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Diffstat (limited to 'SRC/ztbcon.f')
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diff --git a/SRC/ztbcon.f b/SRC/ztbcon.f new file mode 100644 index 00000000..2d94db4a --- /dev/null +++ b/SRC/ztbcon.f @@ -0,0 +1,209 @@ + SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, + $ RWORK, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. +* +* .. Scalar Arguments .. + CHARACTER DIAG, NORM, UPLO + INTEGER INFO, KD, LDAB, N + DOUBLE PRECISION RCOND +* .. +* .. Array Arguments .. + DOUBLE PRECISION RWORK( * ) + COMPLEX*16 AB( LDAB, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* ZTBCON estimates the reciprocal of the condition number of a +* triangular band matrix A, in either the 1-norm or the infinity-norm. +* +* The norm of A is computed and an estimate is obtained for +* norm(inv(A)), then the reciprocal of the condition number is +* computed as +* RCOND = 1 / ( norm(A) * norm(inv(A)) ). +* +* Arguments +* ========= +* +* NORM (input) CHARACTER*1 +* Specifies whether the 1-norm condition number or the +* infinity-norm condition number is required: +* = '1' or 'O': 1-norm; +* = 'I': Infinity-norm. +* +* 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. +* +* KD (input) INTEGER +* The number of superdiagonals or subdiagonals of the +* triangular band matrix A. KD >= 0. +* +* AB (input) COMPLEX*16 array, dimension (LDAB,N) +* The upper or lower triangular band matrix A, stored in the +* first kd+1 rows of the array. The j-th column of A is stored +* in the j-th column of the array AB as follows: +* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; +* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). +* If DIAG = 'U', the diagonal elements of A are not referenced +* and are assumed to be 1. +* +* LDAB (input) INTEGER +* The leading dimension of the array AB. LDAB >= KD+1. +* +* RCOND (output) DOUBLE PRECISION +* The reciprocal of the condition number of the matrix A, +* computed as RCOND = 1/(norm(A) * norm(inv(A))). +* +* WORK (workspace) COMPLEX*16 array, dimension (2*N) +* +* RWORK (workspace) DOUBLE PRECISION array, dimension (N) +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL NOUNIT, ONENRM, UPPER + CHARACTER NORMIN + INTEGER IX, KASE, KASE1 + DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM + COMPLEX*16 ZDUM +* .. +* .. Local Arrays .. + INTEGER ISAVE( 3 ) +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER IZAMAX + DOUBLE PRECISION DLAMCH, ZLANTB + EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTB +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATBS +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, DIMAG, MAX +* .. +* .. Statement Functions .. + DOUBLE PRECISION CABS1 +* .. +* .. Statement Function definitions .. + CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) + NOUNIT = LSAME( DIAG, 'N' ) +* + IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN + INFO = -1 + ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -2 + ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN + INFO = -3 + ELSE IF( N.LT.0 ) THEN + INFO = -4 + ELSE IF( KD.LT.0 ) THEN + INFO = -5 + ELSE IF( LDAB.LT.KD+1 ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZTBCON', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) THEN + RCOND = ONE + RETURN + END IF +* + RCOND = ZERO + SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( N, 1 ) ) +* +* Compute the 1-norm of the triangular matrix A or A'. +* + ANORM = ZLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, RWORK ) +* +* Continue only if ANORM > 0. +* + IF( ANORM.GT.ZERO ) THEN +* +* Estimate the 1-norm of the inverse of A. +* + AINVNM = ZERO + NORMIN = 'N' + IF( ONENRM ) THEN + KASE1 = 1 + ELSE + KASE1 = 2 + END IF + KASE = 0 + 10 CONTINUE + CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) + IF( KASE.NE.0 ) THEN + IF( KASE.EQ.KASE1 ) THEN +* +* Multiply by inv(A). +* + CALL ZLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD, + $ AB, LDAB, WORK, SCALE, RWORK, INFO ) + ELSE +* +* Multiply by inv(A'). +* + CALL ZLATBS( UPLO, 'Conjugate transpose', DIAG, NORMIN, + $ N, KD, AB, LDAB, WORK, SCALE, RWORK, INFO ) + END IF + NORMIN = 'Y' +* +* Multiply by 1/SCALE if doing so will not cause overflow. +* + IF( SCALE.NE.ONE ) THEN + IX = IZAMAX( N, WORK, 1 ) + XNORM = CABS1( WORK( IX ) ) + IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO ) + $ GO TO 20 + CALL ZDRSCL( N, SCALE, WORK, 1 ) + END IF + GO TO 10 + END IF +* +* Compute the estimate of the reciprocal condition number. +* + IF( AINVNM.NE.ZERO ) + $ RCOND = ( ONE / ANORM ) / AINVNM + END IF +* + 20 CONTINUE + RETURN +* +* End of ZTBCON +* + END |