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diff --git a/SRC/slansb.f b/SRC/slansb.f new file mode 100644 index 00000000..04f8ec04 --- /dev/null +++ b/SRC/slansb.f @@ -0,0 +1,186 @@ + REAL FUNCTION SLANSB( NORM, UPLO, N, K, AB, LDAB, + $ WORK ) +* +* -- LAPACK auxiliary routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER NORM, UPLO + INTEGER K, LDAB, N +* .. +* .. Array Arguments .. + REAL AB( LDAB, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* SLANSB returns the value of the one norm, or the Frobenius norm, or +* the infinity norm, or the element of largest absolute value of an +* n by n symmetric band matrix A, with k super-diagonals. +* +* Description +* =========== +* +* SLANSB returns the value +* +* SLANSB = ( max(abs(A(i,j))), NORM = 'M' or 'm' +* ( +* ( norm1(A), NORM = '1', 'O' or 'o' +* ( +* ( normI(A), NORM = 'I' or 'i' +* ( +* ( normF(A), NORM = 'F', 'f', 'E' or 'e' +* +* where norm1 denotes the one norm of a matrix (maximum column sum), +* normI denotes the infinity norm of a matrix (maximum row sum) and +* normF denotes the Frobenius norm of a matrix (square root of sum of +* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. +* +* Arguments +* ========= +* +* NORM (input) CHARACTER*1 +* Specifies the value to be returned in SLANSB as described +* above. +* +* UPLO (input) CHARACTER*1 +* Specifies whether the upper or lower triangular part of the +* band matrix A is supplied. +* = 'U': Upper triangular part is supplied +* = 'L': Lower triangular part is supplied +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. When N = 0, SLANSB is +* set to zero. +* +* K (input) INTEGER +* The number of super-diagonals or sub-diagonals of the +* band matrix A. K >= 0. +* +* AB (input) REAL array, dimension (LDAB,N) +* The upper or lower triangle of the symmetric band matrix A, +* stored in the first K+1 rows of AB. The j-th column of A is +* stored in the j-th column of the array AB as follows: +* if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; +* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). +* +* LDAB (input) INTEGER +* The leading dimension of the array AB. LDAB >= K+1. +* +* WORK (workspace) REAL array, dimension (MAX(1,LWORK)), +* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, +* WORK is not referenced. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, ZERO + PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J, L + REAL ABSA, SCALE, SUM, VALUE +* .. +* .. External Subroutines .. + EXTERNAL SLASSQ +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN, SQRT +* .. +* .. Executable Statements .. +* + IF( N.EQ.0 ) THEN + VALUE = ZERO + ELSE IF( LSAME( NORM, 'M' ) ) THEN +* +* Find max(abs(A(i,j))). +* + VALUE = ZERO + IF( LSAME( UPLO, 'U' ) ) THEN + DO 20 J = 1, N + DO 10 I = MAX( K+2-J, 1 ), K + 1 + VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) + 10 CONTINUE + 20 CONTINUE + ELSE + DO 40 J = 1, N + DO 30 I = 1, MIN( N+1-J, K+1 ) + VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) + 30 CONTINUE + 40 CONTINUE + END IF + ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. + $ ( NORM.EQ.'1' ) ) THEN +* +* Find normI(A) ( = norm1(A), since A is symmetric). +* + VALUE = ZERO + IF( LSAME( UPLO, 'U' ) ) THEN + DO 60 J = 1, N + SUM = ZERO + L = K + 1 - J + DO 50 I = MAX( 1, J-K ), J - 1 + ABSA = ABS( AB( L+I, J ) ) + SUM = SUM + ABSA + WORK( I ) = WORK( I ) + ABSA + 50 CONTINUE + WORK( J ) = SUM + ABS( AB( K+1, J ) ) + 60 CONTINUE + DO 70 I = 1, N + VALUE = MAX( VALUE, WORK( I ) ) + 70 CONTINUE + ELSE + DO 80 I = 1, N + WORK( I ) = ZERO + 80 CONTINUE + DO 100 J = 1, N + SUM = WORK( J ) + ABS( AB( 1, J ) ) + L = 1 - J + DO 90 I = J + 1, MIN( N, J+K ) + ABSA = ABS( AB( L+I, J ) ) + SUM = SUM + ABSA + WORK( I ) = WORK( I ) + ABSA + 90 CONTINUE + VALUE = MAX( VALUE, SUM ) + 100 CONTINUE + END IF + ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN +* +* Find normF(A). +* + SCALE = ZERO + SUM = ONE + IF( K.GT.0 ) THEN + IF( LSAME( UPLO, 'U' ) ) THEN + DO 110 J = 2, N + CALL SLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ), + $ 1, SCALE, SUM ) + 110 CONTINUE + L = K + 1 + ELSE + DO 120 J = 1, N - 1 + CALL SLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE, + $ SUM ) + 120 CONTINUE + L = 1 + END IF + SUM = 2*SUM + ELSE + L = 1 + END IF + CALL SLASSQ( N, AB( L, 1 ), LDAB, SCALE, SUM ) + VALUE = SCALE*SQRT( SUM ) + END IF +* + SLANSB = VALUE + RETURN +* +* End of SLANSB +* + END |