--- rpl/lapack/lapack/dtftri.f 2010/08/13 21:03:59 1.3
+++ rpl/lapack/lapack/dtftri.f 2023/08/07 08:39:12 1.16
@@ -1,10 +1,205 @@
- SUBROUTINE DTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
+*> \brief \b DTFTRI
+*
+* =========== DOCUMENTATION ===========
*
-* -- LAPACK routine (version 3.2.2) --
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
-* -- Contributed by Fred Gustavson of the IBM Watson Research Center --
-* -- June 2010 --
+*> \htmlonly
+*> Download DTFTRI + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER TRANSR, UPLO, DIAG
+* INTEGER INFO, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( 0: * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DTFTRI computes the inverse of a triangular matrix A stored in RFP
+*> format.
+*>
+*> This is a Level 3 BLAS version of the algorithm.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] TRANSR
+*> \verbatim
+*> TRANSR is CHARACTER*1
+*> = 'N': The Normal TRANSR of RFP A is stored;
+*> = 'T': The 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 DOUBLE PRECISION array, dimension (0:nt-1);
+*> nt=N*(N+1)/2. On entry, the triangular factor of a Hermitian
+*> Positive Definite 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 = 'T' then RFP is
+*> the 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 = 'T'. 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.
+*> \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:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> We first consider Rectangular Full Packed (RFP) 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
+*> the 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
+*> the transpose of the last three columns of AP lower.
+*> 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 = 'T'. RFP A in both UPLO cases is just the
+*> 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 then consider Rectangular Full Packed (RFP) 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
+*> the 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
+*> the transpose of the last two columns of AP lower.
+*> 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 = 'T'. RFP A in both UPLO cases is just the
+*> 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 DTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
*
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
@@ -16,139 +211,6 @@
DOUBLE PRECISION A( 0: * )
* ..
*
-* Purpose
-* =======
-*
-* DTFTRI computes the inverse of a triangular matrix A stored in RFP
-* format.
-*
-* This is a Level 3 BLAS version of the algorithm.
-*
-* Arguments
-* =========
-*
-* TRANSR (input) CHARACTER
-* = 'N': The Normal TRANSR of RFP A is stored;
-* = 'T': The Transpose TRANSR of RFP A is stored.
-*
-* UPLO (input) CHARACTER
-* = 'U': A is upper triangular;
-* = 'L': A is lower triangular.
-*
-* DIAG (input) CHARACTER
-* = '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) DOUBLE PRECISION array, dimension (0:nt-1);
-* nt=N*(N+1)/2. On entry, the triangular factor of a Hermitian
-* Positive Definite 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 = 'T' then RFP is
-* the 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 = 'T'. 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 Rectangular Full Packed (RFP) 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
-* the 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
-* the transpose of the last three columns of AP lower.
-* 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 = 'T'. RFP A in both UPLO cases is just the
-* 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 then consider Rectangular Full Packed (RFP) 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
-* the 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
-* the transpose of the last two columns of AP lower.
-* 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 = 'T'. RFP A in both UPLO cases is just the
-* 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
-*
* =====================================================================
*
* .. Parameters ..
@@ -181,7 +243,7 @@
ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
INFO = -2
ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
- + THEN
+ $ THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
@@ -194,7 +256,7 @@
* Quick return if possible
*
IF( N.EQ.0 )
- + RETURN
+ $ RETURN
*
* If N is odd, set NISODD = .TRUE.
* If N is even, set K = N/2 and NISODD = .FALSE.
@@ -235,16 +297,16 @@
*
CALL DTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'R', 'L', 'N', DIAG, N2, N1, -ONE, A( 0 ),
- + N, A( N1 ), N )
+ $ N, A( N1 ), N )
CALL DTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + N1
+ $ INFO = INFO + N1
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'L', 'U', 'T', DIAG, N2, N1, ONE, A( N ), N,
- + A( N1 ), N )
+ $ A( N1 ), N )
*
ELSE
*
@@ -254,16 +316,16 @@
*
CALL DTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'L', 'L', 'T', DIAG, N1, N2, -ONE, A( N2 ),
- + N, A( 0 ), N )
+ $ N, A( 0 ), N )
CALL DTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + N1
+ $ INFO = INFO + N1
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'R', 'U', 'N', DIAG, N1, N2, ONE, A( N1 ),
- + N, A( 0 ), N )
+ $ N, A( 0 ), N )
*
END IF
*
@@ -278,16 +340,16 @@
*
CALL DTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'L', 'U', 'N', DIAG, N1, N2, -ONE, A( 0 ),
- + N1, A( N1*N1 ), N1 )
+ $ N1, A( N1*N1 ), N1 )
CALL DTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + N1
+ $ INFO = INFO + N1
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'R', 'L', 'T', DIAG, N1, N2, ONE, A( 1 ),
- + N1, A( N1*N1 ), N1 )
+ $ N1, A( N1*N1 ), N1 )
*
ELSE
*
@@ -296,16 +358,16 @@
*
CALL DTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'R', 'U', 'T', DIAG, N2, N1, -ONE,
- + A( N2*N2 ), N2, A( 0 ), N2 )
+ $ A( N2*N2 ), N2, A( 0 ), N2 )
CALL DTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + N1
+ $ INFO = INFO + N1
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'L', 'L', 'N', DIAG, N2, N1, ONE,
- + A( N1*N2 ), N2, A( 0 ), N2 )
+ $ A( N1*N2 ), N2, A( 0 ), N2 )
END IF
*
END IF
@@ -326,16 +388,16 @@
*
CALL DTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'R', 'L', 'N', DIAG, K, K, -ONE, A( 1 ),
- + N+1, A( K+1 ), N+1 )
+ $ N+1, A( K+1 ), N+1 )
CALL DTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + K
+ $ INFO = INFO + K
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'L', 'U', 'T', DIAG, K, K, ONE, A( 0 ), N+1,
- + A( K+1 ), N+1 )
+ $ A( K+1 ), N+1 )
*
ELSE
*
@@ -345,16 +407,16 @@
*
CALL DTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'L', 'L', 'T', DIAG, K, K, -ONE, A( K+1 ),
- + N+1, A( 0 ), N+1 )
+ $ N+1, A( 0 ), N+1 )
CALL DTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + K
+ $ INFO = INFO + K
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'R', 'U', 'N', DIAG, K, K, ONE, A( K ), N+1,
- + A( 0 ), N+1 )
+ $ A( 0 ), N+1 )
END IF
ELSE
*
@@ -368,16 +430,16 @@
*
CALL DTRTRI( 'U', DIAG, K, A( K ), K, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'L', 'U', 'N', DIAG, K, K, -ONE, A( K ), K,
- + A( K*( K+1 ) ), K )
+ $ A( K*( K+1 ) ), K )
CALL DTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + K
+ $ INFO = INFO + K
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'R', 'L', 'T', DIAG, K, K, ONE, A( 0 ), K,
- + A( K*( K+1 ) ), K )
+ $ A( K*( K+1 ) ), K )
ELSE
*
* SRPA for UPPER, TRANSPOSE and N is even (see paper)
@@ -386,16 +448,16 @@
*
CALL DTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'R', 'U', 'T', DIAG, K, K, -ONE,
- + A( K*( K+1 ) ), K, A( 0 ), K )
+ $ A( K*( K+1 ) ), K, A( 0 ), K )
CALL DTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
IF( INFO.GT.0 )
- + INFO = INFO + K
+ $ INFO = INFO + K
IF( INFO.GT.0 )
- + RETURN
+ $ RETURN
CALL DTRMM( 'L', 'L', 'N', DIAG, K, K, ONE, A( K*K ), K,
- + A( 0 ), K )
+ $ A( 0 ), K )
END IF
END IF
END IF