!-------------------------------------- LICENCE BEGIN ------------------------------------
!Environment Canada - Atmospheric Science and Technology License/Disclaimer,
! version 3; Last Modified: May 7, 2008.
!This is free but copyrighted software; you can use/redistribute/modify it under the terms
!of the Environment Canada - Atmospheric Science and Technology License/Disclaimer
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!
!This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
!without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
!See the above mentioned License/Disclaimer for more details.
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!CANADA, H9P 1J3; or send e-mail to service.rpn@ec.gc.ca
!-------------------------------------- LICENCE END --------------------------------------
!
SUBROUTINE MATSQRT(PA,KN,ZSIGN) 3
#if defined (DOC)
*
***s/r MATSQRT - Calculate square root of an error covariance
* . matrix
*
*
*Author : M. Buehner *ARMA/AES February, 2000
*Revision:
* C. Charette ARMA/SMC jan. 2005
* - Replaced write(6,..) statements by write(nulout,...)
* Bin He *ARMA/MRB NOv. 2011
* - replaced MXMA with DGEMUL of ESSL .
*
*Arguments
* . PA(KN,KN) : on entry, the original matrix
* . on exit, the sqrt matrix
* . KN : order of the matrix
#endif
IMPLICIT NONE
*
* Global variables
*
#include "comlun.cdk"
#include "dgemul.h"
* Arguments
*
INTEGER KN
REAL*8 PA(KN,KN)
REAL*8 ZSIGN
*
* Local variables
*
INTEGER JI, J, INFO, IER, IWORK
REAL*8 ZWORK(1), ZRESULT(KN,KN), ZEIGENV2(KN,KN),
+ ZEIGEN(KN,KN), ZEIGENV(KN)
POINTER(PXEIG ,ZEIGEN )
POINTER(PXEIGV ,ZEIGENV )
POINTER(PXEIGV2,ZEIGENV2)
POINTER(PXWRK,ZWORK)
POINTER(PXRES,ZRESULT)
*
* 0. Memory allocation and miscellaneous definitions
*
CALL HPALLOC(PXEIG ,KN*KN,IER,8)
CALL HPALLOC(PXEIGV ,KN ,IER,8)
CALL HPALLOC(PXEIGV2,KN*KN,IER,8)
CALL HPALLOC(PXWRK ,4*KN ,IER,8)
CALL HPALLOC(PXRES ,KN*KN,IER,8)
IWORK=4*KN
*
WRITE(NULOUT,*)' MATSQRT-Sqrt matrix of a symmetric matrix'
WRITE(NULOUT,*)' -----------------------------------------------'
WRITE(NULOUT,*)' '
*
c IF(ZSIGN.lt.0) THEN
c WRITE(NULOUT,*) 'BEFORE'
c WRITE(NULOUT,*)( (PA(JI,J),JI=1,KN),J=1,KN)
c ENDIF
*
* 1. Computation of eigenvalues and eigenvectors
*
100 CONTINUE
ZEIGEN(:,:)=PA(:,:)
CALL DSYEV('V','U',KN, ZEIGEN,KN, ZEIGENV,ZWORK, IWORK, INFO )
*
WRITE(69,'(1x,"ORIGINAL EIGEN VALUES: ")')
WRITE(69,'(1x,10f15.8)') (ZEIGENV(JI),JI=1,KN)
*
* 2. Take SQRT of eigenvalues
*
ZEIGENV2(:,:)= 0.0
DO JI=1,KN
ZEIGENV2(JI,JI)= ZEIGENV(JI)**(0.5*ZSIGN)
END DO
*
!ping CALL MXMA8(ZEIGEN ,1,KN,ZEIGENV2,1 ,KN,ZRESULT,1,KN,KN,KN,KN)
CALL DGEMUL(ZEIGEN,KN,'N',ZEIGENV2,KN,'N',ZRESULT,KN,KN,KN,KN)
!ping CALL MXMA8(ZRESULT,1,KN,ZEIGEN ,KN,1 ,PA ,1,KN,KN,KN,KN)
CALL DGEMUL(ZRESULT,KN,'N',ZEIGEN,KN,'N',PA,KN,KN,KN,KN)
*
c IF(ZSIGN.lt.0) THEN
c WRITE(*,*) 'AFTER'
c WRITE(*,*)( (PA(JI,J),JI=1,KN),J=1,KN)
c ENDIF
*
* 4. Deallocate local arrays
*
CALL HPDEALLC(PXEIG ,IER,1)
CALL HPDEALLC(PXEIGV ,IER,1)
CALL HPDEALLC(PXEIGV2,IER,1)
CALL HPDEALLC(PXWRK ,IER,1)
CALL HPDEALLC(PXRES ,IER,1)
*
WRITE(NULOUT,*)'MATSQRT-----------Done--------------- '
WRITE(NULOUT,*)' '
c 1244 FORMAT( 15(1x,f15.6))
RETURN
END