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Diffstat (limited to 'SRC/zsytrs2.f')
| -rw-r--r-- | SRC/zsytrs2.f | 272 |
1 files changed, 272 insertions, 0 deletions
diff --git a/SRC/zsytrs2.f b/SRC/zsytrs2.f new file mode 100644 index 00000000..88d54408 --- /dev/null +++ b/SRC/zsytrs2.f @@ -0,0 +1,272 @@ + SUBROUTINE ZSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, + $ WORK, INFO ) +* +* -- LAPACK PROTOTYPE routine (version 3.2) -- +* +* -- Written by Julie Langou of the Univ. of TN -- +* May 2010 +* +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, LDA, LDB, N, NRHS +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + DOUBLE COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* ZSYTRS2 solves a system of linear equations A*X = B with a real +* symmetric matrix A using the factorization A = U*D*U**T or +* A = L*D*L**T computed by ZSYTRF and converted by ZSYCONV. +* +* Arguments +* ========= +* +* UPLO (input) CHARACTER*1 +* Specifies whether the details of the factorization are stored +* as an upper or lower triangular matrix. +* = 'U': Upper triangular, form is A = U*D*U**T; +* = 'L': Lower triangular, form is A = L*D*L**T. +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* NRHS (input) INTEGER +* The number of right hand sides, i.e., the number of columns +* of the matrix B. NRHS >= 0. +* +* A (input) DOUBLE COMPLEX array, dimension (LDA,N) +* The block diagonal matrix D and the multipliers used to +* obtain the factor U or L as computed by ZSYTRF. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* IPIV (input) INTEGER array, dimension (N) +* Details of the interchanges and the block structure of D +* as determined by ZSYTRF. +* +* B (input/output) DOUBLE COMPLEX array, dimension (LDB,NRHS) +* On entry, the right hand side matrix B. +* On exit, the solution matrix X. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* WORK (workspace) REAL array, dimension (N) +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE COMPLEX ONE + PARAMETER ( ONE = (1.0D+0,0.0D+0) ) +* .. +* .. Local Scalars .. + LOGICAL UPPER + INTEGER I, J, K, KP + DOUBLE COMPLEX AK, AKM1, AKM1K, BK, BKM1, DENOM +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL ZSCAL, ZSWAP, ZTRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZSYTRS2', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 .OR. NRHS.EQ.0 ) + $ RETURN +* + IF( UPPER ) THEN +* +* Solve A*X = B, where A = U*D*U'. +* +* P' * B + K=N + DO WHILE ( K .GE. 1 ) + IF( IPIV( K ).GT.0 ) THEN +* 1 x 1 diagonal block +* Interchange rows K and IPIV(K). + KP = IPIV( K ) + IF( KP.NE.K ) + $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) + K=K-1 + ELSE +* 2 x 2 diagonal block +* Interchange rows K-1 and -IPIV(K). + KP = -IPIV( K ) + IF( KP.EQ.-IPIV( K-1 ) ) + $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB ) + K=K-2 + END IF + END DO +* +* Compute (U \P' * B) -> B [ (U \P' * B) ] +* + CALL ZTRSM('L','U','N','U',N,NRHS,ONE,A,N,B,N) +* +* Compute D \ B -> B [ D \ (U \P' * B) ] +* + I=N + DO WHILE ( I .GE. 1 ) + IF( IPIV(I) .GT. 0 ) THEN + CALL ZSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N ) + ELSEIF ( I .GT. 1) THEN + IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN + AKM1K = WORK(I) + AKM1 = A( I-1, I-1 ) / AKM1K + AK = A( I, I ) / AKM1K + DENOM = AKM1*AK - ONE + DO 15 J = 1, NRHS + BKM1 = B( I-1, J ) / AKM1K + BK = B( I, J ) / AKM1K + B( I-1, J ) = ( AK*BKM1-BK ) / DENOM + B( I, J ) = ( AKM1*BK-BKM1 ) / DENOM + 15 CONTINUE + I = I - 1 + ENDIF + ENDIF + I = I - 1 + END DO +* +* Compute (U' \ B) -> B [ U' \ (D \ (U \P' * B) ) ] +* + CALL ZTRSM('L','U','T','U',N,NRHS,ONE,A,N,B,N) +* +* P * B [ P * (U' \ (D \ (U \P' * B) )) ] +* + K=1 + DO WHILE ( K .LE. N ) + IF( IPIV( K ).GT.0 ) THEN +* 1 x 1 diagonal block +* Interchange rows K and IPIV(K). + KP = IPIV( K ) + IF( KP.NE.K ) + $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) + K=K+1 + ELSE +* 2 x 2 diagonal block +* Interchange rows K-1 and -IPIV(K). + KP = -IPIV( K ) + IF( K .LT. N .AND. KP.EQ.-IPIV( K+1 ) ) + $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) + K=K+2 + ENDIF + END DO +* + ELSE +* +* Solve A*X = B, where A = L*D*L'. +* +* P' * B + K=1 + DO WHILE ( K .LE. N ) + IF( IPIV( K ).GT.0 ) THEN +* 1 x 1 diagonal block +* Interchange rows K and IPIV(K). + KP = IPIV( K ) + IF( KP.NE.K ) + $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) + K=K+1 + ELSE +* 2 x 2 diagonal block +* Interchange rows K and -IPIV(K+1). + KP = -IPIV( K+1 ) + IF( KP.EQ.-IPIV( K ) ) + $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB ) + K=K+2 + ENDIF + END DO +* +* Compute (L \P' * B) -> B [ (L \P' * B) ] +* + CALL ZTRSM('L','L','N','U',N,NRHS,ONE,A,N,B,N) +* +* Compute D \ B -> B [ D \ (L \P' * B) ] +* + I=1 + DO WHILE ( I .LE. N ) + IF( IPIV(I) .GT. 0 ) THEN + CALL ZSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N ) + ELSE + AKM1K = WORK(I) + AKM1 = A( I, I ) / AKM1K + AK = A( I+1, I+1 ) / AKM1K + DENOM = AKM1*AK - ONE + DO 25 J = 1, NRHS + BKM1 = B( I, J ) / AKM1K + BK = B( I+1, J ) / AKM1K + B( I, J ) = ( AK*BKM1-BK ) / DENOM + B( I+1, J ) = ( AKM1*BK-BKM1 ) / DENOM + 25 CONTINUE + I = I + 1 + ENDIF + I = I + 1 + END DO +* +* Compute (L' \ B) -> B [ L' \ (D \ (L \P' * B) ) ] +* + CALL ZTRSM('L','L','T','U',N,NRHS,ONE,A,N,B,N) +* +* P * B [ P * (L' \ (D \ (L \P' * B) )) ] +* + K=N + DO WHILE ( K .GE. 1 ) + IF( IPIV( K ).GT.0 ) THEN +* 1 x 1 diagonal block +* Interchange rows K and IPIV(K). + KP = IPIV( K ) + IF( KP.NE.K ) + $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) + K=K-1 + ELSE +* 2 x 2 diagonal block +* Interchange rows K-1 and -IPIV(K). + KP = -IPIV( K ) + IF( K.GT.1 .AND. KP.EQ.-IPIV( K-1 ) ) + $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) + K=K-2 + ENDIF + END DO +* + END IF +* + RETURN +* +* End of ZSYTRS2 +* + END |