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Diffstat (limited to 'src/fortran/lapack/zgehd2.f')
| -rw-r--r-- | src/fortran/lapack/zgehd2.f | 148 |
1 files changed, 148 insertions, 0 deletions
diff --git a/src/fortran/lapack/zgehd2.f b/src/fortran/lapack/zgehd2.f new file mode 100644 index 0000000..c73f420 --- /dev/null +++ b/src/fortran/lapack/zgehd2.f @@ -0,0 +1,148 @@ + SUBROUTINE ZGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + INTEGER IHI, ILO, INFO, LDA, N +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H +* by a unitary similarity transformation: Q' * A * Q = H . +* +* Arguments +* ========= +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* ILO (input) INTEGER +* IHI (input) INTEGER +* 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 ZGEBAL; otherwise they should be +* set to 1 and N respectively. See Further Details. +* 1 <= ILO <= IHI <= max(1,N). +* +* A (input/output) COMPLEX*16 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 +* elements below the first subdiagonal, with the array TAU, +* represent the unitary matrix Q as a product of elementary +* reflectors. See Further Details. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* TAU (output) COMPLEX*16 array, dimension (N-1) +* The scalar factors of the elementary reflectors (see Further +* Details). +* +* WORK (workspace) COMPLEX*16 array, dimension (N) +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value. +* +* Further Details +* =============== +* +* The matrix Q is represented as a product of (ihi-ilo) elementary +* reflectors +* +* Q = H(ilo) H(ilo+1) . . . H(ihi-1). +* +* Each H(i) has the form +* +* H(i) = I - tau * v * v' +* +* where tau is a complex scalar, and v is a complex vector with +* v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on +* exit in A(i+2:ihi,i), and tau in TAU(i). +* +* The contents of A are illustrated by the following example, with +* n = 7, ilo = 2 and ihi = 6: +* +* on entry, on exit, +* +* ( a a a a a a a ) ( a a h h h h a ) +* ( a a a a a a ) ( a h h h h a ) +* ( a a a a a a ) ( h h h h h h ) +* ( a a a a a a ) ( v2 h h h h h ) +* ( a a a a a a ) ( v2 v3 h h h h ) +* ( a a a a a a ) ( v2 v3 v4 h h h ) +* ( a ) ( a ) +* +* where a denotes an element of the original matrix A, h denotes a +* modified element of the upper Hessenberg matrix H, and vi denotes an +* element of the vector defining H(i). +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + INTEGER I + COMPLEX*16 ALPHA +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZLARF, ZLARFG +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG, MAX, MIN +* .. +* .. Executable Statements .. +* +* Test the input parameters +* + INFO = 0 + IF( N.LT.0 ) THEN + INFO = -1 + ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN + INFO = -2 + ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZGEHD2', -INFO ) + RETURN + END IF +* + DO 10 I = ILO, IHI - 1 +* +* Compute elementary reflector H(i) to annihilate A(i+2:ihi,i) +* + ALPHA = A( I+1, I ) + CALL ZLARFG( IHI-I, ALPHA, A( MIN( I+2, N ), I ), 1, TAU( I ) ) + A( I+1, I ) = ONE +* +* Apply H(i) to A(1:ihi,i+1:ihi) from the right +* + CALL ZLARF( 'Right', IHI, IHI-I, A( I+1, I ), 1, TAU( I ), + $ A( 1, I+1 ), LDA, WORK ) +* +* Apply H(i)' to A(i+1:ihi,i+1:n) from the left +* + CALL ZLARF( 'Left', IHI-I, N-I, A( I+1, I ), 1, + $ DCONJG( TAU( I ) ), A( I+1, I+1 ), LDA, WORK ) +* + A( I+1, I ) = ALPHA + 10 CONTINUE +* + RETURN +* +* End of ZGEHD2 +* + END |