Factorisation parallèle de Cholesky pour matrices creuses sur une mémoire virtuelle partagée

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(1)Factorisation parallèle de Cholesky pour matrices creuses sur une mémoire virtuelle partagée Jocelyne Erhel, Mounir Hahad, Thierry Priol. To cite this version: Jocelyne Erhel, Mounir Hahad, Thierry Priol. Factorisation parallèle de Cholesky pour matrices creuses sur une mémoire virtuelle partagée. [Rapport de recherche] RR-1988, INRIA. 1993. �inria00074684�. HAL Id: inria-00074684 https://hal.inria.fr/inria-00074684 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Factorisation parallèle de Cholesky pour matrices creuses sur une mémoire virtuelle partagée Jocelyne Erhel, Mounir Hahad, Thierry Priol. N˚ 1988 Juillet 1993. PROGRAMME 1. Architectures parallèles, bases de données, réseaux et systèmes distribués. ISSN 0249-6399. apport de recherche. 1993.

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(113) DO j = 1, n. DO j = 1, n. DO i = j, n. DO k = 1, j-1. DO k = 1, j-1. k. i. DO i = j, n. A[i,j] = A[i,j] - A[i,k] * A[j,k]. A[i,j] = A[i,j] - A[i,k] * A[j,k]. i. ENDDO. ENDDO. If (i = j) THEN A[i,i] = SQR(A[i,i]). A[j,j] = SQR(A[j,j]). ELSE A[i,j] = A[i,j] / A[j,j]. j. DO i = j + 1, n. k. ENDIF ENDDO. 1. j. A[i,j] = A[i,j] / A[j,j] ENDDO. 2. ENDDO. ENDDO ENDDO. DO i = 1, n. DO i = 1, n. DO j = 1, i. j i. j. DO k = 1, j - 1. k. k. DO k = 1, i If (k = i) THEN A[i,i] = SQR(A[i,i]). A[i,j] = A[i,j] - A[i,k] * A[j,k]. ELSE A[i,k] = A[i,k] / A[k,k]. i. ENDDO. ENDIF. If (i = j) THEN A[i,i] = SQR(A[i,i]). DO j = k + 1, i A[i,j] = A[i,j] - A[i,k] * A[j,k]. ELSE A[i,j] = A[i,j] / A[j,j]. ENDDO. ENDIF ENDDO. 3. ENDDO. 4. ENDDO. ENDDO. DO k = 1, n. DO k = 1, n. A[k,k] = SQR(A[k,k]). A[k,k] = SQR(A[k,k]). DO i = k + 1, n. DO i = k + 1, n. A[i,k] = A[i,k] / A[k,k]. j k. 5. A[i,k] = A[i,k] / A[k,k]. DO j = k + 1, i. i. ENDDO. i. A[i,j] = A[i,j] - A[i,k] * A[j,k]. DO j = k + 1, n. ENDDO. DO i = j, n. k. ENDDO ENDDO. 5. 6. epWXjfTV\ .C5fabsbX\q lYjf~Jv;Uyfyw\sz \l¦. j. A[i,j] = A[i,j] - A[i,k] * A[j,k] ENDDO ENDDO ENDDO.

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(175) TV\so¡Ygkep©\lYRq jfy9\bUXohUyfyf\ Cdiv(8). Cmod(8, 7). Cmod(8, 6). Cmod(8, 5). Cdiv(7). Cmod(7, 3). Cmod(7, 1). Cdiv(3). Cdiv(1). Cmod(7, 6). Cdiv(6). Cmod(3, 2). Cmod(6, 4). Cdiv(2). Cdiv(4). 5. Cmod(6, 5). Cdiv(5). epWXjfTV\^; 5(4TZYmfdf\xv;\lwv\z m\ynvfYybi\l0£ L ~;\s[]mfoh\.

(176) ^0.

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(179) ^7. FN %

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(206) % 1. Contrainte de précédence Cdiv(8). Dépendance Communication inter-processeurs. Cmod(8, 7). Cdiv(7). Cmod(7, 6). Cdiv(6). Cdiv(3). Cmod(3, 2). Cmod(8, 6). Cmod(7, 3). Cmod(6, 5). Cmod(6, 4). Cmod(7, 1). Cdiv(2). Cdiv(1). Processeur 1. Processeur 2. 5. Cmod(8, 5). Cdiv(4). Processeur 3. epWXjfTV\^N. G5 ¤*Uy;gVTcYehygk\lwv;\3mfT9\z b\z v\synbi\. Cdiv(5). Processeur 4.

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