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| author | stainer_t <thomas.stainer@oecd-nea.org> | 2025-09-08 13:48:49 +0200 |
|---|---|---|
| committer | stainer_t <thomas.stainer@oecd-nea.org> | 2025-09-08 13:48:49 +0200 |
| commit | 7dfcc480ba1e19bd3232349fc733caef94034292 (patch) | |
| tree | 03ee104eb8846d5cc1a981d267687a729185d3f3 /Utilib/src/ALST2F.f | |
Initial commit from Polytechnique Montreal
Diffstat (limited to 'Utilib/src/ALST2F.f')
| -rw-r--r-- | Utilib/src/ALST2F.f | 87 |
1 files changed, 87 insertions, 0 deletions
diff --git a/Utilib/src/ALST2F.f b/Utilib/src/ALST2F.f new file mode 100644 index 0000000..fe74a74 --- /dev/null +++ b/Utilib/src/ALST2F.f @@ -0,0 +1,87 @@ +*DECK ALST2F + SUBROUTINE ALST2F(MDIM,M,N,A,TAU) +* +*----------------------------------------------------------------------- +* +*Purpose: +* to obtain the QR factorization of the matrix a using Householder +* transformations. Use LAPACK's DGEQRF routine storage. Douple precision +* routine. +* +*Copyright: +* Copyright (C) 1993 Ecole Polytechnique de Montreal +* This library is free software; you can redistribute it and/or +* modify it under the terms of the GNU Lesser General Public +* License as published by the Free Software Foundation; either +* version 2.1 of the License, or (at your option) any later version +* +*Author(s): A. Hebert +* +*Reference: +* P.A. BUSINGER, Num. Math. 7, 269-276 (1965). +* +*Parameters: input +* MDIM dimensioned column length of A. +* M number of rows of A +* N number of columns of A. N.le.M is assumed. +* A matrix A. +* +*Parameters: output +* A decomposed matrix. On exit, the elements on and above the +* diagonal of the array contain the m by n upper trapezoidal +* matrix R (R is upper triangular if m >= n); the elements +* below the diagonal, with the array TAU, represent the +* orthogonal matrix Q as a product of elementary reflectors. +* TAU scalar factors of the elementary reflectors. +* +*----------------------------------------------------------------------- +* + IMPLICIT REAL(KIND=8)(A-H,O-Z) +*---- +* SUBROUTINE ARGUMENTS +*---- + INTEGER MDIM,M,N + REAL(KIND=8) A(MDIM,N),TAU(N) +*---- +* LOCAL VARIABLES +*---- + CHARACTER HSMG*131 +*---- +* ALLOCATABLE ARRAYS +*---- + REAL(KIND=8), ALLOCATABLE, DIMENSION(:,:) :: W +*---- +* CHECK THE INPUT +*---- + IF(MDIM.LT.M) CALL XABORT('ALST2F: MDIM.LT.M') + IF(N.LT.1) CALL XABORT('ALST2F: N.LT.1') + IF(N.GT.M) THEN + WRITE(HSMG,'(18HALST2F: N.GT.M (N=,I3,3H M=,I3,2H).)') N,M + CALL XABORT(HSMG) + ENDIF +*---- +* PERFORM QR FACTORIZATION. +*---- + ALLOCATE(W(M,1)) + DO J=1,N + M1 = M-J+1; W(:M1,1) = A(J:M,J); X1 = W(1,1); + AX = SQRT(DOT_PRODUCT(W(:M1,1),W(:M1,1))) + A1 = ABS(X1); S = SIGN(1.0D0,W(1,1)); + SSSS = -AX*S; A1 = A1+AX; + W(1,1) = A1*S + DD2 = A1*AX + IF(DD2 == 0.0D0) CALL XABORT('ALST2F: SINGULAR REFLECTION') + W(:M1,1) = W(:M1,1)/SQRT(DD2) + A(J:M,J) = W(:M1,1) + IF(J < N) THEN + A(J:M,J+1:N) = A(J:M,J+1:N) + 1 -MATMUL(W(:M1,:),(MATMUL(TRANSPOSE(W(:M1,:)),A(J:M,J+1:N)))) + ENDIF + DIAG = A(J,J) + A(J:M,J) = A(J:M,J)/DIAG + A(J,J) = SSSS + TAU(J) = -DIAG*DIAG + ENDDO + DEALLOCATE(W) + RETURN + END |
