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---
:name: cla_heamv
:md5sum: a9e12928b232d452b69031ceb12d1748
:category: :subroutine
:arguments:
- uplo:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- alpha:
:type: real
:intent: input
- a:
:type: real
:intent: input
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- x:
:type: complex
:intent: input
:dims:
- 1 + ( n - 1 )*abs( incx )
- incx:
:type: integer
:intent: input
- beta:
:type: real
:intent: input
- y:
:type: real
:intent: input/output
:dims:
- 1 + ( n - 1 )*abs( incy )
- incy:
:type: integer
:intent: input
:substitutions:
lda: n
:fortran_help: " SUBROUTINE CLA_HEAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CLA_SYAMV performs the matrix-vector operation\n\
*\n\
* y := alpha*abs(A)*abs(x) + beta*abs(y),\n\
*\n\
* where alpha and beta are scalars, x and y are vectors and A is an\n\
* n by n symmetric matrix.\n\
*\n\
* This function is primarily used in calculating error bounds.\n\
* To protect against underflow during evaluation, components in\n\
* the resulting vector are perturbed away from zero by (N+1)\n\
* times the underflow threshold. To prevent unnecessarily large\n\
* errors for block-structure embedded in general matrices,\n\
* \"symbolically\" zero components are not perturbed. A zero\n\
* entry is considered \"symbolic\" if all multiplications involved\n\
* in computing that entry have at least one zero multiplicand.\n\
*\n\n\
* Arguments\n\
* ==========\n\
*\n\
* UPLO (input) INTEGER\n\
* On entry, UPLO specifies whether the upper or lower\n\
* triangular part of the array A is to be referenced as\n\
* follows:\n\
*\n\
* UPLO = BLAS_UPPER Only the upper triangular part of A\n\
* is to be referenced.\n\
*\n\
* UPLO = BLAS_LOWER Only the lower triangular part of A\n\
* is to be referenced.\n\
*\n\
* Unchanged on exit.\n\
*\n\
* N (input) INTEGER\n\
* On entry, N specifies the number of columns of the matrix A.\n\
* N must be at least zero.\n\
* Unchanged on exit.\n\
*\n\
* ALPHA (input) REAL .\n\
* On entry, ALPHA specifies the scalar alpha.\n\
* Unchanged on exit.\n\
*\n\
* A - COMPLEX array of DIMENSION ( LDA, n ).\n\
* Before entry, the leading m by n part of the array A must\n\
* contain the matrix of coefficients.\n\
* Unchanged on exit.\n\
*\n\
* LDA (input) INTEGER\n\
* On entry, LDA specifies the first dimension of A as declared\n\
* in the calling (sub) program. LDA must be at least\n\
* max( 1, n ).\n\
* Unchanged on exit.\n\
*\n\
* X (input) COMPLEX array, dimension\n\
* ( 1 + ( n - 1 )*abs( INCX ) )\n\
* Before entry, the incremented array X must contain the\n\
* vector x.\n\
* Unchanged on exit.\n\
*\n\
* INCX (input) INTEGER\n\
* On entry, INCX specifies the increment for the elements of\n\
* X. INCX must not be zero.\n\
* Unchanged on exit.\n\
*\n\
* BETA (input) REAL .\n\
* On entry, BETA specifies the scalar beta. When BETA is\n\
* supplied as zero then Y need not be set on input.\n\
* Unchanged on exit.\n\
*\n\
* Y (input/output) REAL array, dimension\n\
* ( 1 + ( n - 1 )*abs( INCY ) )\n\
* Before entry with BETA non-zero, the incremented array Y\n\
* must contain the vector y. On exit, Y is overwritten by the\n\
* updated vector y.\n\
*\n\
* INCY (input) INTEGER\n\
* On entry, INCY specifies the increment for the elements of\n\
* Y. INCY must not be zero.\n\
* Unchanged on exit.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Level 2 Blas routine.\n\
*\n\
* -- Written on 22-October-1986.\n\
* Jack Dongarra, Argonne National Lab.\n\
* Jeremy Du Croz, Nag Central Office.\n\
* Sven Hammarling, Nag Central Office.\n\
* Richard Hanson, Sandia National Labs.\n\
* -- Modified for the absolute-value product, April 2006\n\
* Jason Riedy, UC Berkeley\n\
*\n\
* =====================================================================\n\
*\n"
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