julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
470 lines
14 KiB
FortranFixed
470 lines
14 KiB
FortranFixed
SUBROUTINE CTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
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*
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* -- LAPACK routine (version 3.2.1) --
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*
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* -- Contributed by Fred Gustavson of the IBM Watson Research Center --
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* -- April 2009 --
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*
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER TRANSR, UPLO
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INTEGER INFO, N, LDA
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* ..
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* .. Array Arguments ..
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COMPLEX A( 0: LDA-1, 0: * ), ARF( 0: * )
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* ..
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*
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* Purpose
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* =======
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*
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* CTRTTF copies a triangular matrix A from standard full format (TR)
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* to rectangular full packed format (TF) .
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*
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* Arguments
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* =========
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*
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* TRANSR (input) CHARACTER
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* = 'N': ARF in Normal mode is wanted;
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* = 'C': ARF in Conjugate Transpose mode is wanted;
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*
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* UPLO (input) CHARACTER
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* = 'U': A is upper triangular;
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* = 'L': A is lower triangular.
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* A (input) COMPLEX array, dimension ( LDA, N )
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* On entry, the triangular matrix A. If UPLO = 'U', the
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* leading N-by-N upper triangular part of the array A contains
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* the upper triangular matrix, and the strictly lower
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* triangular part of A is not referenced. If UPLO = 'L', the
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* leading N-by-N lower triangular part of the array A contains
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* the lower triangular matrix, and the strictly upper
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* triangular part of A is not referenced.
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*
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* LDA (input) INTEGER
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* The leading dimension of the matrix A. LDA >= max(1,N).
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*
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* ARF (output) COMPLEX*16 array, dimension ( N*(N+1)/2 ),
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* On exit, the upper or lower triangular matrix A stored in
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* RFP format. For a further discussion see Notes below.
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* Further Details
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* ===============
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*
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* We first consider Standard Packed Format when N is even.
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* We give an example where N = 6.
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*
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* AP is Upper AP is Lower
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*
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* 00 01 02 03 04 05 00
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* 11 12 13 14 15 10 11
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* 22 23 24 25 20 21 22
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* 33 34 35 30 31 32 33
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* 44 45 40 41 42 43 44
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* 55 50 51 52 53 54 55
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*
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*
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* Let TRANSR = `N'. RFP holds AP as follows:
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* For UPLO = `U' the upper trapezoid A(0:5,0:2) consists of the last
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* three columns of AP upper. The lower triangle A(4:6,0:2) consists of
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* conjugate-transpose of the first three columns of AP upper.
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* For UPLO = `L' the lower trapezoid A(1:6,0:2) consists of the first
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* three columns of AP lower. The upper triangle A(0:2,0:2) consists of
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* conjugate-transpose of the last three columns of AP lower.
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* To denote conjugate we place -- above the element. This covers the
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* case N even and TRANSR = `N'.
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*
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* RFP A RFP A
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*
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* -- -- --
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* 03 04 05 33 43 53
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* -- --
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* 13 14 15 00 44 54
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* --
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* 23 24 25 10 11 55
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*
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* 33 34 35 20 21 22
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* --
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* 00 44 45 30 31 32
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* -- --
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* 01 11 55 40 41 42
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* -- -- --
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* 02 12 22 50 51 52
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*
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* Now let TRANSR = `C'. RFP A in both UPLO cases is just the conjugate-
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* transpose of RFP A above. One therefore gets:
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*
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*
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* RFP A RFP A
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*
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* -- -- -- -- -- -- -- -- -- --
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* 03 13 23 33 00 01 02 33 00 10 20 30 40 50
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* -- -- -- -- -- -- -- -- -- --
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* 04 14 24 34 44 11 12 43 44 11 21 31 41 51
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* -- -- -- -- -- -- -- -- -- --
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* 05 15 25 35 45 55 22 53 54 55 22 32 42 52
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*
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*
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* We next consider Standard Packed Format when N is odd.
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* We give an example where N = 5.
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*
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* AP is Upper AP is Lower
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*
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* 00 01 02 03 04 00
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* 11 12 13 14 10 11
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* 22 23 24 20 21 22
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* 33 34 30 31 32 33
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* 44 40 41 42 43 44
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*
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*
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* Let TRANSR = `N'. RFP holds AP as follows:
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* For UPLO = `U' the upper trapezoid A(0:4,0:2) consists of the last
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* three columns of AP upper. The lower triangle A(3:4,0:1) consists of
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* conjugate-transpose of the first two columns of AP upper.
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* For UPLO = `L' the lower trapezoid A(0:4,0:2) consists of the first
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* three columns of AP lower. The upper triangle A(0:1,1:2) consists of
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* conjugate-transpose of the last two columns of AP lower.
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* To denote conjugate we place -- above the element. This covers the
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* case N odd and TRANSR = `N'.
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*
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* RFP A RFP A
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*
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* -- --
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* 02 03 04 00 33 43
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* --
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* 12 13 14 10 11 44
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*
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* 22 23 24 20 21 22
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* --
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* 00 33 34 30 31 32
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* -- --
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* 01 11 44 40 41 42
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*
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* Now let TRANSR = `C'. RFP A in both UPLO cases is just the conjugate-
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* transpose of RFP A above. One therefore gets:
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*
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*
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* RFP A RFP A
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*
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* -- -- -- -- -- -- -- -- --
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* 02 12 22 00 01 00 10 20 30 40 50
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* -- -- -- -- -- -- -- -- --
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* 03 13 23 33 11 33 11 21 31 41 51
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* -- -- -- -- -- -- -- -- --
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* 04 14 24 34 44 43 44 22 32 42 52
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*
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* =====================================================================
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*
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* .. Parameters ..
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* ..
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* .. Local Scalars ..
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LOGICAL LOWER, NISODD, NORMALTRANSR
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INTEGER I, IJ, J, K, L, N1, N2, NT, NX2, NP1X2
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CONJG, MAX, MOD
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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NORMALTRANSR = LSAME( TRANSR, 'N' )
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LOWER = LSAME( UPLO, 'L' )
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IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CTRTTF', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.LE.1 ) THEN
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IF( N.EQ.1 ) THEN
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IF( NORMALTRANSR ) THEN
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ARF( 0 ) = A( 0, 0 )
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ELSE
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ARF( 0 ) = CONJG( A( 0, 0 ) )
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END IF
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END IF
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RETURN
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END IF
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*
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* Size of array ARF(1:2,0:nt-1)
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*
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NT = N*( N+1 ) / 2
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*
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* set N1 and N2 depending on LOWER: for N even N1=N2=K
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*
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IF( LOWER ) THEN
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N2 = N / 2
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N1 = N - N2
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ELSE
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N1 = N / 2
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N2 = N - N1
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END IF
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*
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* If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
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* If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
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* N--by--(N+1)/2.
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*
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IF( MOD( N, 2 ).EQ.0 ) THEN
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K = N / 2
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NISODD = .FALSE.
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IF( .NOT.LOWER )
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+ NP1X2 = N + N + 2
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ELSE
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NISODD = .TRUE.
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IF( .NOT.LOWER )
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+ NX2 = N + N
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END IF
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*
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IF( NISODD ) THEN
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*
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* N is odd
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*
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IF( NORMALTRANSR ) THEN
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*
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* N is odd and TRANSR = 'N'
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*
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IF( LOWER ) THEN
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*
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* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
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* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
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* T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
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*
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IJ = 0
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DO J = 0, N2
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DO I = N1, N2 + J
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ARF( IJ ) = CONJG( A( N2+J, I ) )
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IJ = IJ + 1
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END DO
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DO I = J, N - 1
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ARF( IJ ) = A( I, J )
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IJ = IJ + 1
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END DO
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END DO
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*
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ELSE
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*
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* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
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* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
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* T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
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*
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IJ = NT - N
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DO J = N - 1, N1, -1
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DO I = 0, J
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ARF( IJ ) = A( I, J )
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IJ = IJ + 1
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END DO
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DO L = J - N1, N1 - 1
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ARF( IJ ) = CONJG( A( J-N1, L ) )
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IJ = IJ + 1
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END DO
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IJ = IJ - NX2
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END DO
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*
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END IF
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*
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ELSE
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*
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* N is odd and TRANSR = 'C'
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*
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IF( LOWER ) THEN
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*
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* SRPA for LOWER, TRANSPOSE and N is odd
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* T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
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* T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
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*
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IJ = 0
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DO J = 0, N2 - 1
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DO I = 0, J
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ARF( IJ ) = CONJG( A( J, I ) )
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IJ = IJ + 1
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END DO
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DO I = N1 + J, N - 1
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ARF( IJ ) = A( I, N1+J )
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IJ = IJ + 1
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END DO
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END DO
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DO J = N2, N - 1
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DO I = 0, N1 - 1
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ARF( IJ ) = CONJG( A( J, I ) )
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IJ = IJ + 1
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END DO
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END DO
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*
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ELSE
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*
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* SRPA for UPPER, TRANSPOSE and N is odd
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* T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
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* T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda=n2
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*
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IJ = 0
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DO J = 0, N1
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DO I = N1, N - 1
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ARF( IJ ) = CONJG( A( J, I ) )
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IJ = IJ + 1
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END DO
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END DO
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DO J = 0, N1 - 1
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DO I = 0, J
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ARF( IJ ) = A( I, J )
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IJ = IJ + 1
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END DO
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DO L = N2 + J, N - 1
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ARF( IJ ) = CONJG( A( N2+J, L ) )
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IJ = IJ + 1
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END DO
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END DO
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*
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END IF
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*
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END IF
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*
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ELSE
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*
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* N is even
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*
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IF( NORMALTRANSR ) THEN
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*
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* N is even and TRANSR = 'N'
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*
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IF( LOWER ) THEN
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*
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* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
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* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
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* T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
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*
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IJ = 0
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DO J = 0, K - 1
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DO I = K, K + J
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ARF( IJ ) = CONJG( A( K+J, I ) )
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IJ = IJ + 1
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END DO
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DO I = J, N - 1
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ARF( IJ ) = A( I, J )
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IJ = IJ + 1
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END DO
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END DO
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*
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ELSE
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*
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* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
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* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
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* T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
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*
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IJ = NT - N - 1
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DO J = N - 1, K, -1
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DO I = 0, J
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ARF( IJ ) = A( I, J )
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IJ = IJ + 1
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END DO
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DO L = J - K, K - 1
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ARF( IJ ) = CONJG( A( J-K, L ) )
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IJ = IJ + 1
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END DO
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IJ = IJ - NP1X2
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END DO
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*
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END IF
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*
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ELSE
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*
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* N is even and TRANSR = 'C'
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*
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IF( LOWER ) THEN
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*
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* SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
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* T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
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* T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
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*
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IJ = 0
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J = K
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DO I = K, N - 1
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ARF( IJ ) = A( I, J )
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IJ = IJ + 1
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END DO
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DO J = 0, K - 2
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DO I = 0, J
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ARF( IJ ) = CONJG( A( J, I ) )
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IJ = IJ + 1
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END DO
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DO I = K + 1 + J, N - 1
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ARF( IJ ) = A( I, K+1+J )
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IJ = IJ + 1
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END DO
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END DO
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DO J = K - 1, N - 1
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DO I = 0, K - 1
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ARF( IJ ) = CONJG( A( J, I ) )
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IJ = IJ + 1
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END DO
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END DO
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*
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ELSE
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*
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* SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
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* T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
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* T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
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*
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IJ = 0
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DO J = 0, K
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DO I = K, N - 1
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ARF( IJ ) = CONJG( A( J, I ) )
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IJ = IJ + 1
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END DO
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END DO
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DO J = 0, K - 2
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DO I = 0, J
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ARF( IJ ) = A( I, J )
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IJ = IJ + 1
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END DO
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DO L = K + 1 + J, N - 1
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ARF( IJ ) = CONJG( A( K+1+J, L ) )
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IJ = IJ + 1
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END DO
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END DO
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*
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* Note that here J = K-1
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*
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DO I = 0, J
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ARF( IJ ) = A( I, J )
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IJ = IJ + 1
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END DO
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*
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END IF
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*
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END IF
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*
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END IF
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*
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RETURN
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*
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* End of CTRTTF
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*
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END
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