank 2k operations C := alpha*A*B**T + alpha*B*A**T + beta*C, or C := alpha*A**T*B + alpha*B**T*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case\&. .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 array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced\&. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced\&. .fi .PP .br \fITRANS\fP .PP .nf TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + beta*C\&. TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + beta*C\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER On entry, N specifies the order of the matrix C\&. N must be at least zero\&. .fi .PP .br \fIK\fP .PP .nf K is INTEGER On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'T' or 't', K specifies the number of rows of the matrices A and B\&. K 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 \fIA\fP .PP .nf A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k )\&. .fi .PP .br \fIB\fP .PP .nf B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise\&. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program\&. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k )\&. .fi .PP .br \fIBETA\fP .PP .nf BETA is COMPLEX*16 On entry, BETA specifies the scalar beta\&. .fi .PP .br \fIC\fP .PP .nf C is COMPLEX*16 array, dimension ( LDC, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced\&. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix\&. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced\&. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix\&. .fi .PP .br \fILDC\fP .PP .nf LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program\&. LDC must be at least max( 1, n )\&. .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 3 Blas routine\&. -- Written on 8-February-1989\&. Jack Dongarra, Argonne National Laboratory\&. Iain Duff, AERE Harwell\&. Jeremy Du Croz, Numerical Algorithms Group Ltd\&. Sven Hammarling, Numerical Algorithms Group Ltd\&. .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.