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authorjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
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- SUBROUTINE ZTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
-*
-* -- LAPACK routine (version 3.3.1) --
-*
-* -- Contributed by Fred Gustavson of the IBM Watson Research Center --
-* -- April 2011 --
-*
-* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*
-* .. Scalar Arguments ..
- CHARACTER TRANSR, UPLO, DIAG
- INTEGER INFO, N
-* ..
-* .. Array Arguments ..
- COMPLEX*16 A( 0: * )
-* ..
-*
+*> \brief \b ZTFTRI
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition
+* ==========
+*
+* SUBROUTINE ZTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER TRANSR, UPLO, DIAG
+* INTEGER INFO, N
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 A( 0: * )
+* ..
+*
* Purpose
* =======
*
-* ZTFTRI computes the inverse of a triangular matrix A stored in RFP
-* format.
-*
-* This is a Level 3 BLAS version of the algorithm.
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> ZTFTRI computes the inverse of a triangular matrix A stored in RFP
+*> format.
+*>
+*> This is a Level 3 BLAS version of the algorithm.
+*>
+*>\endverbatim
*
* Arguments
* =========
*
-* TRANSR (input) CHARACTER*1
-* = 'N': The Normal TRANSR of RFP A is stored;
-* = 'C': The Conjugate-transpose TRANSR of RFP A is stored.
-*
-* UPLO (input) CHARACTER*1
-* = 'U': A is upper triangular;
-* = 'L': A is lower triangular.
-*
-* DIAG (input) CHARACTER*1
-* = 'N': A is non-unit triangular;
-* = 'U': A is unit triangular.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) COMPLEX*16 array, dimension ( N*(N+1)/2 );
-* On entry, the triangular matrix A in RFP format. RFP format
-* is described by TRANSR, UPLO, and N as follows: If TRANSR =
-* 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
-* (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
-* the Conjugate-transpose of RFP A as defined when
-* TRANSR = 'N'. The contents of RFP A are defined by UPLO as
-* follows: If UPLO = 'U' the RFP A contains the nt elements of
-* upper packed A; If UPLO = 'L' the RFP A contains the nt
-* elements of lower packed A. The LDA of RFP A is (N+1)/2 when
-* TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
-* even and N is odd. See the Note below for more details.
-*
-* On exit, the (triangular) inverse of the original matrix, in
-* the same storage format.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, A(i,i) is exactly zero. The triangular
-* matrix is singular and its inverse can not be computed.
-*
-* Further Details
-* ===============
-*
-* We first consider Standard Packed Format when N is even.
-* We give an example where N = 6.
-*
-* AP is Upper AP is Lower
-*
-* 00 01 02 03 04 05 00
-* 11 12 13 14 15 10 11
-* 22 23 24 25 20 21 22
-* 33 34 35 30 31 32 33
-* 44 45 40 41 42 43 44
-* 55 50 51 52 53 54 55
-*
-*
-* Let TRANSR = 'N'. RFP holds AP as follows:
-* For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
-* three columns of AP upper. The lower triangle A(4:6,0:2) consists of
-* conjugate-transpose of the first three columns of AP upper.
-* For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
-* three columns of AP lower. The upper triangle A(0:2,0:2) consists of
-* conjugate-transpose of the last three columns of AP lower.
-* To denote conjugate we place -- above the element. This covers the
-* case N even and TRANSR = 'N'.
-*
-* RFP A RFP A
-*
-* -- -- --
-* 03 04 05 33 43 53
-* -- --
-* 13 14 15 00 44 54
-* --
-* 23 24 25 10 11 55
-*
-* 33 34 35 20 21 22
-* --
-* 00 44 45 30 31 32
-* -- --
-* 01 11 55 40 41 42
-* -- -- --
-* 02 12 22 50 51 52
-*
-* Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
-* transpose of RFP A above. One therefore gets:
-*
-*
-* RFP A RFP A
-*
-* -- -- -- -- -- -- -- -- -- --
-* 03 13 23 33 00 01 02 33 00 10 20 30 40 50
-* -- -- -- -- -- -- -- -- -- --
-* 04 14 24 34 44 11 12 43 44 11 21 31 41 51
-* -- -- -- -- -- -- -- -- -- --
-* 05 15 25 35 45 55 22 53 54 55 22 32 42 52
-*
-*
-* We next consider Standard Packed Format when N is odd.
-* We give an example where N = 5.
-*
-* AP is Upper AP is Lower
-*
-* 00 01 02 03 04 00
-* 11 12 13 14 10 11
-* 22 23 24 20 21 22
-* 33 34 30 31 32 33
-* 44 40 41 42 43 44
-*
-*
-* Let TRANSR = 'N'. RFP holds AP as follows:
-* For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
-* three columns of AP upper. The lower triangle A(3:4,0:1) consists of
-* conjugate-transpose of the first two columns of AP upper.
-* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
-* three columns of AP lower. The upper triangle A(0:1,1:2) consists of
-* conjugate-transpose of the last two columns of AP lower.
-* To denote conjugate we place -- above the element. This covers the
-* case N odd and TRANSR = 'N'.
+*> \param[in] TRANSR
+*> \verbatim
+*> TRANSR is CHARACTER*1
+*> = 'N': The Normal TRANSR of RFP A is stored;
+*> = 'C': The Conjugate-transpose TRANSR of RFP A is stored.
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': A is upper triangular;
+*> = 'L': A is lower triangular.
+*> \endverbatim
+*>
+*> \param[in] DIAG
+*> \verbatim
+*> DIAG is CHARACTER*1
+*> = 'N': A is non-unit triangular;
+*> = 'U': A is unit triangular.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension ( N*(N+1)/2 );
+*> On entry, the triangular matrix A in RFP format. RFP format
+*> is described by TRANSR, UPLO, and N as follows: If TRANSR =
+*> 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
+*> (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
+*> the Conjugate-transpose of RFP A as defined when
+*> TRANSR = 'N'. The contents of RFP A are defined by UPLO as
+*> follows: If UPLO = 'U' the RFP A contains the nt elements of
+*> upper packed A; If UPLO = 'L' the RFP A contains the nt
+*> elements of lower packed A. The LDA of RFP A is (N+1)/2 when
+*> TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
+*> even and N is odd. See the Note below for more details.
+*> \endverbatim
+*> \verbatim
+*> On exit, the (triangular) inverse of the original matrix, in
+*> the same storage format.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
+*> matrix is singular and its inverse can not be computed.
+*> \endverbatim
+*>
+*
+* Authors
+* =======
*
-* RFP A RFP A
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-* -- --
-* 02 03 04 00 33 43
-* --
-* 12 13 14 10 11 44
+*> \date November 2011
*
-* 22 23 24 20 21 22
-* --
-* 00 33 34 30 31 32
-* -- --
-* 01 11 44 40 41 42
+*> \ingroup complex16OTHERcomputational
*
-* Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
-* transpose of RFP A above. One therefore gets:
*
+* Further Details
+* ===============
+*>\details \b Further \b Details
+*> \verbatim
+*>
+*> We first consider Standard Packed Format when N is even.
+*> We give an example where N = 6.
+*>
+*> AP is Upper AP is Lower
+*>
+*> 00 01 02 03 04 05 00
+*> 11 12 13 14 15 10 11
+*> 22 23 24 25 20 21 22
+*> 33 34 35 30 31 32 33
+*> 44 45 40 41 42 43 44
+*> 55 50 51 52 53 54 55
+*>
+*>
+*> Let TRANSR = 'N'. RFP holds AP as follows:
+*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
+*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
+*> conjugate-transpose of the first three columns of AP upper.
+*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
+*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
+*> conjugate-transpose of the last three columns of AP lower.
+*> To denote conjugate we place -- above the element. This covers the
+*> case N even and TRANSR = 'N'.
+*>
+*> RFP A RFP A
+*>
+*> -- -- --
+*> 03 04 05 33 43 53
+*> -- --
+*> 13 14 15 00 44 54
+*> --
+*> 23 24 25 10 11 55
+*>
+*> 33 34 35 20 21 22
+*> --
+*> 00 44 45 30 31 32
+*> -- --
+*> 01 11 55 40 41 42
+*> -- -- --
+*> 02 12 22 50 51 52
+*>
+*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
+*> transpose of RFP A above. One therefore gets:
+*>
+*>
+*> RFP A RFP A
+*>
+*> -- -- -- -- -- -- -- -- -- --
+*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
+*> -- -- -- -- -- -- -- -- -- --
+*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
+*> -- -- -- -- -- -- -- -- -- --
+*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
+*>
+*>
+*> We next consider Standard Packed Format when N is odd.
+*> We give an example where N = 5.
+*>
+*> AP is Upper AP is Lower
+*>
+*> 00 01 02 03 04 00
+*> 11 12 13 14 10 11
+*> 22 23 24 20 21 22
+*> 33 34 30 31 32 33
+*> 44 40 41 42 43 44
+*>
+*>
+*> Let TRANSR = 'N'. RFP holds AP as follows:
+*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
+*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
+*> conjugate-transpose of the first two columns of AP upper.
+*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
+*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
+*> conjugate-transpose of the last two columns of AP lower.
+*> To denote conjugate we place -- above the element. This covers the
+*> case N odd and TRANSR = 'N'.
+*>
+*> RFP A RFP A
+*>
+*> -- --
+*> 02 03 04 00 33 43
+*> --
+*> 12 13 14 10 11 44
+*>
+*> 22 23 24 20 21 22
+*> --
+*> 00 33 34 30 31 32
+*> -- --
+*> 01 11 44 40 41 42
+*>
+*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
+*> transpose of RFP A above. One therefore gets:
+*>
+*>
+*> RFP A RFP A
+*>
+*> -- -- -- -- -- -- -- -- --
+*> 02 12 22 00 01 00 10 20 30 40 50
+*> -- -- -- -- -- -- -- -- --
+*> 03 13 23 33 11 33 11 21 31 41 51
+*> -- -- -- -- -- -- -- -- --
+*> 04 14 24 34 44 43 44 22 32 42 52
+*>
+*> \endverbatim
+*>
+* =====================================================================
+ SUBROUTINE ZTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
*
-* RFP A RFP A
+* -- LAPACK computational routine (version 3.3.1) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
*
-* -- -- -- -- -- -- -- -- --
-* 02 12 22 00 01 00 10 20 30 40 50
-* -- -- -- -- -- -- -- -- --
-* 03 13 23 33 11 33 11 21 31 41 51
-* -- -- -- -- -- -- -- -- --
-* 04 14 24 34 44 43 44 22 32 42 52
+* .. Scalar Arguments ..
+ CHARACTER TRANSR, UPLO, DIAG
+ INTEGER INFO, N
+* ..
+* .. Array Arguments ..
+ COMPLEX*16 A( 0: * )
+* ..
*
* =====================================================================
*