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---
:name: cspr
:md5sum: d07736c23393e9ea356860b4e3d8a14b
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- alpha:
:type: complex
:intent: input
- x:
:type: complex
:intent: input
:dims:
- 1 + ( n - 1 )*abs( incx )
- incx:
:type: integer
:intent: input
- ap:
:type: complex
:intent: input/output
:dims:
- ( n*( n + 1 ) )/2
:substitutions: {}
:fortran_help: " SUBROUTINE CSPR( UPLO, N, ALPHA, X, INCX, AP )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CSPR performs the symmetric rank 1 operation\n\
*\n\
* A := alpha*x*conjg( x' ) + A,\n\
*\n\
* where alpha is a complex scalar, x is an n element vector and A is an\n\
* n by n symmetric matrix, supplied in packed form.\n\
*\n\n\
* Arguments\n\
* ==========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* On entry, UPLO specifies whether the upper or lower\n\
* triangular part of the matrix A is supplied in the packed\n\
* array AP as follows:\n\
*\n\
* UPLO = 'U' or 'u' The upper triangular part of A is\n\
* supplied in AP.\n\
*\n\
* UPLO = 'L' or 'l' The lower triangular part of A is\n\
* supplied in AP.\n\
*\n\
* Unchanged on exit.\n\
*\n\
* N (input) INTEGER\n\
* On entry, N specifies the order of the matrix A.\n\
* N must be at least zero.\n\
* Unchanged on exit.\n\
*\n\
* ALPHA (input) COMPLEX\n\
* On entry, ALPHA specifies the scalar alpha.\n\
* Unchanged on exit.\n\
*\n\
* X (input) COMPLEX array, dimension at least\n\
* ( 1 + ( N - 1 )*abs( INCX ) ).\n\
* Before entry, the incremented array X must contain the N-\n\
* element 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\
* AP (input/output) COMPLEX array, dimension at least\n\
* ( ( N*( N + 1 ) )/2 ).\n\
* Before entry, with UPLO = 'U' or 'u', the array AP must\n\
* contain the upper triangular part of the symmetric matrix\n\
* packed sequentially, column by column, so that AP( 1 )\n\
* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )\n\
* and a( 2, 2 ) respectively, and so on. On exit, the array\n\
* AP is overwritten by the upper triangular part of the\n\
* updated matrix.\n\
* Before entry, with UPLO = 'L' or 'l', the array AP must\n\
* contain the lower triangular part of the symmetric matrix\n\
* packed sequentially, column by column, so that AP( 1 )\n\
* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )\n\
* and a( 3, 1 ) respectively, and so on. On exit, the array\n\
* AP is overwritten by the lower triangular part of the\n\
* updated matrix.\n\
* Note that the imaginary parts of the diagonal elements need\n\
* not be set, they are assumed to be zero, and on exit they\n\
* are set to zero.\n\
*\n\n\
* =====================================================================\n\
*\n"
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