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author | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
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committer | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
commit | baba851215b44ac3b60b9248eb02bcce7eb76247 (patch) | |
tree | 8c0f5c006875532a30d4409f5e94b0f310ff00a7 /SRC/zlanhp.f | |
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Move LAPACK trunk into position.
Diffstat (limited to 'SRC/zlanhp.f')
-rw-r--r-- | SRC/zlanhp.f | 201 |
1 files changed, 201 insertions, 0 deletions
diff --git a/SRC/zlanhp.f b/SRC/zlanhp.f new file mode 100644 index 00000000..c0ff3b94 --- /dev/null +++ b/SRC/zlanhp.f @@ -0,0 +1,201 @@ + DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, 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 N +* .. +* .. Array Arguments .. + DOUBLE PRECISION WORK( * ) + COMPLEX*16 AP( * ) +* .. +* +* Purpose +* ======= +* +* ZLANHP returns the value of the one norm, or the Frobenius norm, or +* the infinity norm, or the element of largest absolute value of a +* complex hermitian matrix A, supplied in packed form. +* +* Description +* =========== +* +* ZLANHP returns the value +* +* ZLANHP = ( 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 ZLANHP as described +* above. +* +* UPLO (input) CHARACTER*1 +* Specifies whether the upper or lower triangular part of the +* hermitian matrix A is supplied. +* = 'U': Upper triangular part of A is supplied +* = 'L': Lower triangular part of A is supplied +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. When N = 0, ZLANHP is +* set to zero. +* +* AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) +* The upper or lower triangle of the hermitian matrix A, packed +* columnwise in a linear array. The j-th column of A is stored +* in the array AP as follows: +* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; +* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. +* Note that the imaginary parts of the diagonal elements need +* not be set and are assumed to be zero. +* +* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), +* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, +* WORK is not referenced. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J, K + DOUBLE PRECISION ABSA, SCALE, SUM, VALUE +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL ZLASSQ +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, MAX, 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 + K = 0 + DO 20 J = 1, N + DO 10 I = K + 1, K + J - 1 + VALUE = MAX( VALUE, ABS( AP( I ) ) ) + 10 CONTINUE + K = K + J + VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) ) + 20 CONTINUE + ELSE + K = 1 + DO 40 J = 1, N + VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) ) + DO 30 I = K + 1, K + N - J + VALUE = MAX( VALUE, ABS( AP( I ) ) ) + 30 CONTINUE + K = K + N - J + 1 + 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 hermitian). +* + VALUE = ZERO + K = 1 + IF( LSAME( UPLO, 'U' ) ) THEN + DO 60 J = 1, N + SUM = ZERO + DO 50 I = 1, J - 1 + ABSA = ABS( AP( K ) ) + SUM = SUM + ABSA + WORK( I ) = WORK( I ) + ABSA + K = K + 1 + 50 CONTINUE + WORK( J ) = SUM + ABS( DBLE( AP( K ) ) ) + K = K + 1 + 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( DBLE( AP( K ) ) ) + K = K + 1 + DO 90 I = J + 1, N + ABSA = ABS( AP( K ) ) + SUM = SUM + ABSA + WORK( I ) = WORK( I ) + ABSA + K = K + 1 + 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 + K = 2 + IF( LSAME( UPLO, 'U' ) ) THEN + DO 110 J = 2, N + CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM ) + K = K + J + 110 CONTINUE + ELSE + DO 120 J = 1, N - 1 + CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM ) + K = K + N - J + 1 + 120 CONTINUE + END IF + SUM = 2*SUM + K = 1 + DO 130 I = 1, N + IF( DBLE( AP( K ) ).NE.ZERO ) THEN + ABSA = ABS( DBLE( AP( K ) ) ) + IF( SCALE.LT.ABSA ) THEN + SUM = ONE + SUM*( SCALE / ABSA )**2 + SCALE = ABSA + ELSE + SUM = SUM + ( ABSA / SCALE )**2 + END IF + END IF + IF( LSAME( UPLO, 'U' ) ) THEN + K = K + I + 1 + ELSE + K = K + N - I + 1 + END IF + 130 CONTINUE + VALUE = SCALE*SQRT( SUM ) + END IF +* + ZLANHP = VALUE + RETURN +* +* End of ZLANHP +* + END |