version 1.5, 2010/08/13 21:03:41
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version 1.14, 2018/05/29 06:55:15
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*> \brief \b ZHERK |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) |
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* |
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* .. Scalar Arguments .. |
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* DOUBLE PRECISION ALPHA,BETA |
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* INTEGER K,LDA,LDC,N |
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* CHARACTER TRANS,UPLO |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 A(LDA,*),C(LDC,*) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZHERK performs one of the hermitian rank k operations |
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*> |
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*> C := alpha*A*A**H + beta*C, |
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*> |
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*> or |
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*> |
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*> C := alpha*A**H*A + beta*C, |
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*> |
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*> where alpha and beta are real scalars, C is an n by n hermitian |
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*> matrix and A is an n by k matrix in the first case and a k by n |
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*> matrix in the second case. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> On entry, UPLO specifies whether the upper or lower |
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*> triangular part of the array C is to be referenced as |
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*> follows: |
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*> |
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*> UPLO = 'U' or 'u' Only the upper triangular part of C |
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*> is to be referenced. |
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*> |
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*> UPLO = 'L' or 'l' Only the lower triangular part of C |
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*> is to be referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] TRANS |
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*> \verbatim |
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*> TRANS is CHARACTER*1 |
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*> On entry, TRANS specifies the operation to be performed as |
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*> follows: |
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*> |
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*> TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C. |
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*> |
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*> TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> On entry, N specifies the order of the matrix C. N must be |
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*> at least zero. |
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*> \endverbatim |
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*> |
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*> \param[in] K |
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*> \verbatim |
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*> K is INTEGER |
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*> On entry with TRANS = 'N' or 'n', K specifies the number |
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*> of columns of the matrix A, and on entry with |
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*> TRANS = 'C' or 'c', K specifies the number of rows of the |
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*> matrix A. K must be at least zero. |
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*> \endverbatim |
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*> |
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*> \param[in] ALPHA |
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*> \verbatim |
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*> ALPHA is DOUBLE PRECISION . |
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*> On entry, ALPHA specifies the scalar alpha. |
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*> \endverbatim |
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*> |
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*> \param[in] A |
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*> \verbatim |
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*> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is |
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*> k when TRANS = 'N' or 'n', and is n otherwise. |
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*> Before entry with TRANS = 'N' or 'n', the leading n by k |
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*> part of the array A must contain the matrix A, otherwise |
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*> the leading k by n part of the array A must contain the |
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*> matrix A. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> On entry, LDA specifies the first dimension of A as declared |
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*> in the calling (sub) program. When TRANS = 'N' or 'n' |
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*> then LDA must be at least max( 1, n ), otherwise LDA must |
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*> be at least max( 1, k ). |
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*> \endverbatim |
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*> |
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*> \param[in] BETA |
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*> \verbatim |
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*> BETA is DOUBLE PRECISION. |
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*> On entry, BETA specifies the scalar beta. |
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*> \endverbatim |
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*> |
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*> \param[in,out] C |
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*> \verbatim |
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*> C is COMPLEX*16 array, dimension ( LDC, N ) |
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*> Before entry with UPLO = 'U' or 'u', the leading n by n |
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*> upper triangular part of the array C must contain the upper |
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*> triangular part of the hermitian matrix and the strictly |
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*> lower triangular part of C is not referenced. On exit, the |
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*> upper triangular part of the array C is overwritten by the |
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*> upper triangular part of the updated matrix. |
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*> Before entry with UPLO = 'L' or 'l', the leading n by n |
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*> lower triangular part of the array C must contain the lower |
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*> triangular part of the hermitian matrix and the strictly |
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*> upper triangular part of C is not referenced. On exit, the |
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*> lower triangular part of the array C is overwritten by the |
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*> lower triangular part of the updated matrix. |
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*> Note that the imaginary parts of the diagonal elements need |
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*> not be set, they are assumed to be zero, and on exit they |
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*> are set to zero. |
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*> \endverbatim |
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*> |
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*> \param[in] LDC |
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*> \verbatim |
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*> LDC is INTEGER |
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*> On entry, LDC specifies the first dimension of C as declared |
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*> in the calling (sub) program. LDC must be at least |
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*> max( 1, n ). |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date December 2016 |
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* |
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*> \ingroup complex16_blas_level3 |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> Level 3 Blas routine. |
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*> |
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*> -- Written on 8-February-1989. |
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*> Jack Dongarra, Argonne National Laboratory. |
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*> Iain Duff, AERE Harwell. |
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*> Jeremy Du Croz, Numerical Algorithms Group Ltd. |
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*> Sven Hammarling, Numerical Algorithms Group Ltd. |
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*> |
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*> -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. |
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*> Ed Anderson, Cray Research Inc. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) |
SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) |
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* |
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* -- Reference BLAS level3 routine (version 3.7.0) -- |
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* December 2016 |
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* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
DOUBLE PRECISION ALPHA,BETA |
DOUBLE PRECISION ALPHA,BETA |
INTEGER K,LDA,LDC,N |
INTEGER K,LDA,LDC,N |
CHARACTER TRANS,UPLO |
CHARACTER TRANS,UPLO |
* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
DOUBLE COMPLEX A(LDA,*),C(LDC,*) |
COMPLEX*16 A(LDA,*),C(LDC,*) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZHERK performs one of the hermitian rank k operations |
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* |
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* C := alpha*A*conjg( A' ) + beta*C, |
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* |
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* or |
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* |
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* C := alpha*conjg( A' )*A + beta*C, |
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* |
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* where alpha and beta are real scalars, C is an n by n hermitian |
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* matrix and A is an n by k matrix in the first case and a k by n |
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* matrix in the second case. |
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* |
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* Arguments |
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* ========== |
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* |
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* UPLO - CHARACTER*1. |
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* On entry, UPLO specifies whether the upper or lower |
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* triangular part of the array C is to be referenced as |
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* follows: |
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* |
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* UPLO = 'U' or 'u' Only the upper triangular part of C |
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* is to be referenced. |
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* |
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* UPLO = 'L' or 'l' Only the lower triangular part of C |
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* is to be referenced. |
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* |
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* Unchanged on exit. |
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* |
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* TRANS - CHARACTER*1. |
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* On entry, TRANS specifies the operation to be performed as |
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* follows: |
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* |
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* TRANS = 'N' or 'n' C := alpha*A*conjg( A' ) + beta*C. |
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* |
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* TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C. |
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* |
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* Unchanged on exit. |
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* |
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* N - INTEGER. |
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* On entry, N specifies the order of the matrix C. N must be |
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* at least zero. |
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* Unchanged on exit. |
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* |
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* K - INTEGER. |
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* On entry with TRANS = 'N' or 'n', K specifies the number |
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* of columns of the matrix A, and on entry with |
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* TRANS = 'C' or 'c', K specifies the number of rows of the |
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* matrix A. K must be at least zero. |
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* Unchanged on exit. |
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* |
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* ALPHA - DOUBLE PRECISION . |
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* On entry, ALPHA specifies the scalar alpha. |
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* Unchanged on exit. |
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* |
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* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is |
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* k when TRANS = 'N' or 'n', and is n otherwise. |
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* Before entry with TRANS = 'N' or 'n', the leading n by k |
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* part of the array A must contain the matrix A, otherwise |
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* the leading k by n part of the array A must contain the |
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* matrix A. |
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* Unchanged on exit. |
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* |
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* LDA - INTEGER. |
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* On entry, LDA specifies the first dimension of A as declared |
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* in the calling (sub) program. When TRANS = 'N' or 'n' |
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* then LDA must be at least max( 1, n ), otherwise LDA must |
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* be at least max( 1, k ). |
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* Unchanged on exit. |
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* |
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* BETA - DOUBLE PRECISION. |
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* On entry, BETA specifies the scalar beta. |
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* Unchanged on exit. |
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* |
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* C - COMPLEX*16 array of DIMENSION ( LDC, n ). |
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* Before entry with UPLO = 'U' or 'u', the leading n by n |
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* upper triangular part of the array C must contain the upper |
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* triangular part of the hermitian matrix and the strictly |
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* lower triangular part of C is not referenced. On exit, the |
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* upper triangular part of the array C is overwritten by the |
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* upper triangular part of the updated matrix. |
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* Before entry with UPLO = 'L' or 'l', the leading n by n |
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* lower triangular part of the array C must contain the lower |
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* triangular part of the hermitian matrix and the strictly |
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* upper triangular part of C is not referenced. On exit, the |
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* lower triangular part of the array C is overwritten by the |
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* lower triangular part of the updated matrix. |
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* Note that the imaginary parts of the diagonal elements need |
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* not be set, they are assumed to be zero, and on exit they |
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* are set to zero. |
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* |
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* LDC - INTEGER. |
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* On entry, LDC specifies the first dimension of C as declared |
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* in the calling (sub) program. LDC must be at least |
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* max( 1, n ). |
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* Unchanged on exit. |
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* |
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* Further Details |
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* =============== |
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* |
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* Level 3 Blas routine. |
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* |
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* -- Written on 8-February-1989. |
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* Jack Dongarra, Argonne National Laboratory. |
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* Iain Duff, AERE Harwell. |
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* Jeremy Du Croz, Numerical Algorithms Group Ltd. |
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* Sven Hammarling, Numerical Algorithms Group Ltd. |
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* |
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* -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. |
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* Ed Anderson, Cray Research Inc. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. External Functions .. |
* .. External Functions .. |
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INTRINSIC DBLE,DCMPLX,DCONJG,MAX |
INTRINSIC DBLE,DCMPLX,DCONJG,MAX |
* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
DOUBLE COMPLEX TEMP |
COMPLEX*16 TEMP |
DOUBLE PRECISION RTEMP |
DOUBLE PRECISION RTEMP |
INTEGER I,INFO,J,L,NROWA |
INTEGER I,INFO,J,L,NROWA |
LOGICAL UPPER |
LOGICAL UPPER |
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* |
* |
IF (LSAME(TRANS,'N')) THEN |
IF (LSAME(TRANS,'N')) THEN |
* |
* |
* Form C := alpha*A*conjg( A' ) + beta*C. |
* Form C := alpha*A*A**H + beta*C. |
* |
* |
IF (UPPER) THEN |
IF (UPPER) THEN |
DO 130 J = 1,N |
DO 130 J = 1,N |
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END IF |
END IF |
ELSE |
ELSE |
* |
* |
* Form C := alpha*conjg( A' )*A + beta*C. |
* Form C := alpha*A**H*A + beta*C. |
* |
* |
IF (UPPER) THEN |
IF (UPPER) THEN |
DO 220 J = 1,N |
DO 220 J = 1,N |