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dtrti2.f
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dtrti2.f
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SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
*
* -- LAPACK ROUTINE (VERSION 1.0B) --
* UNIV. OF TENNESSEE, UNIV. OF CALIFORNIA BERKELEY, NAG LTD.,
* COURANT INSTITUTE, ARGONNE NATIONAL LAB, AND RICE UNIVERSITY
* FEBRUARY 29, 1992
*
* .. SCALAR ARGUMENTS ..
CHARACTER DIAG, UPLO
INTEGER INFO, LDA, N
* ..
* .. ARRAY ARGUMENTS ..
DOUBLE PRECISION A( LDA, * )
* ..
*
* PURPOSE
* =======
*
* DTRTI2 COMPUTES THE INVERSE OF A REAL UPPER OR LOWER TRIANGULAR
* MATRIX.
*
* THIS IS THE LEVEL 2 BLAS VERSION OF THE ALGORITHM.
*
* ARGUMENTS
* =========
*
* UPLO (INPUT) CHARACTER*1
* SPECIFIES WHETHER THE MATRIX A IS UPPER OR LOWER TRIANGULAR.
* = 'U': UPPER TRIANGULAR
* = 'L': LOWER TRIANGULAR
*
* DIAG (INPUT) CHARACTER*1
* SPECIFIES WHETHER OR NOT THE MATRIX A IS UNIT TRIANGULAR.
* = 'N': NON-UNIT TRIANGULAR
* = 'U': UNIT TRIANGULAR
*
* N (INPUT) INTEGER
* THE ORDER OF THE MATRIX A. N >= 0.
*
* A (INPUT/OUTPUT) DOUBLE PRECISION ARRAY, DIMENSION (LDA,N)
* ON ENTRY, THE TRIANGULAR MATRIX A. IF UPLO = 'U', THE
* LEADING N BY N UPPER TRIANGULAR PART OF THE ARRAY A CONTAINS
* THE UPPER TRIANGULAR MATRIX, AND THE STRICTLY LOWER
* TRIANGULAR PART OF A IS NOT REFERENCED. IF UPLO = 'L', THE
* LEADING N BY N LOWER TRIANGULAR PART OF THE ARRAY A CONTAINS
* THE LOWER TRIANGULAR MATRIX, AND THE STRICTLY UPPER
* TRIANGULAR PART OF A IS NOT REFERENCED. IF DIAG = 'U', THE
* DIAGONAL ELEMENTS OF A ARE ALSO NOT REFERENCED AND ARE
* ASSUMED TO BE 1.
*
* ON EXIT, THE (TRIANGULAR) INVERSE OF THE ORIGINAL MATRIX, IN
* THE SAME STORAGE FORMAT.
*
* LDA (INPUT) INTEGER
* THE LEADING DIMENSION OF THE ARRAY A. LDA >= MAX(1,N).
*
* INFO (OUTPUT) INTEGER
* = 0: SUCCESSFUL EXIT
* < 0: IF INFO = -K, THE K-TH ARGUMENT HAD AN ILLEGAL VALUE
*
* =====================================================================
*
* .. PARAMETERS ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. LOCAL SCALARS ..
LOGICAL NOUNIT, UPPER
INTEGER J
DOUBLE PRECISION AJJ
* ..
* .. EXTERNAL FUNCTIONS ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. EXTERNAL SUBROUTINES ..
EXTERNAL DSCAL, DTRMV, XERBLA
* ..
* .. INTRINSIC FUNCTIONS ..
INTRINSIC MAX
* ..
* .. EXECUTABLE STATEMENTS ..
*
* TEST THE INPUT PARAMETERS.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
NOUNIT = LSAME( DIAG, 'N' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DTRTI2', -INFO )
RETURN
END IF
*
IF( UPPER ) THEN
*
* COMPUTE INVERSE OF UPPER TRIANGULAR MATRIX.
*
DO 10 J = 1, N
IF( NOUNIT ) THEN
A( J, J ) = ONE / A( J, J )
AJJ = -A( J, J )
ELSE
AJJ = -ONE
END IF
*
* COMPUTE ELEMENTS 1:J-1 OF J-TH COLUMN.
*
CALL DTRMV( 'UPPER', 'NO TRANSPOSE', DIAG, J-1, A, LDA,
$ A( 1, J ), 1 )
CALL DSCAL( J-1, AJJ, A( 1, J ), 1 )
10 CONTINUE
ELSE
*
* COMPUTE INVERSE OF LOWER TRIANGULAR MATRIX.
*
DO 20 J = N, 1, -1
IF( NOUNIT ) THEN
A( J, J ) = ONE / A( J, J )
AJJ = -A( J, J )
ELSE
AJJ = -ONE
END IF
IF( J.LT.N ) THEN
*
* COMPUTE ELEMENTS J+1:N OF J-TH COLUMN.
*
CALL DTRMV( 'LOWER', 'NO TRANSPOSE', DIAG, N-J,
$ A( J+1, J+1 ), LDA, A( J+1, J ), 1 )
CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 )
END IF
20 CONTINUE
END IF
*
RETURN
*
* END OF DTRTI2
*
END