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Diffstat (limited to '2.3-1/src/fortran/lapack/dgghrd.f')
| -rw-r--r-- | 2.3-1/src/fortran/lapack/dgghrd.f | 264 |
1 files changed, 264 insertions, 0 deletions
diff --git a/2.3-1/src/fortran/lapack/dgghrd.f b/2.3-1/src/fortran/lapack/dgghrd.f new file mode 100644 index 00000000..6b8bbb08 --- /dev/null +++ b/2.3-1/src/fortran/lapack/dgghrd.f @@ -0,0 +1,264 @@ + SUBROUTINE DGGHRD( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, + $ LDQ, Z, LDZ, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER COMPQ, COMPZ + INTEGER IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), + $ Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +* DGGHRD reduces a pair of real matrices (A,B) to generalized upper +* Hessenberg form using orthogonal transformations, where A is a +* general matrix and B is upper triangular. The form of the +* generalized eigenvalue problem is +* A*x = lambda*B*x, +* and B is typically made upper triangular by computing its QR +* factorization and moving the orthogonal matrix Q to the left side +* of the equation. +* +* This subroutine simultaneously reduces A to a Hessenberg matrix H: +* Q**T*A*Z = H +* and transforms B to another upper triangular matrix T: +* Q**T*B*Z = T +* in order to reduce the problem to its standard form +* H*y = lambda*T*y +* where y = Z**T*x. +* +* The orthogonal matrices Q and Z are determined as products of Givens +* rotations. They may either be formed explicitly, or they may be +* postmultiplied into input matrices Q1 and Z1, so that +* +* Q1 * A * Z1**T = (Q1*Q) * H * (Z1*Z)**T +* +* Q1 * B * Z1**T = (Q1*Q) * T * (Z1*Z)**T +* +* If Q1 is the orthogonal matrix from the QR factorization of B in the +* original equation A*x = lambda*B*x, then DGGHRD reduces the original +* problem to generalized Hessenberg form. +* +* Arguments +* ========= +* +* COMPQ (input) CHARACTER*1 +* = 'N': do not compute Q; +* = 'I': Q is initialized to the unit matrix, and the +* orthogonal matrix Q is returned; +* = 'V': Q must contain an orthogonal matrix Q1 on entry, +* and the product Q1*Q is returned. +* +* COMPZ (input) CHARACTER*1 +* = 'N': do not compute Z; +* = 'I': Z is initialized to the unit matrix, and the +* orthogonal matrix Z is returned; +* = 'V': Z must contain an orthogonal matrix Z1 on entry, +* and the product Z1*Z is returned. +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* ILO (input) INTEGER +* IHI (input) INTEGER +* ILO and IHI mark the rows and columns of A which are to be +* reduced. It is assumed that A is already upper triangular +* in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are +* normally set by a previous call to SGGBAL; otherwise they +* should be set to 1 and N respectively. +* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. +* +* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) +* On entry, the N-by-N general matrix to be reduced. +* On exit, the upper triangle and the first subdiagonal of A +* are overwritten with the upper Hessenberg matrix H, and the +* rest is set to zero. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input/output) DOUBLE PRECISION array, dimension (LDB, N) +* On entry, the N-by-N upper triangular matrix B. +* On exit, the upper triangular matrix T = Q**T B Z. The +* elements below the diagonal are set to zero. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N) +* On entry, if COMPQ = 'V', the orthogonal matrix Q1, +* typically from the QR factorization of B. +* On exit, if COMPQ='I', the orthogonal matrix Q, and if +* COMPQ = 'V', the product Q1*Q. +* Not referenced if COMPQ='N'. +* +* LDQ (input) INTEGER +* The leading dimension of the array Q. +* LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise. +* +* Z (input/output) DOUBLE PRECISION array, dimension (LDZ, N) +* On entry, if COMPZ = 'V', the orthogonal matrix Z1. +* On exit, if COMPZ='I', the orthogonal matrix Z, and if +* COMPZ = 'V', the product Z1*Z. +* Not referenced if COMPZ='N'. +* +* LDZ (input) INTEGER +* The leading dimension of the array Z. +* LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise. +* +* INFO (output) INTEGER +* = 0: successful exit. +* < 0: if INFO = -i, the i-th argument had an illegal value. +* +* Further Details +* =============== +* +* This routine reduces A to Hessenberg and B to triangular form by +* an unblocked reduction, as described in _Matrix_Computations_, +* by Golub and Van Loan (Johns Hopkins Press.) +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL ILQ, ILZ + INTEGER ICOMPQ, ICOMPZ, JCOL, JROW + DOUBLE PRECISION C, S, TEMP +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL DLARTG, DLASET, DROT, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Decode COMPQ +* + IF( LSAME( COMPQ, 'N' ) ) THEN + ILQ = .FALSE. + ICOMPQ = 1 + ELSE IF( LSAME( COMPQ, 'V' ) ) THEN + ILQ = .TRUE. + ICOMPQ = 2 + ELSE IF( LSAME( COMPQ, 'I' ) ) THEN + ILQ = .TRUE. + ICOMPQ = 3 + ELSE + ICOMPQ = 0 + END IF +* +* Decode COMPZ +* + IF( LSAME( COMPZ, 'N' ) ) THEN + ILZ = .FALSE. + ICOMPZ = 1 + ELSE IF( LSAME( COMPZ, 'V' ) ) THEN + ILZ = .TRUE. + ICOMPZ = 2 + ELSE IF( LSAME( COMPZ, 'I' ) ) THEN + ILZ = .TRUE. + ICOMPZ = 3 + ELSE + ICOMPZ = 0 + END IF +* +* Test the input parameters. +* + INFO = 0 + IF( ICOMPQ.LE.0 ) THEN + INFO = -1 + ELSE IF( ICOMPZ.LE.0 ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( ILO.LT.1 ) THEN + INFO = -4 + ELSE IF( IHI.GT.N .OR. IHI.LT.ILO-1 ) THEN + INFO = -5 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -7 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -9 + ELSE IF( ( ILQ .AND. LDQ.LT.N ) .OR. LDQ.LT.1 ) THEN + INFO = -11 + ELSE IF( ( ILZ .AND. LDZ.LT.N ) .OR. LDZ.LT.1 ) THEN + INFO = -13 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DGGHRD', -INFO ) + RETURN + END IF +* +* Initialize Q and Z if desired. +* + IF( ICOMPQ.EQ.3 ) + $ CALL DLASET( 'Full', N, N, ZERO, ONE, Q, LDQ ) + IF( ICOMPZ.EQ.3 ) + $ CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ ) +* +* Quick return if possible +* + IF( N.LE.1 ) + $ RETURN +* +* Zero out lower triangle of B +* + DO 20 JCOL = 1, N - 1 + DO 10 JROW = JCOL + 1, N + B( JROW, JCOL ) = ZERO + 10 CONTINUE + 20 CONTINUE +* +* Reduce A and B +* + DO 40 JCOL = ILO, IHI - 2 +* + DO 30 JROW = IHI, JCOL + 2, -1 +* +* Step 1: rotate rows JROW-1, JROW to kill A(JROW,JCOL) +* + TEMP = A( JROW-1, JCOL ) + CALL DLARTG( TEMP, A( JROW, JCOL ), C, S, + $ A( JROW-1, JCOL ) ) + A( JROW, JCOL ) = ZERO + CALL DROT( N-JCOL, A( JROW-1, JCOL+1 ), LDA, + $ A( JROW, JCOL+1 ), LDA, C, S ) + CALL DROT( N+2-JROW, B( JROW-1, JROW-1 ), LDB, + $ B( JROW, JROW-1 ), LDB, C, S ) + IF( ILQ ) + $ CALL DROT( N, Q( 1, JROW-1 ), 1, Q( 1, JROW ), 1, C, S ) +* +* Step 2: rotate columns JROW, JROW-1 to kill B(JROW,JROW-1) +* + TEMP = B( JROW, JROW ) + CALL DLARTG( TEMP, B( JROW, JROW-1 ), C, S, + $ B( JROW, JROW ) ) + B( JROW, JROW-1 ) = ZERO + CALL DROT( IHI, A( 1, JROW ), 1, A( 1, JROW-1 ), 1, C, S ) + CALL DROT( JROW-1, B( 1, JROW ), 1, B( 1, JROW-1 ), 1, C, + $ S ) + IF( ILZ ) + $ CALL DROT( N, Z( 1, JROW ), 1, Z( 1, JROW-1 ), 1, C, S ) + 30 CONTINUE + 40 CONTINUE +* + RETURN +* +* End of DGGHRD +* + END |